Tablas Conveccion v20140112

Resumen de correlaciones para transferencia de calor por conveccion

12 de enero de 2014

Indice1. Numeros adimensionales importantes 1

2. Conveccion forzada, flujo externo 22.1. Flujo externo sobre objetos aislados . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2. Flujo externo en bancos de tubos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3. Conveccion forzada, flujo interno 53.1. Flujo interno desarrollado en conductos circulares lisos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2. Flujo interno desarrollado en conductos no circulares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. Conveccion natural 64.1. Correlaciones generales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2. Correlaciones simplificadas para aire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5. Historial de cambios 7

Apendice: Propiedades de fluidos 8Tabla extendida de propiedades del aire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Tabla extendida de propiedades del agua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Tablas de propiedades del libro ItoTSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1. Numeros adimensionales importantes

Tabla 17.1 ItoTSE. Numeros adimensionales importantes en transferencia de calor por conveccion410 Chapter 17. Heat Transfer by Convection

Table 17.1 Important Dimensionless Groups in Convection Heat Transfer

Groupa Definitiona Interpretation/Application

Nusselt number, NuL

Reynolds number, ReL

Prandtl number, Pr

Grashof number, GrL

Rayleigh number, RaL

Dimensionless temperature gradient at the surface. Measureof the convection heat transfer coefficient.

Ratio of the inertia and viscous forces. Characterizes forcedconvection flows.

Ratio of the momentum and thermal diffusivities. Property ofthe fluid.

Ratio of buoyancy to viscous forces. Characterizes free con-vection flows.

Product of Grashof and Prandtl numbers, Gr Pr. Character-izes free convection flows.

(17.9)

(17.12)

(17.13)

(17.16)

(17.19)g�1Ts � T�2L3

��

g�1Ts � T�2L3

�2

cp�

k�

�

�

VL

�

hL

k

aThe subscript L represents the characteristic length on the surface of interest.

where the subscript x has been added to emphasize our interest in conditions at a particularlocation on the surface identified by the dimensionless distance x*. The overbar indicates anaverage over the surface from x* � 0 to the location of interest.

The Reynolds number, ReL, is the ratio of the inertia to viscous forces, and is used tocharacterize boundary layer flows (Sec. 13.5)

(17.12)

where V represents the reference velocity of the fluid, L is the characteristic length of thesurface, and � is the kinematic viscosity of the fluid.

The Prandtl number, Pr, is a transport property of the fluid and provides a measure ofthe relative effectiveness of momentum and energy transport in the hydrodynamic and ther-mal boundary layers, respectively

(17.13)

where � is the dynamic viscosity and � is the thermal diffusivity of the fluid (Eq. 16.5).From Table HT-3, we see that the Prandtl number for gases is near unity, in which case

momentum and energy transport are comparable. In contrast, for oils and some liquids withPr � 1 (Tables HT-4, 5), momentum transport is more significant, and the effects extend fur-ther into the free stream. From this interpretation, it follows that the value of Pr stronglyinfluences the relative growth of the velocity and thermal boundary layers. In fact, for alaminar boundary layer, it has been shown that

(17.14)

where n is a positive constant, typically n � 1�3. Hence for a gas, �t � �; for an oil �t � �.However, for all fluids in the turbulent region, because of extensive mixing, we expect �t � �.

The forms of the functions associated with Eqs. 17.10 and 17.11 are most commonly de-termined from extensive sets of experimental measurements performed on specific surfacegeometries and types of flows. Such functions are termed empirical correlations and are al-ways accompanied by specifications regarding surface geometry and flow conditions. ForExample… the most general correlation for forced convection external flow over flat platesand other immersed geometries has the form

(17.15)Nux � C Remx Pr n

�

�t

� Prn

Pr �cp�

k�

�

�

ReL �VL

�Reynolds number

Prandtl number

empirical correlations

c17.qxd 6/10/02 20:13 Page 410

1

2. Conveccion forzada, flujo externo

2.1. Flujo externo sobre objetos aislados

Tabla 17.3 ItoTSE.Resumen de correlaciones de transferencia de calor por conveccion en flujo externo forzado.17.3 Internal Flow 423

17.2.4 Guide for Selection of External Flow Correlations

In this section you have been introduced to empirical correlations to estimate the convection co-efficients for forced convection flow over flat plates, cylinders, and spheres. For your conveniencein selecting appropriate correlations for your problems, the recommended correlations have beensummarized in Table 17.3. While specific conditions are associated with each of the correlations,you are reminded to follow the rules for performing convection calculations outlined in Sec. 17.1.3.

Internal FlowIn the previous section you saw that an external flow, such as for the flat plate, is one forwhich boundary layer development on a surface continues without external constraints. Incontrast, for internal flow in a pipe or tube, the fluid is constrained by a surface, and henceeventually the boundary layer development will be constrained. In Chap. 14 you learned thatwhen flow enters a tube, a hydrodynamic boundary layer forms in the entrance region,growing in thickness to eventually fill the tube. Beyond this location, referred to as the fullydeveloped region, the velocity profile no longer changes in the flow direction.

We begin by considering thermal boundary layer formation in the entrance and fullydeveloped regions, and how the convection coefficient is determined from the resultingtemperature profile. We will introduce empirical correlations to estimate convectioncoefficients for laminar and turbulent flows in the fully developed region, deferring consid-eration of correlations for the entrance region to a more advanced course in heat transfer.

17.3

Table 17.3 Summary of Convection Heat Transfer Correlations for External Flow

Flow Coefficient Correlationa Range of Applicability

Flat plateLaminar

Turbulent

Mixed

Cylindersb

Sphere

—

Local

—

Average

Local

Local

Average

Average

Average

Average

Average

(17.21)

(17.23)

�t � � Pr�1�3 (17.24)

(17.26)

(17.27)

(17.28)

(17.32)

� (0.037 � 871)Pr1�3 (17.31)

(Table 7.2) (17.34)

(17.35)

(17.36) � 0.06 Re2�3D 2Pr0.41��s21�4

NuD � 2 � 10.4 Re1�2D

� 31 � 1ReD�282,00025�8 4 4�5� 31 � 10.4�Pr22�3 4�1�46 NuD � 0.3 � 50.62 Re1�2

D Pr1�3

NuD � C RemD Pr1�3

Re4�5LNuL

NuL � 0.037 Re4�5L Pr1�3

Nux � 0.0296 Re4�5x Pr1�3

� � 0.37x Re�1�5x

NuL � 0.664 Re1�2L Pr1�3

Nux � 0.332 Re1�2x Pr1�3

� � 5x Re�1�2x

0.6 � Pr � 50

0.6 � Pr � 50

Rex � 108

Rex � 108, 0.6 � Pr � 60

Rex,c � 0, 0.6 � Pr � 60

Rex,c � 5 � 105, 105 � ReL � 108

0.6 � Pr � 60

Pr � 0.70

ReD Pr � 0.2

3.5 ReD 7.6 � 104

0.71 Pr 380

aThermophysical properties are evaluated at the film temperature, Tf � (T� � Ts)�2, for all the correlations except Eq. 17.36. For that correlation,properties are evaluated at the free stream temperature T� or at the surface temperature Ts if designated with the subscript s.bFor the cylinder with noncircular cross section, use Eq. 17.34 with the constants listed in Table 17.2.

c17.qxd 6/10/02 20:13 Page 423

Tabla 17.2 ItoTSE.Constantes utilizadas en la correlacion de Hilpert para flujo externo cruzado.17.2 External Flow 419

with the Nusselt number as a function of the Reynolds and Prandtl numbers. The Hilpertcorrelation is one of the most widely used and has the form

(17.34)

where the cylinder diameter D is the characteristic length for the Nusselt number. The con-stants C and m, which are dependent upon the Reynolds number range, are listed in Table 17.2.All properties are evaluated at the film temperature, Tf, Eq. 17.20.

The Hilpert correlation, Eq. 17.34, may also be used for gas flow over cylinders of noncircularcross section, with the characteristic length D and the constants obtained from Table 17.2.

The Churchill-Bernstein correlation is a single comprehensive equation that covers a widerange of Reynolds and Prandtl numbers. The equation is recommended for all ReD Pr � 0.2and has the form

(17.35)

where all properties are evaluated at the film temperature. This correlation is normally pre-ferred, unless the simplicity of the Hilpert equation is advantageous.

NuD � 0.3 �0.62 Re1�2

D Pr1�3

31 � 10.4�Pr22�3 4 1�4 c1 � a ReD

282,000b5�8 d 4�5

3ReD Pr 7 0.2 4

NuD �hD

k� C Rem

D Pr1�3 3Pr � 0.7 4

Experiments have been conducted to measure the convection coefficient on a polished metallic cylinder 12.7 mm in diameterand 94 mm long (Fig. E17.4a). The cylinder is heated internally by an electrical resistance heater and is subjected to a crossflow of air in a low-speed wind tunnel. Under a specific set of operating conditions for which the free stream air velocity andtemperature were maintained at u� � 10 m/s and 26.2�C, respectively, the heater power dissipation was measured to be Pe �46 W, while the average cylinder surface temperature was determined to be Ts � 128.4�C. It is estimated that 15% of thepower dissipation is lost by conduction through the endpieces.

Example 17.4 Cylindrical Test Section: Measurement of the Convection Coefficient

Table 17.2 Constants for the Hilpert Correlation, Eq. 17.34, for Circular (Pr � 0.7) and Noncircular (Gases only) Cylinders inCross Flow

Geometry ReD C m

5 � 103–105 0.246 0.588

5 � 103–105 0.102 0.675

5 � 103–1.95 � 104 0.160 0.6381.95 � 104–105 0.0385 0.782

5 � 103–105 0.153 0.638

4 � 103–1.5 � 104 0.228 0.731

Geometry ReD C m

0.4–4 0.989 0.330

4–40 0.911 0.385

40–4000 0.683 0.466

4000–40,000 0.193 0.618

40,000–400,000 0.027 0.805 D

D

D

D

Du∞

u∞

u∞

u∞

u∞

Square

Hexagon

Vertical plate

Du∞

Circular

c17.qxd 6/10/02 20:13 Page 419

2

2.2. Flujo externo en bancos de tubos

The maximum velocity is determined from the conservation of mass re-quirement for steady incompressible flow. For in-line arrangement, the maxi-mum velocity occurs at the minimum flow area between the tubes, and theconservation of mass can be expressed as (see Fig. 7-26a) � � A1 � � �maxAT

or �ST � �max(ST � D). Then the maximum velocity becomes

� (7-40)

In staggered arrangement, the fluid approaching through area A1 in Fig-ure 7–26b passes through area AT and then through area 2AD as it wrapsaround the pipe in the next row. If 2AD � AT, maximum velocity will still oc-cur at AT between the tubes, and thus the �max relation Eq. 7-40 can also beused for staggered tube banks. But if 2AD � �� [or, if 2(SD � D) � (ST � D)],maximum velocity will occur at the diagonal cross sections, and the maximumvelocity in this case becomes

Staggered and SD � (ST � D)/2: � (7-41)

since � �A1 � ��max(2AD) or �ST � 2�max(SD � D).The nature of flow around a tube in the first row resembles flow over a sin-

gle tube discussed in section 7–3, especially when the tubes are not too closeto each other. Therefore, each tube in a tube bank that consists of a singletransverse row can be treated as a single tube in cross-flow. The nature of flowaround a tube in the second and subsequent rows is very different, however,because of wakes formed and the turbulence caused by the tubes upstream.The level of turbulence, and thus the heat transfer coefficient, increases withrow number because of the combined effects of upstream rows. But there is nosignificant change in turbulence level after the first few rows, and thus theheat transfer coefficient remains constant.

Flow through tube banks is studied experimentally since it is too complexto be treated analytically. We are primarily interested in the average heat trans-fer coefficient for the entire tube bank, which depends on the number of tuberows along the flow as well as the arrangement and the size of the tubes.

Several correlations, all based on experimental data, have been proposed forthe average Nusselt number for cross flow over tube banks. More recently,Zukauskas has proposed correlations whose general form is

(7-42)

where the values of the constants C, m, and n depend on value Reynolds num-ber. Such correlations are given in Table 7–2 explicitly for 0.7 � Pr � 500 and0 � ReD � 2 106. The uncertainty in the values of Nusselt number obtainedfrom these relations is �15 percent. Note that all properties except Prs are tobe evaluated at the arithmetic mean temperature of the fluid determined from

(7-43)

where Ti and Te are the fluid temperatures at the inlet and the exit of the tubebank, respectively.

Tm �Ti � Te

2

NuD �hDk

� C RemD Pr n(Pr/Prs)0.25

�max �ST

2(SD � D)

�max �ST

ST � D

390HEAT TRANSFER

D

D

SL

ST

A1 AT

1st row 2nd row

(a) In-line

3rd row

A1 = ST LAT = (ST �D)LAD = (SD �D)L

, T1�

SL

ST

A1 AT

AD

SD

AD

(b) Staggered

, T1�

FIGURE 7–26Arrangement of the tubes in in-lineand staggered tube banks (A1, AT, andAD are flow areas at indicatedlocations, and L is the length of thetubes).

cen58933_ch07.qxd 9/4/2002 12:12 PM Page 390

Figura 7-26a Cengel, configuracion en lınea (in-line or aligned)

The maximum velocity is determined from the conservation of mass re-quirement for steady incompressible flow. For in-line arrangement, the maxi-mum velocity occurs at the minimum flow area between the tubes, and theconservation of mass can be expressed as (see Fig. 7-26a) � � A1 � � �maxAT

or �ST � �max(ST � D). Then the maximum velocity becomes

� (7-40)

In staggered arrangement, the fluid approaching through area A1 in Fig-ure 7–26b passes through area AT and then through area 2AD as it wrapsaround the pipe in the next row. If 2AD � AT, maximum velocity will still oc-cur at AT between the tubes, and thus the �max relation Eq. 7-40 can also beused for staggered tube banks. But if 2AD � �� [or, if 2(SD � D) � (ST � D)],maximum velocity will occur at the diagonal cross sections, and the maximumvelocity in this case becomes

Staggered and SD � (ST � D)/2: � (7-41)

since � �A1 � ��max(2AD) or �ST � 2�max(SD � D).The nature of flow around a tube in the first row resembles flow over a sin-

gle tube discussed in section 7–3, especially when the tubes are not too closeto each other. Therefore, each tube in a tube bank that consists of a singletransverse row can be treated as a single tube in cross-flow. The nature of flowaround a tube in the second and subsequent rows is very different, however,because of wakes formed and the turbulence caused by the tubes upstream.The level of turbulence, and thus the heat transfer coefficient, increases withrow number because of the combined effects of upstream rows. But there is nosignificant change in turbulence level after the first few rows, and thus theheat transfer coefficient remains constant.

Flow through tube banks is studied experimentally since it is too complexto be treated analytically. We are primarily interested in the average heat trans-fer coefficient for the entire tube bank, which depends on the number of tuberows along the flow as well as the arrangement and the size of the tubes.

Several correlations, all based on experimental data, have been proposed forthe average Nusselt number for cross flow over tube banks. More recently,Zukauskas has proposed correlations whose general form is

(7-42)

where the values of the constants C, m, and n depend on value Reynolds num-ber. Such correlations are given in Table 7–2 explicitly for 0.7 � Pr � 500 and0 � ReD � 2 106. The uncertainty in the values of Nusselt number obtainedfrom these relations is �15 percent. Note that all properties except Prs are tobe evaluated at the arithmetic mean temperature of the fluid determined from

(7-43)

where Ti and Te are the fluid temperatures at the inlet and the exit of the tubebank, respectively.

Tm �Ti � Te

2

NuD �hDk

� C RemD Pr n(Pr/Prs)0.25

�max �ST

2(SD � D)

�max �ST

ST � D

390HEAT TRANSFER

D

D

SL

ST

A1 AT

1st row 2nd row

(a) In-line

3rd row

A1 = ST LAT = (ST �D)LAD = (SD �D)L

, T1�

SL

ST

A1 AT

AD

SD

AD

(b) Staggered

, T1�

FIGURE 7–26Arrangement of the tubes in in-lineand staggered tube banks (A1, AT, andAD are flow areas at indicatedlocations, and L is the length of thetubes).

cen58933_ch07.qxd 9/4/2002 12:12 PM Page 390

Figura 7-26b Cengel, configuracion al tresbolillo (staggered)

Velocidad maxima, se calcula a partir de la velocidad de aproximacion del fluido V. En el caso de la configuracion enlınea,ecuacion Cengel 7-40:

Vmax =ST

ST −DV

En el caso de la configuracion al tresbolillo, se tienen dos situaciones. Si SD > (ST +D) /2, el maximo estrechamientotiene lugar en el area transversal y se utiliza la misma expresion que en la configuracion en lınea. Por el contrario,siSD 6 (ST +D) /2 entonces el maximo estrechamiento tiene lugar en el area diagonal y se utilizarıa la ecuacion Cengel7-41:

Vmax =ST

2 (SD −D)V

Calculo de Nusselt: correlacion de Zukauskas, ecuacion Cengel 7-42. Ver tabla Cengel 7-2 para los diferentes casos:

NuD =hD

k= C RemD Prn(Pr /Prs)

0,25

donde ReD = VmaxDν

y todas las propiedades se deben evaluar a la temperatura media aritmetica del fluido entre laentrada y salida del banco de tubos, excepto Prs que se evalua a la temperatura de pared del tubo.

3

Tabla 7-2 Cengel. Correlacion de Zukauskas para el numero de Nusselt en flujo cruzado sobre banco de tubos.

The average Nusselt number relations in Table 7–2 are for tube banks with16 or more rows. Those relations can also be used for tube banks with NL pro-vided that they are modified as

(7-44)

where F is a correction factor F whose values are given in Table 7–3. ForReD � 1000, the correction factor is independent of Reynolds number.

Once the Nusselt number and thus the average heat transfer coefficient forthe entire tube bank is known, the heat transfer rate can be determined fromNewton’s law of cooling using a suitable temperature difference �T. The firstthought that comes to mind is to use �T � Ts � Tm � Ts � (Ti � Te)/2. Butthis will, in general, over predict the heat transfer rate. We will show in thenext chapter that the proper temperature difference for internal flow (flowover tube banks is still internal flow through the shell) is the 1ogarithmicmean temperature difference �Tln defined as

(7-45)

We will also show that the exit temperature of the fluid Te can be determinedfrom

�Tln �(Ts � Te) � (Ts � Ti)ln[(Ts � Te)/(Ts � Ti)]

��Te � �Ti

ln(�Te /�Ti)

NuD, NL� FNuD

CHAPTER 7391

TABLE 7–2

Nusselt number correlations for cross flow over tube banks for N � 16 and0.7 � Pr � 500 (from Zukauskas, Ref. 15, 1987)*

Arrangement Range of ReD Correlation

0–100

100–1000In-line

1000–2 105

2 105–2 106

0–500

500–1000Staggered

1000–2 105

2 105–2 106

*All properties except Prs are to be evaluated at the arithmetic mean of the inlet and outlet temperaturesof the fluid (Prs is to be evaluated at Ts ).

NuD � 0.031(ST /SL)0.2 Re0.8D Pr0.36(Pr/Prs)0.25


NuD � 0.71 Re0.5D Pr0.36(Pr/Prs)0.25

NuD � 1.04 Re0.4D Pr0.36(Pr/Prs)0.25

NuD � 0.033 Re0.8D Pr0.4(Pr/Prs)0.25

NuD � 0.27 Re0.63D Pr0.36(Pr/Prs)0.25

NuD � 0.52 Re0.5D Pr0.36(Pr/Prs)0.25

NuD � 0.9 Re0.4D Pr0.36(Pr/Prs)0.25

TABLE 7–3

Correction factor F to be used in , = FNuD for NL � 16 and ReD � 1000(from Zukauskas, Ref 15, 1987).

NL 1 2 3 4 5 7 10 13

In-line 0.70 0.80 0.86 0.90 0.93 0.96 0.98 0.99

Staggered 0.64 0.76 0.84 0.89 0.93 0.96 0.98 0.99

NuD, NL

cen58933_ch07.qxd 9/4/2002 12:12 PM Page 391

Correcion para numero de filas menor de 16: si el banco de tubos tuviese un numero de filas menor de 16 hay quecorregir el numero de Nusselt con la ecuacion Cengel 7-44:

NuD,NL = FNuD

donde el factor de correccion F se obtiene de la tabla Cengel 7-3, que es valida si ReD > 1000. A partir de este valor deReD el factor de correccion resulta independiente del numero de Reynolds.

Tabla 7-3 Cengel. Factor de correccion en caso de que el banco de tubos tenga menos de 16 filas.

The average Nusselt number relations in Table 7–2 are for tube banks with16 or more rows. Those relations can also be used for tube banks with NL pro-vided that they are modified as

(7-44)

where F is a correction factor F whose values are given in Table 7–3. ForReD � 1000, the correction factor is independent of Reynolds number.

Once the Nusselt number and thus the average heat transfer coefficient forthe entire tube bank is known, the heat transfer rate can be determined fromNewton’s law of cooling using a suitable temperature difference �T. The firstthought that comes to mind is to use �T � Ts � Tm � Ts � (Ti � Te)/2. Butthis will, in general, over predict the heat transfer rate. We will show in thenext chapter that the proper temperature difference for internal flow (flowover tube banks is still internal flow through the shell) is the 1ogarithmicmean temperature difference �Tln defined as

(7-45)

We will also show that the exit temperature of the fluid Te can be determinedfrom

�Tln �(Ts � Te) � (Ts � Ti)ln[(Ts � Te)/(Ts � Ti)]

��Te � �Ti

ln(�Te /�Ti)

NuD, NL� FNuD

CHAPTER 7391

TABLE 7–2

Nusselt number correlations for cross flow over tube banks for N � 16 and0.7 � Pr � 500 (from Zukauskas, Ref. 15, 1987)*

Arrangement Range of ReD Correlation

0–100

100–1000In-line

1000–2 105

2 105–2 106

0–500

500–1000Staggered

1000–2 105

2 105–2 106

*All properties except Prs are to be evaluated at the arithmetic mean of the inlet and outlet temperaturesof the fluid (Prs is to be evaluated at Ts ).



NuD � 0.71 Re0.5D Pr0.36(Pr/Prs)0.25

NuD � 1.04 Re0.4D Pr0.36(Pr/Prs)0.25

NuD � 0.033 Re0.8D Pr0.4(Pr/Prs)0.25

NuD � 0.27 Re0.63D Pr0.36(Pr/Prs)0.25

NuD � 0.52 Re0.5D Pr0.36(Pr/Prs)0.25

NuD � 0.9 Re0.4D Pr0.36(Pr/Prs)0.25

TABLE 7–3

Correction factor F to be used in , = FNuD for NL � 16 and ReD � 1000(from Zukauskas, Ref 15, 1987).

NL 1 2 3 4 5 7 10 13

In-line 0.70 0.80 0.86 0.90 0.93 0.96 0.98 0.99

Staggered 0.64 0.76 0.84 0.89 0.93 0.96 0.98 0.99

NuD, NL

cen58933_ch07.qxd 9/4/2002 12:12 PM Page 391

4

3. Conveccion forzada, flujo interno

3.1. Flujo interno desarrollado en conductos circulares lisos

Tabla 17.5 ItoTSE. Correlaciones de transferencia de calor en flujo interno forzado en conductos circulares lisos.438 Chapter 17. Heat Transfer by Convection

Table 17.5 Summary of Forced Convection Heat Transfer Correlations for Internal Flow in Smooth Circular Tubesc

Flow/Surface Thermal Conditions Correlationa,b Restrictions on Applicability

Laminar, fully developed, (xfd�D) � 0.05 ReDPr

Constant NuD � 4.36 (17.61) Pr � 0.6, ReD � 2300

Constant Ts NuD � 3.66 (17.62) Pr � 0.6, ReD � 2300

Turbulent, fully developed, (xfd�D) � 10

Constant or Ts (Dittus-Boelter) (17.64) 0.6 � Pr � 160, ReD � 10,000,n � 0.4 for Ts � Tm and n � 0.3for Ts Tm

Constant or Ts (Sieder-Tate) (17.65) 0.7 � Pr � 16,700, ReD � 10,000

aThermophysical properties in Eqs. 17.61, 17.62, and 17.64 are based upon the mean temperature, Tm. If the correlations are used to estimate theaverage Nusselt number over the entire tube length, the properties should be based upon the average of the mean temperatures, � (Tm,i � Tm,o)�2.bThermophysical properties in Eq. 17.65 should be evaluated at Tm or , except for �s, which is evaluated at the tube wall temperature Ts or cFor tubes of noncircular cross section, use the hydraulic diameter, Dh, Eq. 17.63, as the characteristic length for the Reynolds and Nusseltnumbers. Results for fully developed laminar flow are provided in Table 17.4. For turbulent flow, Eq. 17.64 may be used as a first approximation.

Ts.Tm

Tm

NuD � 0.027 Re4�5D Pr1�3 a �

�sb0.14

q–s

NuD � 0.023 Re4�D

5 Prnq–s

q–s

Free Convection

Free ConvectionIn the preceding sections of this chapter, we considered convection heat transfer in fluid flowsthat originate from an external forcing condition. Now we consider situations for which thereis no forced motion, but heat transfer occurs because of convection currents that are inducedby buoyancy forces, which arise from density differences caused by temperature variationsin the fluid. Heat transfer by this means is referred to as free (or natural) convection.

Since free convection flow velocities are generally much smaller than those associated withforced convection, the corresponding heat transfer rates are also smaller. However, in manythermal systems, free convection may provide the largest resistance to heat transfer and there-fore plays an important role in the design or performance of the system. Free convection is of-ten the preferred mode of convection heat transfer, especially in electronic systems, for reasonsof space limitations, maintenance-free operation, and reduced operating costs. Free convectionstrongly influences heat transfer from pipes, transmission lines, transformers, baseboard heaters,as well as appliances such as your stereo, television and laptop computer. It is also relevant tothe environmental sciences, where it is responsible for oceanic and atmospheric motions.

We begin by considering the physical origins and nature of buoyancy-driven flows, andintroduce empirical correlations to estimate convection coefficients for common geometries.

17.4.1 Flow and Thermal Considerations

To illustrate the nature of the boundary layer development in free convection flows, considerthe heated vertical plate (Fig. 17.20a) that is immersed in a cooler extensive, quiescent fluid.An extensive medium is, in principle, an infinite one; a quiescent fluid is one that is other-wise at rest, except in the vicinity of the surface.

Since the plate is hotter than the fluid, Ts � T�, the fluid close to the plate is less densethan fluid in the quiescent region. The fluid density gradient and the gravitational field cre-ate the buoyancy force that induces the free convection boundary layer flow in which theheated fluid rises. The boundary layer grows as more fluid from the quiescent region is

17.4

c17.qxd 6/10/02 20:13 Page 438

3.2. Flujo interno desarrollado en conductos no circulares

Tabla 17.4 ItoTSE. Numero de Nusselt para flujo laminar completamente desarrollado en el interior de conductos nocirculares.

17.3 Internal Flow 433

Surface Thermal Condition: External Fluid (CD-ROM)

17.3.3 Convection Correlations for Tubes: Fully Developed Region

To use many of the foregoing results for internal flow, the convection coefficients must beknown. In this section we present correlations for estimating the coefficients for fullydeveloped laminar and turbulent flows in circular and noncircular tubes. The correlationsfor internal flow are summarized in Table 17.5 (page 438) along with guidelines to facilitatetheir selection for your application.

Laminar FlowThe problem of laminar flow (ReD 2300) in tubes has been treated theoretically, and theresults can be used to determine the convection coefficients. For flow in a circular tubecharacterized by uniform surface heat flux and laminar, fully developed conditions, the Nusseltnumber is a constant, independent of ReD, Pr, and axial location

(17.61)

When the thermal surface condition is characterized by a constant surface temperature, theresults are of similar form, but with a smaller value for the Nusselt number

(17.62)

In using these equations to determine h, the thermal conductivity should be evaluated at Tm.

NuD �hD

k� 3.66 3Ts � constant 4

NuD �hD

k� 4.36 3q–s � constant 4

Table 17.4 Nusselt Numbers for Fully Developed Laminar Flow in Noncircular Tubes forConstant Ts and qs Surface Thermal Conditionsa

Cross Section Constant qs Constant Ts

— 4.36 3.66

1.0 3.61 2.98

1.43 3.73 3.08

2.0 4.12 3.39

3.0 4.79 3.96

4.0 5.33 4.44

8.0 6.49 5.60

� 8.23 7.54

� 5.39 4.86

— 3.11 2.47

aThe characteristic length is the hydraulic diameter, Dh, Eq. 17.63.

b

a

NuD �hDh

k

ba

a

a

a

a

a

b

b

b

b

b

Insulated

Heated

c17.qxd 6/10/02 20:13 Page 433

Para flujo turbulento usar la ecuacion 17.64 con el diametro hidraulico: Dh ≡ 4AcP

, ecuacion ItoTSE 17.63, donde Aces el area transversal de paso y P es el perımetro mojado.

5

4. Conveccion natural

4.1. Correlaciones generales

Tabla 17.6 ItoTSE. Correlaciones de transferencia de calor por conveccion natural en geometrıas sumergidas.446 Chapter 17. Heat Transfer by Convection

Table 17.6 Summary of Free Convection Correlations for Immersed Geometries

Geometry Recommended Correlation Restrictions

(17.74) RaL 1013

(17.78) 105 RaL 1010

(17.79) 104 RaL 107

(17.80) 107 RaL 1011

(17.84) RaD 1012

(17.85)

aThe correlation may be applied to a vertical cylinder if (D�L) � (35� ).bThe characteristic length is defined as L � As�P, Eq. 17.77.

Gr1�4L

RaD 1011

Pr � 0.7NuD � 2 �

0.589 Ra1�4D

31 � 10.469 Pr29�16 4 4�9

NuD � e0.60 �0.387 Ra1�6

D

31 � 10.559�Pr 29�16 4 8�27 f2

NuL � 0.15 Ra1�3L

NuL � 0.54 Ra1�4L

NuL � 0.27 Ra1�4L

NuL � e0.825 �0.387 Ra1�6

L

31 � 10.492�Pr29�16 4 8�27 f2

Vertical platesa

Horizontal platesb

Case A or B:Hot surface down or cold surface up

Case C or D:Hot surface up or cold surface down

Horizontal cylinder

Sphere

17.4.5 Guide for Selection of Free Convection Correlations

In this section you have been introduced to empirical correlations to estimate the convectioncoefficients for free convection heat transfer for vertical and horizontal plates, the horizon-tal cylinder, and the sphere. For your convenience in selecting appropriate correlations foryour problems, the recommended correlations have been summarized in Table 17.6. Specificconditions are associated with each of the correlations, and you are reminded to follow therules for peforming convection calculations outlined in Sec. 17.1.3.

Convection Application: Heat Exchangers

Heat ExchangersThe process of heat exchange between two fluids that are at different temperatures andseparated by a solid wall occurs in many engineering applications. The device used toimplement this exchange is termed a heat exchanger, and specific applications can be found

17.5

c17.qxd 6/10/02 20:14 Page 446

Correlacion de Morgan para cilindros largos horizontales (alternativa mas sencilla a la correlacion 17.84)

Ecuacion Rango Ecuacion ItoTSE

NuD = 0,850Ra0,188D 102 ≤ RaL ≤ 104 (17.81)

NuD = 0,480Ra0,250D 104 ≤ RaL ≤ 107 (17.82)

NuD = 0,125Ra0,333D 107 ≤ RaL ≤ 1012 (17.83)

Temperatura de referencia: En conveccion natural, las propiedades del fluido se evaluan a temperatura de pelıculaexcepto el coeficiente de expansion volumetrica β que se debe evaluar a la temperatura de fluido sin perturbar.

Longitud caracterıstica en placas horizontales: es la razon entre la superficie de la placa (una sola cara) y elperımetro, ecuacion ItoTSE 17.77:

L ≡ AsP

6

4.2. Correlaciones simplificadas para aire

Tabla de correlaciones para calcular el coeficiente de pelıcula en conveccion natural no confinada (flujo externo)**solo validas para aire a temperatura ambiente**

Configuracion geometrica Ecuacion Regimen de flujo

Placa plana (o cilindro) verticalhcv = 1,42 · (∆T/L)

1/4Laminar 104 < RaL < 109

hcv = 1,31 · (∆T )1/3

Turbulento 109 < RaL < 1013

Placa plana horizontal, conveccion favorecidahcv = 1,32 · (∆T/L)

1/4Laminar 104 < RaL < 109

hcv = 1,52 · (∆T )1/3

Turbulento 109 < RaL < 1013

Placa plana horizontal, conveccion impedida hcv = 0,59 · (∆T/L)1/4

Laminar 104 < RaL < 109

Cilindro horizontalhcv = 1,32 · (∆T/D)

1/4Laminar 104 < RaD < 109

hcv = 1,24 · (∆T )1/3

Turbulento 109 < RaD < 1013

5. Historial de cambios8-dic-2012 primera version10-ene-2013 # anadida la correlacion de Morgan de conveccion natural

# aclaracion sobre la temperatura de referencia en conveccion natural# anadida la tabla extendida de propiedades del agua

12-ene-2014 # bancos de tubos, correccion de errata en formula Vmax para trebolillo, Cengel 7-41# varias aclaraciones y mejoras en la seccion de bancos de tubos# mejorada la seccion de flujo interno

7

Propiedades del aire seco a presion atmosferica.EES v.9.250. 29-Nov-2012 1

T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

-150 2.87 1.002 8.64 3.01 11.71 4.08 0.7391-145 2.75 1.002 8.99 3.26 12.13 4.39 0.7427-140 2.65 1.002 9.33 3.52 12.54 4.72 0.7457-135 2.56 1.002 9.67 3.79 12.95 5.06 0.7480-130 2.47 1.002 10.00 4.06 13.37 5.41 0.7499-125 2.38 1.002 10.33 4.34 13.78 5.77 0.7514-120 2.30 1.002 10.65 4.62 14.19 6.14 0.7524-115 2.23 1.002 10.97 4.92 14.60 6.53 0.7532-110 2.16 1.002 11.28 5.22 15.01 6.92 0.7536-105 2.10 1.002 11.59 5.52 15.41 7.33 0.7539-100 2.04 1.002 11.90 5.84 15.82 7.74 0.7538-95 1.98 1.002 12.20 6.16 16.22 8.17 0.7537-90 1.93 1.002 12.49 6.48 16.62 8.61 0.7533-85 1.88 1.002 12.79 6.82 17.02 9.05 0.7528-80 1.83 1.002 13.07 7.16 17.42 9.51 0.7522-75 1.78 1.002 13.36 7.50 17.82 9.98 0.7515-70 1.74 1.002 13.64 7.85 18.22 10.46 0.7506-65 1.70 1.002 13.92 8.21 18.61 10.95 0.7497-60 1.66 1.002 14.20 8.57 19.01 11.45 0.7487-55 1.62 1.002 14.47 8.94 19.40 11.96 0.7477-50 1.58 1.003 14.74 9.32 19.79 12.48 0.7466-45 1.55 1.003 15.01 9.70 20.18 13.01 0.7455-40 1.51 1.003 15.27 10.09 20.57 13.55 0.7443-35 1.48 1.003 15.53 10.48 20.96 14.10 0.7431-30 1.45 1.003 15.79 10.88 21.34 14.66 0.7419-25 1.42 1.003 16.05 11.28 21.73 15.23 0.7407-20 1.39 1.003 16.30 11.69 22.11 15.81 0.7394-15 1.37 1.003 16.55 12.11 22.50 16.40 0.7381-10 1.34 1.003 16.80 12.53 22.88 17.00 0.7369-5 1.32 1.003 17.05 12.95 23.26 17.61 0.73560 1.29 1.004 17.29 13.38 23.64 18.23 0.73435 1.27 1.004 17.54 13.82 24.01 18.85 0.733010 1.25 1.004 17.78 14.26 24.39 19.49 0.731815 1.23 1.004 18.02 14.71 24.76 20.13 0.730520 1.20 1.004 18.25 15.16 25.14 20.79 0.729325 1.18 1.005 18.49 15.62 25.51 21.45 0.728130 1.16 1.005 18.72 16.08 25.88 22.12 0.726835 1.15 1.005 18.95 16.55 26.25 22.80 0.725640 1.13 1.005 19.18 17.02 26.62 23.49 0.724445 1.11 1.006 19.41 17.50 26.99 24.19 0.723350 1.09 1.006 19.63 17.98 27.35 24.90 0.722155 1.08 1.006 19.86 18.47 27.72 25.61 0.721060 1.06 1.007 20.08 18.96 28.08 26.33 0.719965 1.04 1.007 20.30 19.45 28.45 27.06 0.718870 1.03 1.007 20.52 19.95 28.81 27.80 0.717775 1.01 1.008 20.74 20.46 29.17 28.55 0.716780 1.00 1.008 20.96 20.97 29.53 29.30 0.715785 0.99 1.009 21.17 21.49 29.88 30.06 0.714790 0.97 1.009 21.39 22.01 30.24 30.83 0.713795 0.96 1.010 21.60 22.53 30.60 31.61 0.7128100 0.95 1.010 21.81 23.06 30.95 32.39 0.7118105 0.93 1.011 22.02 23.59 31.30 33.18 0.7110110 0.92 1.011 22.23 24.13 31.65 33.98 0.7101115 0.91 1.012 22.43 24.67 32.01 34.79 0.7092120 0.90 1.012 22.64 25.22 32.35 35.60 0.7084125 0.89 1.013 22.84 25.77 32.70 36.42 0.7076130 0.88 1.014 23.05 26.33 33.05 37.24 0.7068135 0.86 1.014 23.25 26.89 33.40 38.08 0.7061140 0.85 1.015 23.45 27.45 33.74 38.92 0.7054145 0.84 1.016 23.65 28.02 34.08 39.76 0.7047150 0.83 1.016 23.85 28.59 34.43 40.61 0.7040155 0.82 1.017 24.04 29.17 34.77 41.47 0.7034160 0.81 1.018 24.24 29.75 35.11 42.34 0.7027165 0.81 1.019 24.44 30.34 35.45 43.21 0.7021170 0.80 1.019 24.63 30.93 35.79 44.08 0.7016175 0.79 1.020 24.82 31.52 36.12 44.96 0.7010180 0.78 1.021 25.01 32.12 36.46 45.85 0.7005185 0.77 1.022 25.20 32.72 36.79 46.74 0.7000190 0.76 1.023 25.39 33.33 37.13 47.64 0.6995195 0.75 1.023 25.58 33.94 37.46 48.55 0.6990

continua en la pagina siguiente –

Grado en Ingenierıa en Tecnologıas Industriales Termotecnia

8


– continua desde la pagina anterior

T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

200 0.75 1.024 25.77 34.55 37.79 49.46 0.6986205 0.74 1.025 25.96 35.17 38.12 50.37 0.6982210 0.73 1.026 26.14 35.79 38.45 51.29 0.6978215 0.72 1.027 26.33 36.42 38.77 52.22 0.6974220 0.72 1.028 26.51 37.05 39.10 53.15 0.6970225 0.71 1.029 26.70 37.68 39.43 54.08 0.6967230 0.70 1.030 26.88 38.32 39.75 55.02 0.6964235 0.69 1.031 27.06 38.96 40.07 55.97 0.6961240 0.69 1.032 27.24 39.61 40.40 56.92 0.6958245 0.68 1.033 27.42 40.26 40.72 57.88 0.6956250 0.67 1.034 27.60 40.91 41.04 58.84 0.6953255 0.67 1.035 27.78 41.57 41.36 59.80 0.6951260 0.66 1.036 27.95 42.23 41.67 60.77 0.6949265 0.66 1.037 28.13 42.89 41.99 61.74 0.6947270 0.65 1.038 28.30 43.56 42.31 62.72 0.6945275 0.64 1.039 28.48 44.23 42.62 63.70 0.6944280 0.64 1.040 28.65 44.91 42.93 64.69 0.6942285 0.63 1.041 28.83 45.59 43.25 65.68 0.6941290 0.63 1.042 29.00 46.27 43.56 66.67 0.6940295 0.62 1.044 29.17 46.96 43.87 67.67 0.6939300 0.62 1.045 29.34 47.65 44.18 68.68 0.6938305 0.61 1.046 29.51 48.34 44.49 69.68 0.6937310 0.61 1.047 29.68 49.04 44.79 70.69 0.6937315 0.60 1.048 29.85 49.74 45.10 71.71 0.6936320 0.60 1.049 30.01 50.44 45.40 72.73 0.6936325 0.59 1.050 30.18 51.15 45.71 73.75 0.6936330 0.59 1.052 30.35 51.86 46.01 74.78 0.6936335 0.58 1.053 30.51 52.58 46.31 75.81 0.6936340 0.58 1.054 30.68 53.30 46.61 76.84 0.6936345 0.57 1.055 30.84 54.02 46.91 77.88 0.6936350 0.57 1.056 31.01 54.75 47.21 78.92 0.6937355 0.56 1.057 31.17 55.48 47.51 79.97 0.6937360 0.56 1.059 31.33 56.21 47.81 81.02 0.6938365 0.55 1.060 31.49 56.94 48.10 82.07 0.6938370 0.55 1.061 31.65 57.68 48.40 83.13 0.6939375 0.54 1.062 31.81 58.43 48.69 84.19 0.6940380 0.54 1.063 31.97 59.17 48.99 85.25 0.6941385 0.54 1.065 32.13 59.92 49.28 86.32 0.6942390 0.53 1.066 32.29 60.68 49.57 87.39 0.6943395 0.53 1.067 32.45 61.43 49.86 88.46 0.6944400 0.52 1.068 32.61 62.19 50.15 89.54 0.6946405 0.52 1.069 32.76 62.95 50.43 90.62 0.6947410 0.52 1.071 32.92 63.72 50.72 91.71 0.6948415 0.51 1.072 33.07 64.49 51.01 92.79 0.6950420 0.51 1.073 33.23 65.26 51.29 93.88 0.6952425 0.51 1.074 33.38 66.04 51.58 94.98 0.6953430 0.50 1.075 33.54 66.82 51.86 96.07 0.6955435 0.50 1.077 33.69 67.60 52.14 97.17 0.6957440 0.49 1.078 33.84 68.39 52.42 98.28 0.6958445 0.49 1.079 34.00 69.18 52.70 99.39 0.6960450 0.49 1.080 34.15 69.97 52.98 100.50 0.6962455 0.48 1.081 34.30 70.76 53.26 101.60 0.6964460 0.48 1.083 34.45 71.56 53.54 102.70 0.6966465 0.48 1.084 34.60 72.36 53.81 103.80 0.6968470 0.47 1.085 34.75 73.17 54.09 105.00 0.6970475 0.47 1.086 34.90 73.97 54.36 106.10 0.6973480 0.47 1.087 35.04 74.79 54.64 107.20 0.6975485 0.47 1.089 35.19 75.60 54.91 108.40 0.6977490 0.46 1.090 35.34 76.42 55.18 109.50 0.6979495 0.46 1.091 35.49 77.24 55.45 110.60 0.6982500 0.46 1.092 35.63 78.06 55.72 111.80 0.6984505 0.45 1.093 35.78 78.89 55.99 112.90 0.6986510 0.45 1.095 35.92 79.72 56.26 114.10 0.6989515 0.45 1.096 36.07 80.55 56.53 115.20 0.6991520 0.45 1.097 36.21 81.38 56.79 116.40 0.6994525 0.44 1.098 36.36 82.22 57.06 117.50 0.6996530 0.44 1.099 36.50 83.06 57.32 118.70 0.6999535 0.44 1.100 36.64 83.91 57.59 119.80 0.7002540 0.43 1.101 36.78 84.75 57.85 121.00 0.7004



9



T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

545 0.43 1.103 36.93 85.60 58.11 122.20 0.7007550 0.43 1.104 37.07 86.46 58.37 123.30 0.7009555 0.43 1.105 37.21 87.31 58.63 124.50 0.7012560 0.42 1.106 37.35 88.17 58.89 125.70 0.7015565 0.42 1.107 37.49 89.03 59.15 126.90 0.7018570 0.42 1.108 37.63 89.90 59.41 128.10 0.7020575 0.42 1.109 37.77 90.77 59.66 129.20 0.7023580 0.41 1.111 37.91 91.64 59.92 130.40 0.7026585 0.41 1.112 38.05 92.51 60.17 131.60 0.7029590 0.41 1.113 38.18 93.39 60.43 132.80 0.7031595 0.41 1.114 38.32 94.27 60.68 134.00 0.7034600 0.40 1.115 38.46 95.15 60.93 135.20 0.7037605 0.40 1.116 38.60 96.03 61.18 136.40 0.7040610 0.40 1.117 38.73 96.92 61.43 137.60 0.7043615 0.40 1.118 38.87 97.81 61.68 138.80 0.7046620 0.40 1.119 39.00 98.70 61.93 140.00 0.7048625 0.39 1.120 39.14 99.60 62.18 141.20 0.7051630 0.39 1.121 39.27 100.50 62.43 142.50 0.7054635 0.39 1.122 39.41 101.40 62.68 143.70 0.7057640 0.39 1.123 39.54 102.30 62.92 144.90 0.7060645 0.38 1.125 39.67 103.20 63.17 146.10 0.7063650 0.38 1.126 39.81 104.10 63.41 147.40 0.7066655 0.38 1.127 39.94 105.00 63.65 148.60 0.7069660 0.38 1.128 40.07 105.90 63.90 149.80 0.7072665 0.38 1.129 40.20 106.90 64.14 151.10 0.7075670 0.37 1.130 40.33 107.80 64.38 152.30 0.7078675 0.37 1.131 40.46 108.70 64.62 153.50 0.7081680 0.37 1.132 40.60 109.60 64.86 154.80 0.7083685 0.37 1.133 40.73 110.60 65.10 156.00 0.7086690 0.37 1.134 40.86 111.50 65.33 157.30 0.7089695 0.36 1.135 40.98 112.40 65.57 158.50 0.7092700 0.36 1.136 41.11 113.40 65.81 159.80 0.7095705 0.36 1.137 41.24 114.30 66.04 161.00 0.7098710 0.36 1.138 41.37 115.20 66.28 162.30 0.7101715 0.36 1.139 41.50 116.20 66.51 163.60 0.7104720 0.36 1.140 41.63 117.10 66.74 164.80 0.7107725 0.35 1.140 41.75 118.10 66.97 166.10 0.7110730 0.35 1.141 41.88 119.00 67.21 167.40 0.7113735 0.35 1.142 42.01 120.00 67.44 168.60 0.7116740 0.35 1.143 42.13 121.00 67.67 169.90 0.7119745 0.35 1.144 42.26 121.90 67.90 171.20 0.7122750 0.34 1.145 42.39 122.90 68.12 172.50 0.7125755 0.34 1.146 42.51 123.80 68.35 173.70 0.7128760 0.34 1.147 42.64 124.80 68.58 175.00 0.7131765 0.34 1.148 42.76 125.80 68.81 176.30 0.7134770 0.34 1.149 42.88 126.80 69.03 177.60 0.7137775 0.34 1.150 43.01 127.70 69.26 178.90 0.7140780 0.34 1.151 43.13 128.70 69.48 180.20 0.7143785 0.33 1.151 43.25 129.70 69.70 181.50 0.7145790 0.33 1.152 43.38 130.70 69.93 182.80 0.7148795 0.33 1.153 43.50 131.70 70.15 184.10 0.7151800 0.33 1.154 43.62 132.60 70.37 185.40 0.7154805 0.33 1.155 43.74 133.60 70.59 186.70 0.7157810 0.33 1.156 43.87 134.60 70.81 188.00 0.7160815 0.32 1.157 43.99 135.60 71.03 189.30 0.7163820 0.32 1.158 44.11 136.60 71.25 190.70 0.7166825 0.32 1.158 44.23 137.60 71.47 192.00 0.7169830 0.32 1.159 44.35 138.60 71.68 193.30 0.7172835 0.32 1.160 44.47 139.60 71.90 194.60 0.7175840 0.32 1.161 44.59 140.60 72.11 195.90 0.7177845 0.32 1.162 44.71 141.60 72.33 197.30 0.7180850 0.31 1.162 44.83 142.70 72.54 198.60 0.7183855 0.31 1.163 44.95 143.70 72.76 199.90 0.7186860 0.31 1.164 45.06 144.70 72.97 201.30 0.7189865 0.31 1.165 45.18 145.70 73.18 202.60 0.7192870 0.31 1.166 45.30 146.70 73.39 203.90 0.7195875 0.31 1.166 45.42 147.80 73.61 205.30 0.7197880 0.31 1.167 45.53 148.80 73.82 206.60 0.7200885 0.30 1.168 45.65 149.80 74.03 208.00 0.7203890 0.30 1.169 45.77 150.80 74.24 209.30 0.7206



10



T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

895 0.30 1.170 45.88 151.90 74.44 210.70 0.7209900 0.30 1.170 46.00 152.90 74.65 212.00 0.7212905 0.30 1.171 46.12 153.90 74.86 213.40 0.7214910 0.30 1.172 46.23 155.00 75.07 214.70 0.7217915 0.30 1.173 46.35 156.00 75.27 216.10 0.7220920 0.30 1.173 46.46 157.10 75.48 217.50 0.7223925 0.29 1.174 46.58 158.10 75.68 218.80 0.7226930 0.29 1.175 46.69 159.20 75.89 220.20 0.7228935 0.29 1.176 46.80 160.20 76.09 221.60 0.7231940 0.29 1.176 46.92 161.30 76.29 222.90 0.7234945 0.29 1.177 47.03 162.30 76.49 224.30 0.7237950 0.29 1.178 47.15 163.40 76.70 225.70 0.7239955 0.29 1.178 47.26 164.50 76.90 227.10 0.7242960 0.29 1.179 47.37 165.50 77.10 228.50 0.7245965 0.29 1.180 47.48 166.60 77.30 229.80 0.7247970 0.28 1.181 47.60 167.60 77.50 231.20 0.7250975 0.28 1.181 47.71 168.70 77.69 232.60 0.7253980 0.28 1.182 47.82 169.80 77.89 234.00 0.7256985 0.28 1.183 47.93 170.90 78.09 235.40 0.7258990 0.28 1.183 48.04 171.90 78.29 236.80 0.7261995 0.28 1.184 48.15 173.00 78.48 238.20 0.72641000 0.28 1.185 48.26 174.10 78.68 239.60 0.72661005 0.28 1.185 48.37 175.20 78.87 241.00 0.72691010 0.28 1.186 48.48 176.30 79.07 242.40 0.72721015 0.27 1.187 48.59 177.40 79.26 243.80 0.72741020 0.27 1.187 48.70 178.40 79.46 245.20 0.72771025 0.27 1.188 48.81 179.50 79.65 246.60 0.72791030 0.27 1.189 48.92 180.60 79.84 248.10 0.72821035 0.27 1.189 49.03 181.70 80.03 249.50 0.72851040 0.27 1.190 49.14 182.80 80.23 250.90 0.72871045 0.27 1.190 49.25 183.90 80.42 252.30 0.72901050 0.27 1.191 49.35 185.00 80.61 253.70 0.72921055 0.27 1.192 49.46 186.10 80.80 255.20 0.72951060 0.26 1.192 49.57 187.20 80.99 256.60 0.72981065 0.26 1.193 49.68 188.40 81.18 258.00 0.73001070 0.26 1.194 49.78 189.50 81.36 259.40 0.73031075 0.26 1.194 49.89 190.60 81.55 260.90 0.73051080 0.26 1.195 50.00 191.70 81.74 262.30 0.73081085 0.26 1.195 50.10 192.80 81.92 263.80 0.73101090 0.26 1.196 50.21 193.90 82.11 265.20 0.73131095 0.26 1.197 50.31 195.00 82.30 266.60 0.73151100 0.26 1.197 50.42 196.20 82.48 268.10 0.73181105 0.26 1.198 50.52 197.30 82.67 269.50 0.73201110 0.26 1.198 50.63 198.40 82.85 271.00 0.73231115 0.25 1.199 50.73 199.60 83.03 272.40 0.73251120 0.25 1.199 50.84 200.70 83.22 273.90 0.73281125 0.25 1.200 50.94 201.80 83.40 275.30 0.73301130 0.25 1.201 51.05 203.00 83.58 276.80 0.73321135 0.25 1.201 51.15 204.10 83.76 278.30 0.73351140 0.25 1.202 51.26 205.20 83.95 279.70 0.73371145 0.25 1.202 51.36 206.40 84.13 281.20 0.73401150 0.25 1.203 51.46 207.50 84.31 282.60 0.73421155 0.25 1.203 51.56 208.70 84.49 284.10 0.73441160 0.25 1.204 51.67 209.80 84.67 285.60 0.73471165 0.25 1.204 51.77 211.00 84.85 287.10 0.73491170 0.24 1.205 51.87 212.10 85.02 288.50 0.73511175 0.24 1.206 51.97 213.30 85.20 290.00 0.73541180 0.24 1.206 52.08 214.40 85.38 291.50 0.73561185 0.24 1.207 52.18 215.60 85.56 293.00 0.73581190 0.24 1.207 52.28 216.70 85.73 294.40 0.73611195 0.24 1.208 52.38 217.90 85.91 295.90 0.73631200 0.24 1.208 52.48 219.10 86.09 297.40 0.73651205 0.24 1.209 52.58 220.20 86.26 298.90 0.73681210 0.24 1.209 52.68 221.40 86.44 300.40 0.73701215 0.24 1.210 52.78 222.60 86.61 301.90 0.73721220 0.24 1.210 52.88 223.70 86.79 303.40 0.73741225 0.24 1.211 52.98 224.90 86.96 304.90 0.73771230 0.23 1.211 53.08 226.10 87.13 306.40 0.73791235 0.23 1.212 53.18 227.30 87.31 307.90 0.73811240 0.23 1.212 53.28 228.40 87.48 309.40 0.7383



11



T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

1245 0.23 1.213 53.38 229.60 87.65 310.90 0.73861250 0.23 1.213 53.48 230.80 87.82 312.40 0.73881255 0.23 1.214 53.58 232.00 87.99 313.90 0.73901260 0.23 1.214 53.68 233.20 88.16 315.40 0.73921265 0.23 1.215 53.77 234.40 88.34 317.00 0.73941270 0.23 1.215 53.87 235.60 88.51 318.50 0.73961275 0.23 1.216 53.97 236.70 88.68 320.00 0.73991280 0.23 1.216 54.07 237.90 88.85 321.50 0.74011285 0.23 1.217 54.17 239.10 89.01 323.00 0.74031290 0.23 1.217 54.26 240.30 89.18 324.60 0.74051295 0.23 1.218 54.36 241.50 89.35 326.10 0.74071300 0.22 1.218 54.46 242.70 89.52 327.60 0.74091305 0.22 1.218 54.55 243.90 89.69 329.20 0.74111310 0.22 1.219 54.65 245.10 89.85 330.70 0.74131315 0.22 1.219 54.75 246.40 90.02 332.20 0.74151320 0.22 1.220 54.84 247.60 90.19 333.80 0.74171325 0.22 1.220 54.94 248.80 90.35 335.30 0.74191330 0.22 1.221 55.03 250.00 90.52 336.80 0.74211335 0.22 1.221 55.13 251.20 90.69 338.40 0.74231340 0.22 1.222 55.22 252.40 90.85 339.90 0.74251345 0.22 1.222 55.32 253.60 91.02 341.50 0.74271350 0.22 1.222 55.41 254.90 91.18 343.00 0.74291355 0.22 1.223 55.51 256.10 91.35 344.60 0.74311360 0.22 1.223 55.60 257.30 91.51 346.10 0.74331365 0.22 1.224 55.70 258.50 91.67 347.70 0.74351370 0.21 1.224 55.79 259.70 91.84 349.30 0.74371375 0.21 1.225 55.88 261.00 92.00 350.80 0.74391380 0.21 1.225 55.98 262.20 92.16 352.40 0.74411385 0.21 1.225 56.07 263.40 92.33 354.00 0.74431390 0.21 1.226 56.16 264.70 92.49 355.50 0.74441395 0.21 1.226 56.26 265.90 92.65 357.10 0.74461400 0.21 1.227 56.35 267.10 92.81 358.70 0.74481405 0.21 1.227 56.44 268.40 92.97 360.20 0.74501410 0.21 1.228 56.54 269.60 93.13 361.80 0.74521415 0.21 1.228 56.63 270.90 93.29 363.40 0.74541420 0.21 1.228 56.72 272.10 93.45 365.00 0.74551425 0.21 1.229 56.81 273.40 93.61 366.60 0.74571430 0.21 1.229 56.90 274.60 93.77 368.20 0.74591435 0.21 1.230 56.99 275.90 93.93 369.70 0.74611440 0.21 1.230 57.09 277.10 94.09 371.30 0.74621445 0.21 1.230 57.18 278.40 94.25 372.90 0.74641450 0.20 1.231 57.27 279.60 94.41 374.50 0.74661455 0.20 1.231 57.36 280.90 94.57 376.10 0.74671460 0.20 1.232 57.45 282.10 94.73 377.70 0.74691465 0.20 1.232 57.54 283.40 94.89 379.30 0.74711470 0.20 1.232 57.63 284.60 95.04 380.90 0.74721475 0.20 1.233 57.72 285.90 95.20 382.50 0.74741480 0.20 1.233 57.81 287.20 95.36 384.10 0.74761485 0.20 1.234 57.90 288.40 95.52 385.80 0.74771490 0.20 1.234 57.99 289.70 95.67 387.40 0.74791495 0.20 1.234 58.08 291.00 95.83 389.00 0.74801500 0.20 1.235 58.17 292.20 95.99 390.60 0.74821505 0.20 1.235 58.26 293.50 96.14 392.20 0.74841510 0.20 1.235 58.35 294.80 96.30 393.80 0.74851515 0.20 1.236 58.44 296.10 96.46 395.50 0.74871520 0.20 1.236 58.52 297.40 96.61 397.10 0.74881525 0.20 1.237 58.61 298.60 96.77 398.70 0.74901530 0.20 1.237 58.70 299.90 96.92 400.40 0.74911535 0.20 1.237 58.79 301.20 97.08 402.00 0.74931540 0.19 1.238 58.88 302.50 97.23 403.60 0.74941545 0.19 1.238 58.96 303.80 97.39 405.30 0.74951550 0.19 1.238 59.05 305.10 97.54 406.90 0.74971555 0.19 1.239 59.14 306.30 97.70 408.60 0.74981560 0.19 1.239 59.23 307.60 97.85 410.20 0.75001565 0.19 1.239 59.31 308.90 98.00 411.80 0.75011570 0.19 1.240 59.40 310.20 98.16 413.50 0.75021575 0.19 1.240 59.49 311.50 98.31 415.10 0.75041580 0.19 1.240 59.57 312.80 98.47 416.80 0.75051585 0.19 1.241 59.66 314.10 98.62 418.50 0.75061590 0.19 1.241 59.75 315.40 98.77 420.10 0.7508



12



T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

1595 0.19 1.241 59.83 316.70 98.92 421.80 0.75091600 0.19 1.242 59.92 318.00 99.08 423.50 0.75101605 0.19 1.242 60.00 319.30 99.23 425.10 0.75111610 0.19 1.243 60.09 320.60 99.38 426.80 0.75131615 0.19 1.243 60.17 321.90 99.54 428.50 0.75141620 0.19 1.243 60.26 323.20 99.69 430.10 0.75151625 0.19 1.244 60.35 324.60 99.84 431.80 0.75161630 0.19 1.244 60.43 325.90 100.00 433.50 0.75171635 0.19 1.244 60.51 327.20 100.10 435.20 0.75181640 0.18 1.245 60.60 328.50 100.30 436.90 0.75191645 0.18 1.245 60.68 329.80 100.40 438.60 0.75211650 0.18 1.245 60.77 331.10 100.60 440.20 0.75221655 0.18 1.246 60.85 332.50 100.70 441.90 0.75231660 0.18 1.246 60.94 333.80 100.90 443.60 0.75241665 0.18 1.246 61.02 335.10 101.10 445.30 0.75251670 0.18 1.246 61.10 336.40 101.20 447.00 0.75261675 0.18 1.247 61.19 337.80 101.40 448.70 0.75271680 0.18 1.247 61.27 339.10 101.50 450.40 0.75281685 0.18 1.247 61.35 340.40 101.70 452.10 0.75291690 0.18 1.248 61.44 341.70 101.80 453.90 0.75301695 0.18 1.248 61.52 343.10 102.00 455.60 0.75311700 0.18 1.248 61.60 344.40 102.10 457.30 0.75311705 0.18 1.249 61.68 345.70 102.30 459.00 0.75321710 0.18 1.249 61.77 347.10 102.40 460.70 0.75331715 0.18 1.249 61.85 348.40 102.60 462.50 0.75341720 0.18 1.250 61.93 349.80 102.70 464.20 0.75351725 0.18 1.250 62.01 351.10 102.90 465.90 0.75361730 0.18 1.249 62.09 352.40 103.00 468.00 0.75311735 0.18 1.250 62.18 353.80 103.20 469.70 0.75321740 0.18 1.250 62.26 355.10 103.30 471.50 0.75331745 0.17 1.250 62.34 356.50 103.50 473.20 0.75331750 0.17 1.251 62.42 357.80 103.60 475.00 0.75341755 0.17 1.251 62.50 359.20 103.80 476.70 0.75351760 0.17 1.251 62.58 360.50 103.90 478.50 0.75351765 0.17 1.251 62.66 361.90 104.10 480.20 0.75361770 0.17 1.252 62.74 363.20 104.20 482.00 0.75361775 0.17 1.252 62.82 364.60 104.40 483.70 0.75371780 0.17 1.252 62.90 365.90 104.50 485.50 0.75371785 0.17 1.253 62.98 367.30 104.70 487.30 0.75381790 0.17 1.253 63.06 368.70 104.80 489.00 0.75381795 0.17 1.253 63.14 370.00 105.00 490.80 0.75391800 0.17 1.253 63.22 371.40 105.10 492.60 0.75391805 0.17 1.254 63.30 372.80 105.30 494.40 0.75401810 0.17 1.254 63.38 374.10 105.40 496.20 0.75401815 0.17 1.254 63.46 375.50 105.60 497.90 0.75411820 0.17 1.255 63.54 376.90 105.70 499.70 0.75411825 0.17 1.255 63.62 378.20 105.90 501.50 0.75411830 0.17 1.255 63.70 379.60 106.00 503.30 0.75421835 0.17 1.255 63.78 381.00 106.20 505.10 0.75421840 0.17 1.256 63.86 382.30 106.30 506.90 0.75421845 0.17 1.256 63.93 383.70 106.50 508.70 0.75421850 0.17 1.256 64.01 385.10 106.60 510.50 0.75431855 0.17 1.256 64.09 386.50 106.80 512.40 0.75431860 0.17 1.257 64.17 387.80 106.90 514.20 0.75431865 0.17 1.257 64.25 389.20 107.10 516.00 0.75431870 0.16 1.257 64.32 390.60 107.20 517.80 0.75431875 0.16 1.257 64.40 392.00 107.40 519.60 0.75441880 0.16 1.258 64.48 393.40 107.50 521.50 0.75441885 0.16 1.258 64.56 394.80 107.70 523.30 0.75441890 0.16 1.258 64.63 396.20 107.80 525.10 0.75441895 0.16 1.259 64.71 397.50 108.00 527.00 0.75441900 0.16 1.259 64.79 398.90 108.10 528.80 0.75441905 0.16 1.259 64.86 400.30 108.30 530.70 0.75441910 0.16 1.259 64.94 401.70 108.40 532.50 0.75441915 0.16 1.260 65.02 403.10 108.60 534.40 0.75441920 0.16 1.260 65.09 404.50 108.70 536.20 0.75441925 0.16 1.260 65.17 405.90 108.90 538.10 0.75441930 0.16 1.260 65.25 407.30 109.00 539.90 0.75431935 0.16 1.261 65.32 408.70 109.20 541.80 0.75431940 0.16 1.261 65.40 410.10 109.30 543.70 0.7543



13



T (◦C) ρ(

kgm3

)Cp

(kJ

kg·K)

µ× 106(

Nsm2

)v × 106

(m2

s

)k × 103

(W

m·K)

α× 106(

m2

s

)Pr

1945 0.16 1.261 65.47 411.50 109.50 545.50 0.75431950 0.16 1.261 65.55 412.90 109.60 547.40 0.75431955 0.16 1.262 65.62 414.30 109.80 549.30 0.75421960 0.16 1.262 65.70 415.70 109.90 551.20 0.75421965 0.16 1.262 65.77 417.10 110.10 553.10 0.75421970 0.16 1.262 65.85 418.50 110.20 555.00 0.75421975 0.16 1.263 65.92 419.90 110.40 556.90 0.75411980 0.16 1.263 66.00 421.30 110.50 558.80 0.75411985 0.16 1.263 66.07 422.80 110.70 560.70 0.75401990 0.16 1.263 66.15 424.20 110.80 562.60 0.75401995 0.16 1.263 66.22 425.60 111.00 564.50 0.75402000 0.16 1.264 66.30 427.00 111.10 566.40 0.7539


14

Propiedades del agua saturada para calculos de transmision de calor .EES v.9.250. 26-dic-2012 1

T psat δhliq−gas ρf volg Cpf Cpg µf × 106 µg × 106 νf × 106 νg × 106 kf × 103 kg × 103 Prf Prg βf × 103 βg × 103

(◦C) (bar)(

kJkg

) (kg

m3

) (m3

kg

) (kJ

kg·K) (

kJkg·K

) (Nsm2

) (Nsm2

) (m2

s

) (m2

s

) (W

m·K) (

Wm·K

)- -

(1K

) (1K

)0.01 0.006117 2501 1000 206 4.229 1.868 1792 9.216 1.793 1898 547.5 17.07 13.84 1.008 -0.08045 3.672

1 0.006572 2498 1000 192.4 4.221 1.868 1732 9.239 1.732 1778 549.5 17.12 13.31 1.008 -0.06079 3.6592 0.00706 2496 1000 179.8 4.215 1.869 1675 9.263 1.675 1665 551.5 17.17 12.8 1.008 -0.04175 3.6463 0.007581 2493 1000 168 4.209 1.869 1620 9.287 1.62 1560 553.6 17.23 12.32 1.008 -0.02347 3.6344 0.008136 2491 1000 157.1 4.204 1.87 1568 9.311 1.568 1463 555.6 17.28 11.87 1.007 -0.005888 3.6215 0.008726 2489 1000 147 4.2 1.871 1519 9.336 1.519 1373 557.6 17.34 11.44 1.007 0.01103 3.6096 0.009354 2486 1000 137.6 4.197 1.871 1472 9.36 1.472 1288 559.6 17.39 11.04 1.007 0.02734 3.5967 0.01002 2484 1000 128.9 4.194 1.872 1428 9.385 1.428 1210 561.5 17.45 10.66 1.007 0.04308 3.5848 0.01073 2482 1000 120.8 4.192 1.872 1386 9.41 1.386 1137 563.5 17.5 10.31 1.007 0.05827 3.5729 0.01148 2479 1000 113.3 4.19 1.873 1345 9.436 1.345 1069 565.5 17.56 9.967 1.006 0.07297 3.5610 0.01228 2477 999.7 106.3 4.188 1.874 1307 9.461 1.307 1006 567.4 17.62 9.645 1.006 0.08719 3.54811 0.01313 2475 999.6 99.81 4.187 1.875 1270 9.487 1.27 946.9 569.3 17.68 9.339 1.006 0.101 3.53612 0.01403 2472 999.5 93.74 4.186 1.875 1235 9.513 1.235 891.7 571.2 17.74 9.048 1.006 0.1143 3.52513 0.01498 2470 999.4 88.09 4.185 1.876 1201 9.539 1.202 840.2 573.1 17.8 8.771 1.006 0.1273 3.51314 0.01599 2467 999.2 82.81 4.185 1.877 1169 9.565 1.17 792.1 575 17.86 8.507 1.005 0.1399 3.50215 0.01706 2465 999.1 77.9 4.184 1.878 1138 9.592 1.139 747.2 576.9 17.92 8.255 1.005 0.1522 3.4916 0.01819 2463 998.9 73.31 4.184 1.878 1109 9.618 1.11 705.1 578.8 17.98 8.014 1.005 0.1641 3.47917 0.01938 2460 998.8 69.02 4.184 1.879 1080 9.645 1.082 665.7 580.6 18.04 7.785 1.005 0.1757 3.46818 0.02064 2458 998.6 65.02 4.183 1.88 1053 9.672 1.055 628.9 582.4 18.1 7.565 1.005 0.187 3.45719 0.02198 2456 998.4 61.28 4.183 1.881 1027 9.7 1.029 594.4 584.2 18.16 7.355 1.005 0.1981 3.44620 0.02339 2453 998.2 57.78 4.183 1.882 1002 9.727 1.004 562 586 18.22 7.154 1.004 0.2089 3.43521 0.02488 2451 998 54.5 4.183 1.883 978.1 9.755 0.9801 531.7 587.8 18.29 6.961 1.004 0.2194 3.42422 0.02645 2449 997.7 51.44 4.183 1.884 954.9 9.782 0.9571 503.2 589.6 18.35 6.776 1.004 0.2297 3.41423 0.0281 2446 997.5 48.57 4.183 1.885 932.6 9.81 0.935 476.5 591.3 18.42 6.598 1.004 0.2398 3.40324 0.02985 2444 997.3 45.88 4.183 1.886 911.2 9.838 0.9137 451.4 593 18.48 6.428 1.004 0.2496 3.39325 0.03169 2442 997 43.36 4.183 1.887 890.5 9.867 0.8932 427.8 594.7 18.55 6.264 1.004 0.2593 3.38226 0.03363 2439 996.8 40.99 4.183 1.888 870.6 9.895 0.8735 405.6 596.4 18.61 6.107 1.004 0.2688 3.37227 0.03567 2437 996.5 38.77 4.183 1.889 851.4 9.924 0.8544 384.8 598.1 18.68 5.955 1.003 0.2781 3.36228 0.03782 2434 996.2 36.69 4.183 1.89 832.9 9.952 0.8361 365.1 599.7 18.75 5.81 1.003 0.2872 3.35229 0.04008 2432 995.9 34.73 4.183 1.891 815 9.981 0.8183 346.7 601.3 18.82 5.67 1.003 0.2962 3.34230 0.04246 2430 995.6 32.9 4.183 1.892 797.7 10.01 0.8012 329.3 602.9 18.88 5.535 1.003 0.305 3.33231 0.04495 2427 995.3 31.17 4.183 1.893 781 10.04 0.7847 312.9 604.5 18.95 5.405 1.003 0.3136 3.32232 0.04758 2425 995 29.54 4.183 1.894 764.9 10.07 0.7688 297.5 606.1 19.02 5.28 1.003 0.3222 3.31333 0.05033 2423 994.7 28.01 4.183 1.896 749.3 10.1 0.7533 282.9 607.6 19.09 5.159 1.003 0.3305 3.30334 0.05323 2420 994.3 26.58 4.183 1.897 734.2 10.13 0.7384 269.1 609.1 19.16 5.042 1.002 0.3388 3.29435 0.05627 2418 994 25.22 4.183 1.898 719.6 10.16 0.724 256.2 610.6 19.23 4.93 1.002 0.3469 3.28436 0.05945 2415 993.6 23.94 4.183 1.899 705.5 10.19 0.71 243.9 612.1 19.3 4.821 1.002 0.3549 3.27537 0.0628 2413 993.3 22.74 4.183 1.9 691.8 10.22 0.6965 232.3 613.6 19.38 4.716 1.002 0.3628 3.26638 0.0663 2411 992.9 21.61 4.183 1.902 678.6 10.25 0.6834 221.4 615 19.45 4.615 1.002 0.3706 3.25739 0.06997 2408 992.5 20.54 4.183 1.903 665.7 10.28 0.6707 211.1 616.4 19.52 4.517 1.002 0.3783 3.24840 0.07381 2406 992.2 19.53 4.182 1.904 653.3 10.31 0.6584 201.3 617.8 19.59 4.423 1.002 0.3859 3.23941 0.07784 2403 991.8 18.58 4.182 1.906 641.2 10.34 0.6465 192 619.1 19.67 4.331 1.002 0.3934 3.2342 0.08205 2401 991.4 17.68 4.182 1.907 629.5 10.37 0.6349 183.3 620.5 19.74 4.243 1.002 0.4008 3.22243 0.08646 2399 991 16.83 4.182 1.909 618.1 10.4 0.6237 175 621.8 19.82 4.157 1.001 0.4081 3.21344 0.09108 2396 990.6 16.02 4.182 1.91 607 10.43 0.6128 167.1 623.1 19.89 4.074 1.001 0.4154 3.20545 0.0959 2394 990.2 15.26 4.182 1.912 596.3 10.46 0.6022 159.7 624.4 19.97 3.994 1.001 0.4225 3.19646 0.1009 2391 989.7 14.55 4.182 1.913 585.9 10.49 0.592 152.6 625.6 20.05 3.916 1.001 0.4296 3.18847 0.1062 2389 989.3 13.87 4.182 1.915 575.8 10.52 0.582 145.9 626.9 20.12 3.841 1.001 0.4366 3.1848 0.1117 2387 988.9 13.22 4.182 1.916 565.9 10.55 0.5723 139.5 628.1 20.2 3.768 1.001 0.4435 3.17249 0.1174 2384 988.4 12.61 4.182 1.918 556.4 10.58 0.5629 133.5 629.3 20.28 3.697 1.001 0.4504 3.16450 0.1234 2382 988 12.04 4.182 1.919 547.1 10.62 0.5537 127.8 630.4 20.36 3.629 1.001 0.4572 3.15651 0.1297 2379 987.5 11.49 4.182 1.921 538 10.65 0.5448 122.3 631.6 20.44 3.562 1.001 0.464 3.14852 0.1362 2377 987.1 10.97 4.182 1.923 529.2 10.68 0.5361 117.2 632.7 20.52 3.498 1.001 0.4706 3.14



15

Propiedades del agua saturada para calculos de transmision de calor .EES v.9.250. 26-dic-2012 2


T psat δhliq−gas ρf volg Cpf Cpg µf × 106 µg × 106 νf × 106 νg × 106 kf × 103 kg × 103 Prf Prg βf × 103 βg × 103

(◦C) (bar)(

kJkg

) (kg

m3

) (m3

kg

) (kJ

kg·K) (

kJkg·K

) (Nsm2

) (Nsm2

) (m2

s

) (m2

s

) (W

m·K) (

Wm·K

)- -

(1K

) (1K

)53 0.143 2375 986.6 10.48 4.182 1.924 520.6 10.71 0.5277 112.3 633.8 20.6 3.435 1.001 0.4773 3.13354 0.1501 2372 986.1 10.01 4.182 1.926 512.3 10.74 0.5195 107.6 634.9 20.68 3.374 1.001 0.4838 3.12555 0.1575 2370 985.7 9.573 4.182 1.928 504.2 10.77 0.5115 103.1 636 20.76 3.315 1 0.4903 3.11856 0.1652 2367 985.2 9.153 4.182 1.93 496.2 10.81 0.5037 98.91 637 20.84 3.258 1 0.4968 3.1157 0.1732 2365 984.7 8.754 4.182 1.931 488.5 10.84 0.4961 94.88 638 20.93 3.202 1 0.5032 3.10358 0.1816 2363 984.2 8.376 4.182 1.933 481 10.87 0.4888 91.04 639 21.01 3.148 1 0.5096 3.09659 0.1903 2360 983.7 8.016 4.183 1.935 473.7 10.9 0.4816 87.39 640 21.09 3.096 1 0.5159 3.08960 0.1993 2358 983.2 7.674 4.183 1.937 466.6 10.93 0.4746 83.91 640.9 21.18 3.045 1 0.5222 3.08261 0.2087 2355 982.6 7.349 4.183 1.939 459.6 10.97 0.4677 80.6 641.9 21.26 2.995 1 0.5284 3.07562 0.2185 2353 982.1 7.04 4.183 1.941 452.8 11 0.461 77.43 642.8 21.35 2.947 0.9999 0.5346 3.06863 0.2287 2350 981.6 6.746 4.184 1.943 446.2 11.03 0.4545 74.42 643.7 21.44 2.9 0.9999 0.5407 3.06164 0.2392 2348 981.1 6.466 4.184 1.945 439.7 11.06 0.4482 71.54 644.6 21.52 2.854 0.9998 0.5468 3.05565 0.2502 2345 980.5 6.2 4.184 1.947 433.4 11.1 0.442 68.79 645.4 21.61 2.81 0.9998 0.5529 3.04866 0.2616 2343 980 5.946 4.185 1.949 427.3 11.13 0.436 66.17 646.3 21.7 2.767 0.9997 0.5589 3.04267 0.2735 2340 979.4 5.704 4.185 1.951 421.2 11.16 0.4301 63.67 647.1 21.79 2.725 0.9997 0.5649 3.03668 0.2858 2338 978.9 5.474 4.186 1.954 415.4 11.19 0.4243 61.27 647.9 21.88 2.684 0.9996 0.5709 3.02969 0.2985 2336 978.3 5.254 4.186 1.956 409.6 11.23 0.4187 58.99 648.7 21.97 2.644 0.9996 0.5768 3.02370 0.3118 2333 977.7 5.045 4.187 1.958 404 11.26 0.4132 56.8 649.5 22.06 2.605 0.9995 0.5827 3.01771 0.3255 2331 977.2 4.845 4.188 1.96 398.6 11.29 0.4079 54.71 650.2 22.15 2.567 0.9995 0.5886 3.01172 0.3397 2328 976.6 4.654 4.188 1.963 393.2 11.33 0.4026 52.72 650.9 22.24 2.53 0.9995 0.5945 3.00673 0.3545 2326 976 4.473 4.189 1.965 388 11.36 0.3975 50.8 651.6 22.33 2.494 0.9994 0.6003 374 0.3698 2323 975.4 4.299 4.189 1.967 382.9 11.39 0.3925 48.98 652.3 22.43 2.459 0.9994 0.6061 2.99475 0.3856 2321 974.8 4.133 4.19 1.97 377.9 11.43 0.3876 47.22 653 22.52 2.425 0.9994 0.6118 2.98976 0.402 2318 974.2 3.975 4.191 1.972 373 11.46 0.3828 45.55 653.7 22.62 2.391 0.9993 0.6176 2.98377 0.419 2316 973.6 3.824 4.192 1.975 368.2 11.49 0.3782 43.94 654.3 22.71 2.359 0.9993 0.6233 2.97878 0.4367 2313 973 3.679 4.192 1.977 363.5 11.53 0.3736 42.4 655 22.81 2.327 0.9993 0.629 2.97379 0.4549 2311 972.4 3.541 4.193 1.98 359 11.56 0.3691 40.93 655.6 22.9 2.296 0.9993 0.6346 2.96780 0.4737 2308 971.8 3.409 4.194 1.983 354.5 11.59 0.3648 39.51 656.2 23 2.266 0.9993 0.6403 2.96281 0.4932 2306 971.2 3.282 4.195 1.985 350.1 11.63 0.3605 38.16 656.7 23.1 2.236 0.9993 0.6459 2.95782 0.5134 2303 970.5 3.161 4.196 1.988 345.8 11.66 0.3563 36.86 657.3 23.19 2.207 0.9993 0.6515 2.95283 0.5343 2301 969.9 3.046 4.197 1.991 341.6 11.69 0.3522 35.61 657.9 23.29 2.179 0.9993 0.6571 2.94884 0.5559 2298 969.3 2.935 4.198 1.993 337.5 11.73 0.3482 34.42 658.4 23.39 2.152 0.9993 0.6627 2.94385 0.5781 2295 968.6 2.829 4.199 1.996 333.5 11.76 0.3443 33.27 658.9 23.49 2.125 0.9993 0.6682 2.93886 0.6012 2293 968 2.727 4.2 1.999 329.5 11.79 0.3404 32.16 659.4 23.59 2.099 0.9993 0.6738 2.93487 0.625 2290 967.3 2.63 4.201 2.002 325.7 11.83 0.3367 31.11 659.9 23.7 2.073 0.9993 0.6793 2.9388 0.6496 2288 966.7 2.537 4.202 2.005 321.9 11.86 0.333 30.09 660.4 23.8 2.048 0.9993 0.6848 2.92589 0.675 2285 966 2.447 4.203 2.008 318.2 11.89 0.3294 29.11 660.9 23.9 2.024 0.9993 0.6903 2.92190 0.7012 2283 965.3 2.362 4.204 2.011 314.5 11.93 0.3258 28.17 661.3 24 2 0.9994 0.6958 2.91791 0.7282 2280 964.7 2.279 4.206 2.014 311 11.96 0.3224 27.27 661.7 24.11 1.976 0.9994 0.7013 2.91392 0.7561 2278 964 2.201 4.207 2.017 307.5 12 0.319 26.4 662.2 24.21 1.953 0.9994 0.7067 2.90993 0.7849 2275 963.3 2.125 4.208 2.02 304 12.03 0.3156 25.56 662.6 24.32 1.931 0.9995 0.7122 2.90594 0.8147 2272 962.6 2.052 4.209 2.024 300.7 12.06 0.3124 24.76 663 24.42 1.909 0.9995 0.7176 2.90295 0.8453 2270 961.9 1.983 4.21 2.027 297.4 12.1 0.3092 23.99 663.3 24.53 1.888 0.9996 0.723 2.89896 0.8769 2267 961.2 1.916 4.212 2.03 294.2 12.13 0.306 23.24 663.7 24.64 1.867 0.9997 0.7285 2.89597 0.9094 2265 960.5 1.852 4.213 2.033 291 12.17 0.303 22.53 664.1 24.75 1.846 0.9997 0.7339 2.89198 0.943 2262 959.8 1.79 4.214 2.037 287.9 12.2 0.2999 21.84 664.4 24.86 1.826 0.9998 0.7393 2.88899 0.9776 2259 959.1 1.731 4.216 2.04 284.8 12.23 0.297 21.17 664.7 24.97 1.806 0.9999 0.7447 2.885100 1.013 2257 958.4 1.674 4.217 2.044 281.9 12.27 0.2941 20.53 665.1 25.08 1.787 1 0.7501 2.882


16

518 Heat Transfer Property Tables and Figures

Table HT-3 Thermophysical Properties of Gases at Atmospheric Pressure1

T � cp 107 � 106 k 103 � 106

(K) (kg/m3) (kJ/kg K) (N s/m2) (m2/s) (W/m K) (m2/s) Pr

Air

100 3.5562 1.032 71.1 2.00 9.34 2.54 0.786150 2.3364 1.012 103.4 4.426 13.8 5.84 0.758200 1.7458 1.007 132.5 7.590 18.1 10.3 0.737250 1.3947 1.006 159.6 11.44 22.3 15.9 0.720300 1.1614 1.007 184.6 15.89 26.3 22.5 0.707

350 0.9950 1.009 208.2 20.92 30.0 29.9 0.700400 0.8711 1.014 230.1 26.41 33.8 38.3 0.690450 0.7740 1.021 250.7 32.39 37.3 47.2 0.686500 0.6964 1.030 270.1 38.79 40.7 56.7 0.684550 0.6329 1.040 288.4 45.57 43.9 66.7 0.683

600 0.5804 1.051 305.8 52.69 46.9 76.9 0.685650 0.5356 1.063 322.5 60.21 49.7 87.3 0.690700 0.4975 1.075 338.8 68.10 52.4 98.0 0.695750 0.4643 1.087 354.6 76.37 54.9 109 0.702800 0.4354 1.099 369.8 84.93 57.3 120 0.709

850 0.4097 1.110 384.3 93.80 59.6 131 0.716900 0.3868 1.121 398.1 102.9 62.0 143 0.720950 0.3666 1.131 411.3 112.2 64.3 155 0.723

1000 0.3482 1.141 424.4 121.9 66.7 168 0.7261100 0.3166 1.159 449.0 141.8 71.5 195 0.728

Helium (He)

100 0.4871 5.193 96.3 19.8 73.0 28.9 0.686120 0.4060 5.193 107 26.4 81.9 38.8 0.679140 0.3481 5.193 118 33.9 90.7 50.2 0.676

180 0.2708 5.193 139 51.3 107.2 76.2 0.673220 0.2216 5.193 160 72.2 123.1 107 0.675260 0.1875 5.193 180 96.0 137 141 0.682300 0.1625 5.193 199 122 152 180 0.680

400 0.1219 5.193 243 199 187 295 0.675500 0.09754 5.193 283 290 220 434 0.668

700 0.06969 5.193 350 502 278 768 0.6541000 0.04879 5.193 446 914 354 1400 0.654

1For gases at atmospheric pressure, the ideal gas model (Sec. 4.5) applies, and � � p�RT.

###��

app.qxd 6/27/02 10:16 Page 518

17

Heat Transfer Property Tables and Figures 519

Table HT-4 Thermophysical Properties of Saturated LiquidsSaturated Liquids

T � cp 102 � 106 k 103 � 107 103

(K) (kg/m3) (kJ/kg K) (N s/m2) (m2/s) (W/m K) (m2/s) Pr (K�1)

Engine Oil (Unused)

273 899.1 1.796 385 4280 147 0.910 47,000 0.70280 895.3 1.827 217 2430 144 0.880 27,500 0.70290 890.0 1.868 99.9 1120 145 0.872 12,900 0.70300 884.1 1.909 48.6 550 145 0.859 6400 0.70310 877.9 1.951 25.3 288 145 0.847 3400 0.70320 871.8 1.993 14.1 161 143 0.823 1965 0.70330 865.8 2.035 8.36 96.6 141 0.800 1205 0.70340 859.9 2.076 5.31 61.7 139 0.779 793 0.70

350 853.9 2.118 3.56 41.7 138 0.763 546 0.70360 847.8 2.161 2.52 29.7 138 0.753 395 0.70370 841.8 2.206 1.86 22.0 137 0.738 300 0.70380 836.0 2.250 1.41 16.9 136 0.723 233 0.70390 830.6 2.294 1.10 13.3 135 0.709 187 0.70

400 825.1 2.337 0.874 10.6 134 0.695 152 0.70410 818.9 2.381 0.698 8.52 133 0.682 125 0.70420 812.1 2.427 0.564 6.94 133 0.675 103 0.70430 806.5 2.471 0.470 5.83 132 0.662 88 0.70

Ethylene Glycol [C2H4(OH)2]

273 1130.8 2.294 6.51 57.6 242 0.933 617 0.65280 1125.8 2.323 4.20 37.3 244 0.933 400 0.65290 1118.8 2.368 2.47 22.1 248 0.936 236 0.65

300 1114.4 2.415 1.57 14.1 252 0.939 151 0.65310 1103.7 2.460 1.07 9.65 255 0.939 103 0.65320 1096.2 2.505 0.757 6.91 258 0.940 73.5 0.65330 1089.5 2.549 0.561 5.15 260 0.936 55.0 0.65340 1083.8 2.592 0.431 3.98 261 0.929 42.8 0.65

350 1079.0 2.637 0.342 3.17 261 0.917 34.6 0.65360 1074.0 2.682 0.278 2.59 261 0.906 28.6 0.65370 1066.7 2.728 0.228 2.14 262 0.900 23.7 0.65373 1058.5 2.742 0.215 2.03 263 0.906 22.4 0.65

Glycerin [C3H5(OH)3]

273 1276.0 2.261 1060 8310 282 0.977 85,000 0.47280 1271.9 2.298 534 4200 284 0.972 43,200 0.47290 1265.8 2.367 185 1460 286 0.955 15,300 0.48300 1259.9 2.427 79.9 634 286 0.935 6780 0.48310 1253.9 2.490 35.2 281 286 0.916 3060 0.49320 1247.2 2.564 21.0 168 287 0.897 1870 0.50

###��

app.qxd 6/27/02 10:16 Page 519

18

520 Heat Transfer Property Tables and Figures

Table HT-5 Thermophysical Properties of Saturated Water1

Specific Thermal ExpansionHeat Viscosity Conductivity Prandtl Coeffi-

Tempera- (kJ/kg K) (N s/m2) (W/m K) Number cient,ture, T f 106

(K) cp,f cp,g f 106 g 106 kf 103 kg 103 Prf Prg (K�1)

273.15 4.217 1.854 1750 8.02 569 18.2 12.99 0.815 �68.05275 4.211 1.855 1652 8.09 574 18.3 12.22 0.817 �32.74280 4.198 1.858 1422 8.29 582 18.6 10.26 0.825 46.04285 4.189 1.861 1225 8.49 590 18.9 8.81 0.833 114.1290 4.184 1.864 1080 8.69 598 19.3 7.56 0.841 174.0

295 4.181 1.868 959 8.89 606 19.5 6.62 0.849 227.5300 4.179 1.872 855 9.09 613 19.6 5.83 0.857 276.1305 4.178 1.877 769 9.29 620 20.1 5.20 0.865 320.6310 4.178 1.882 695 9.49 628 20.4 4.62 0.873 361.9315 4.179 1.888 631 9.69 634 20.7 4.16 0.883 400.4

320 4.180 1.895 577 9.89 640 21.0 3.77 0.894 436.7325 4.182 1.903 528 10.09 645 21.3 3.42 0.901 471.2330 4.184 1.911 489 10.29 650 21.7 3.15 0.908 504.0335 4.186 1.920 453 10.49 656 22.0 2.88 0.916 535.5340 4.188 1.930 420 10.69 660 22.3 2.66 0.925 566.0

345 4.191 1.941 389 10.89 665 22.6 2.45 0.933 595.4350 4.195 1.954 365 11.09 668 23.0 2.29 0.942 624.2355 4.199 1.968 343 11.29 671 23.3 2.14 0.951 652.3360 4.203 1.983 324 11.49 674 23.7 2.02 0.960 697.9365 4.209 1.999 306 11.69 677 24.1 1.91 0.969 707.1

370 4.214 2.017 289 11.89 679 24.5 1.80 0.978 728.7373.15 4.217 2.029 279 12.02 680 24.8 1.76 0.984 750.1

1See Table T-2 for specific volume, vf and vg.

��

###

app.qxd 6/27/02 10:16 Page 520

19

Documents

Tablas Conveccion v20140112