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Lecture No. 25Condensation and Boiling Heat Transfer
Condensation and boiling are convection processes associated with phase change of fluid. They are classified as convection because there is a fluid motion near a solid surface.
These processes occur at solid-fluid interfaces and latent heat transfer effects are involved, without a change in fluid temperature.
Heat transfer rates and coefficients are much higher than those encountered in other convection problems.
Example: Conventional home air conditioners, refrigerators and power plants.
2
Condensation Heat Transfer
Condensation
Classification of condensation
a. Dropwise condensation
b. Filmwise condensation
Heat transfer rates in drop wise condensation are 10 times higher than those encountered in filmwise condensation
3
Film Condensation on a vertical flat plate
Film condensation on a vertical flat plate (Nusselt) Note:
δ
TT
dy
dT ws
Tw Ts
A linear temperature profile exists between the condensing vapor and the surface.
4
Film Condensation on a vertical flat plate
Assumptions:
1. The fluid properties are constant
2. No thermal resistance at the liquid-vapour interface.
3. No Momentum effects
4. No shear stress at the liquid-vapour interface.
5. A linear temperature profile exists between the condensing vapor
and the surface.
6. No Enthalpy change
δ
TT
dy
dT ws
5
Film Condensation on a vertical flat plate
1.Forces acting on an element of thickness dx
Gravity force
Viscous force
Buoyancy force
6
Film Condensation on a vertical flat plate
dxy)(δρg
The weight of the fluid element of thickness dx between y and per unit depth
The viscous shear force at y
Buoyancy force = dxy)(δgρv
vρ
= density of the Liquid u = velocity of the liquid film
= density of vapourm = viscosity of the fluid g = acceleration due to gravity.
Gravity force
7
Film Condensation on a vertical flat plate
dxy)(δgρdxdy
duμdxy)(δρg v
dy
duμg)ρ(ρy)(δ v
Under steady-state conditions, a force balance on the element of the fluid gives
On simplification
8
Film Condensation on a vertical flat plate
0yat0u
2v
y y2
1δy
μ
g)ρ(ρu
The boundary condition is
Integrating and using the boundary condition we obtain
9
Film Condensation on a vertical flat plate
The mass flow rate of the condensate per unit depth of the film at any position x is given by
3μ
gδ)ρ(ρρdyy
2
1δy
μ
g)ρ(ρρm
3v2v
δ
0
As the liquid film flows from x to x + dx, the film thickness changes from to + d as a result of additional condensation.
Note:
10
Film Condensation on a vertical flat plate
The change in condensate flow rate between x and x + dx is given by
dδμ
gδ)ρ(ρρdd
dx
dδ
3μ
gδ)ρρ(ρ
dδ
ddx
3μ
gδ)ρρ(ρ
dx
d 3v
3v
3v
This change in condensate flow rate is due to the energy transferred from the condensing vapor to the wall.
11
Film Condensation on a vertical flat plate
That is, the heat transferred from the condensing vapor to the wall is equal to the increased mass flow rate times the latent heat of vaporization.
Therefore,
δ
TTkdxh
μ
dδgδ)ρ(ρρ wsfg
2v
fgh = latent heat of vaporization k = thermal conductivity of the condensate.
12
Film Condensation on a vertical flat plate
0xat0δ
1/4
υfg
wsx )ρρ(ρgh
)T(Tk xμ 4δ
Integrating by using the boundary condition
we get
13
Film Condensation on a vertical flat plate
δ
TTkdx)T(Tdxh ws
swx
xx δ
kh
The heat transfer across the condensate layer is by conduction. We can express the local heat transfer coefficient ‘h x ‘ as
or
14
Film Condensation on a vertical flat plate
1/4
ws
3fgυ
x )T(Tμ x 4
kgh)ρ(ρρh
Heat transfer coefficient for film condensation decreases with increasing distance from the top as the film becomes thicker and thicker.
The thickness of the condensate film is similar to a boundary layer on a flat plate
An increase in the temperature difference (Ts - Tw) causes a decrease in heat transfer coefficient
Substituting the value of X
16
Film Condensation on a vertical flat plate
The local Nusselt number ‘Nux ‘ is then given
by
1/4
ws
3fgυ
x )T(Tμ x 4
kh g)ρ(ρρ
k
X
k
hxNu
The local Nusselt number for film condensation decreases with increasing distance from the top as the film becomes thicker and thicker.
17
Film Condensation on a vertical flat plate
xx0h
3
4dxh
1h
The average value of the heat transfer coefficient is obtained by integrating the local value ‘hx” over the plate and dividing by the length
18
Film Condensation on a vertical flat plate
1/4
wsf
3ffgυ
)T(Tμ
kgh)ρ(ρρ0.943h
Where the subscript f denotes that the properties should be evaluated at
the film temperature ‘Tf ‘ given by
2
TTT ws
f
19
Film Condensation on a vertical flat plate
Rohsenow:
performed a refined analysis of this problem and obtained results which are in better agreement with the experimental data if Pr > 0.5 and c(Ts - Tw)/hfg 1.0.
Similar results can also be obtained by replacing hfg by , where is defined as
= hfg + 0.68c(Ts-Tw)
c - is the specific heat of the condensate
20
Film Condensation on Tubes and Spheres
The average heat transfer coefficient for laminar film condensation on the outside of a sphere or a horizontal tube can be evaluated from the relation
1/4
wsf
3ffgυ
)T(Tdμ
kgh)ρ(ρρAh
A = 0.815 for a sphereA = 0.725 for a tubed = diameter.
Where
21
Film Condensation on Tube Banks.
1/4
wsf
3ffgυ
)T(TdNμ
kgh)ρ(ρρAh
A = 0.725 for a tubed = diameter.
W here
If condensation occurs on a horizontal tube bank with N tubes so arranged that the condensate from one tube flows directly onto the tube below, the average heat transfer coefficient for the system can be obtained by replacing d with N d
22
Film Condensation on Inclined surfacese
If a plate or a cylinder is inclined at an angle with the horizontal, all the above equations be used by replacing g with its component parallel to the heat transfer surface. That is, by replacing g, with g sin .
Note:
23
Film Condensation on a vertical flat plate
A fluid flowing over a surface undergoes a transition from laminar to turbulent flow. Therefore, the motion of the condensate becomes turbulent when its Reynolds number exceeds a critical value of about 1800.
If the plate on which condensation occurs is sufficiently large, or there is a sufficient amount of condensate flow, turbulence may appear in the condensate film. The Reynolds number of the condensate film is defined as
ff
Hf Pμ
m
Pμ
uρA 4
μf
uρ dRe
8001Pμ
uρA 4
μf
uρ dRe
f
Hc
Hd
m
ρAu
Where,
= hydraulic diameter
A = flow cross-sectional area
P = wetted perimeter
V = average velocity of flow
= mass flow of the condensate.
24
Film Condensation on a vertical flat plate
Where
is the condensate flow rate for unit width of the plate
Film Reynolds number
The wetted perimeter P for a vertical tube is equal to d, and for a vertical plate of unit depth, P = 1. The Reynolds number is sometimes expressed in terms of the mass flow per unit width of plate as;
25
Film Condensation on a vertical flat plate
fgws hm)TT(Ahq
The mass flow rate, , can be related to the heat transfer coefficient by
or
fg
ws
fg h
)TT(Ah
h
qm
and
ffg
ws
ff Pμh
)TA(Th4
Pμ
m4Re
ffg
wsf Ph
)TT(h4Re
For a plate of length L and width w, the flow cross-sectional area , A =Lw and the wettedPerimeter P=w, so for plate
26
Film Condensation on a vertical flat plate
For laminar flow of condensate film, the experimental results are found to be in good agreement with the results predicted from these equations. However,
In practice, for turbulent flow it has been found that the theoretical results are approximately 20% lower than the experimental values if ripples develop in the film. In the light of this observation, McAdams suggests the following expression for predicting the average heat transfer coefficient for film condensation on plates, if the flow is turbulent:
4/1
ws
3fg
)TT(
kgh)(13.1h
27
Film Condensation inside Horizontal Tubes
Condensation inside tubes is of considerable importance in refrigeration and air-conditioning systems where the refrigerant flows through the tubes.
The flow rate of condensable vapor through the tubes strongly influences the heat transfer coefficient, which in turn influences the rate of accumulation of liquid in the tubes.
For condensation of refrigerants at low vapor velocities inside horizontal tubes:
4/1
ws
3fg
)TT(d
kgh)(555.0h
This equation is valid for low vapor Reynolds number Rev which should be evaluated at the inlet conditions to the tube.
000,35Vd
Rev
28
Condensation of Superheated Vapors
)TT(Ahq ws
sT
The equations developed earlier are strictly applicable to the condensation of saturated vapors. However, the same equations can also be used with reasonable accuracy for condensation of superheated vapors. The heat transfer rate from a superheated vapor to a wall at Tw is given by
- is the saturation temperature corresponding to the pressure of the super-heated vapor.
where
29
Drop-wise Condensation
If the surface on which condensation takes place is coated with an agent such that the condensate does not wet the surface, the vapor condenses in drops rather than as a continuous film. In drop-wise. condensation, a large part of the surface is not covered by a liquid film which acts as an additional resistance for heat transfer. Therefore, in drop-wise condensation the heat transfer coefficients can be as high as 4 to 8 times that of film condensation.
Note:
30
Effect of Superheated vapour and of Non-Condensable gases
Steam condensation in the presence of small amount of air
31
Boiling Heat Transfer
Boiling:
When heat is added to a liquid from submerged solid surface which is at a temperature higher than saturation temperature of the liquid, The part of the liquid go through phase change. This change of phase is called boiling
33
Classification of Boiling
Pool boiling:
When there is no bulk motion of the fluid. Any motion is due to natural
convection currents or movement of vapour bubble formed due to
boiling.
Example: Boiling of liquid in a vessel placed on heater or
stove.
Flow boiling: The liquid is forced to move by an external agency like a pump
Example: Steam generators
35
Classification of Boiling
Regimes/ or Modes of Pool Boling
1. Convective boiling
2. Nucleate boiling
3. Film boiling
36
Saturated pool boiling curve
Region or mode depending on (Tw
–Ts)
Different regimes of boiling heat transfer
The maximum heat flux is called critical heat flux and occurs at critical excess temperature.
37
Region or mode depending on (Tw –Ts)
1. Natural convection region (Tw –Ts) 10 CHeat flux is proportional to (Tw - Ts) n = 1 to1.3
2. Nucleate boiling region (Tw –Ts) up to 20 or 30 CHeat flux is proportional to (Tw - Ts) n = 3
3. Film boiling region
38
Boiling Heat Transfer
Using experimental data, Rohsehow, developed the correlation
33.0
fgsfn
fg
x
)(gh
qC
Prh
Tc
Nucleate Pool Boiling
c
q
where
= specific heat of saturated liquid
= heat flux for
nucleate boiling
= viscosity of
liquid
= surface tension of the
liquid to vapor interface
Csf = empirical constant
which depends on the nature of the
heating surface-fluid combination
n = 1.0 for water and
1.7 for other fluids
Pr = Prandtl number of the
saturated liquid.
Saturation temperature (oC)
20 40 60 80 100 150 200
Surface tension ( 103)
72.9 69.5 66.1 62.7 58.9 48.7 37.8
Vapor-liquid surface tension for water
It correlates the data for all types of nucleate boiling processes, including pool boiling of saturated liquids and , sub-cooled liquids and also for boiling of sub-cooled and saturated liquids flowing by natural or forced convection in tubes.
39
Boiling Heat Transfer
Zuber, has developed the following expression for the Critical (peak) heat flux q” in nucleate boiling:
4/1fg
2/1 )](g[h24
q
This relation is in good agreement with experimental data. It can be observed from the above equation that the peak heat flux is larger for fluids with larger latent heats of vaporization.
Where - is the vapor-liquid surface tension.
40
Flow Boiling
Flow boiling:Often referred to as forced convection boiling or as two-phase flow with heat transfer
42
Question
A vertical plate of length 1m and width 0.50 m at 92C is exposed to saturated steam at 100 C. Calculate the average heat transfer coefficient and the mass of steam condensed in one second.
43
Question
A tube of 2 m length and 25 mm OD is to be used to condense saturated steam at 100C while the tube surface is maintained at 92C. Estimate the average het transfer coefficient and the rate of condensation of steam if he tube is kept horizontal. The steam condenses on the outside of the tube.