     # Overall - Finned Tube

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SUSTAINABLE ENERGY UTILISATION SEU-LAB4

DETERMINING HEAT TRANSFER COEFFICIENTS FOR A FINNED-TUBE HEAT EXCHANGER WITH FORCED CONVECTIONBefore the lab lesson, you should be able to answer the following questions: 1. What is meant by U and f in eq.3? 2. In eqn.4, which is the main contribution to the heat transfer coefficient? Is it from convection, diffusion or radiation? On what do you base your answer? 3. Is the length used to calculate the average and the inner tube areas, Am and A1, in eqn. 3, the same as the one used to calculate the boiling number in eq. 10? Explain. 4. Is the refrigerant flow in the condenser the same as in the finned coil evaporator? Explain. 5. How is the fin efficiency determined? It is strongly recommended that you make necessary calculations and draw the line to determine fin efficiency before you come to the lab lesson. 6. How is the heat transfer coefficient f calculated according to 8.55 in 1?

Granryd et al., 2008, Refrigerating Engineering, Dept of Energy Technology, KTH, Stockholm, Sweden

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SUSTAINABLE ENERGY UTILISATION LAB LESSON NO. 4

DETERMINING HEAT TRANSFER COEFFICIENTS FOR A FINNED-TUBE HEAT EXCHANGER WITH FORCED CONVECTIONOBJECTIVE: The objective of this lab lesson is to determine the overall heat transfer coefficient and the heat transfer coefficient related to the fin surface of a heat exchanger placed in an air duct with forced convection and cooled on the inside by boiling refrigerant. The theory below is mainly based on Chapter 8 in the textbook Refrigerating Engineering by Granryd et al., 2002 . Bring the book to the lab lesson. THEORY: The following equations describe the heat transfer for a finned-tube heat exchanger (compare with figure 2):

Q = U. A. Q = 1. A1. 1 Q = (t/ t). Am. t Q = (2. A2 + f. . Af). 2. . .

.

= 1= t=

Q /(U. A) Q /(1. A1) Q .t /(t. Am) Q /(2. A2 +f . . Af). . .

.

(1a) (1b) (1c) (1d)

2=

The overall heat transfer is given by eq.1a, while eqns. 1b-1d give the heat transfer on the inside tube, through the tube wall and on the finned outside. The temperature difference over the heat exchanger can be expressed as: = 1+ t+ 2

(2)

The heat transfer for a finned-tube heat exchanger can then, if we assume that 2=f, be expressed as:1 = U. A

1 + f .( A2 + . Af )

.At t

+

m

1 1. A1

(3)

The surfaces are as follows: Af is the finned surface. A2 is the free outer tube area between the fins. Am and A1 are the average and inner tube areas. Finally, A = (A2+ Af) is the overall surface area (for values, see page 4). The overall heat transfer coefficient 2

U is referred to A. The other heat transfer coefficients 1, 2 and f are referred to A1, A2 and Af. Further, is the thermal conductivity of the tube; t = (d2-d1)/2 is the tube wall thickness and is the fin efficiency (compare with figure 2). The heat transfer coefficient between the air and the outer surface of the finned-tube heat exchanger, Af, refer to the total heat transfer coefficient, f, which is the sum of heat transfer coefficients from convection (c), diffusion (d), and radiation (r) where, f = c +d + r (4)

The contribution from radiation in this forced convection finned-tube heat exchanger is very small. It can be neglected since the active area for radiation is only the circumferential area of the heat exchanger. A contribution from diffusion is obtained when dew or frost appears on the tube or finned-tube surface. This occurs when the surface temperature is lower than the dew point of the surrounding air (see also 8.50 in ). As we have a closed air duct and add no water, we do not expect much contribution from diffusion in steady state condition. What temperature difference should be used when calculating the overall heat transfer coefficient (U)? The logarithmic mean temperature difference ( m) is commonly used in parallel and counter-flow heat exchangers and is defined as: m = ( 1 - 2)/ ln( 1/ 2)

(5)

Where 1 and 2 are temperature differences between the fluids at he two ends of the heat exchanger. The overall heat transfer coefficient of finned-tube heat exchanger with forced convection is also usually based on the logarithmic mean temperature difference ( m). The values for U and f, calculated from test results using the logarithmic mean temperature difference as a base, represent surface mean values of the local values along the heat exchanger. Some equations and data for heat transfer coefficients of finned-tube heat exchanger with forced convection can be found in 8.23, 8.54 55 in .

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CALCULATIONS AND REPRESENTATION: To calculate the heat transfer coefficient on the airside (f) from eq.3, we first need to know the overall heat transfer coefficient (U), the heat transfer coefficient on the inside (1), and the fin efficiency (). For the representation, we also need to know the front velocity of the air into the fin battery (Wfr). Calculation of the overall heat transfer coefficient (U): The overall heat transfer coefficient (U) is determined in the following way: Through an energy balance, over the condenser we determine the condenser capacity ( Q 1), the& circulated refrigerant flow ( mR , I ) in the condenser and then finally the refrigerating.

capacity of the evaporator ( Q 2). To get an even temperature in the evaporator, we use the system with flooded finned-coil evaporator with five parallel tubes and a low4

.

pressure receiver, which gives incomplete evaporation. We get he following equations (see also figure 3):& Q 1= ( m cp)wtW.

(6). .

& mR , I =.

Q 1/h1 = Q 1/(h1k-hs) = Q 1/(h14-h11)

.

(7)

& Q 2 = m R,E . (h16-h15)

& & & Q 2= mR ,I . h2 = mR ,I . (h2k-hs) = mR ,I . (h13-h11)

.

(8) (9)

& U= Q2 /(A. m)

The logarithmic mean temperature difference ( m) is determined from eq.5. Assuming incomplete evaporation (x

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