# Granges Metallverken Co. of Sweden has developed a compact fin geometry for a crossflow plate-fin…

Granges Metallverken Co. of Sweden has developed a compact

fin geometry for a crossflow plate-fin exchanger as a car heater. Two layers of

air centers (fins), as shown in Fig. P4.8, made from copper (thermal

conductivity 380 W/m K) are sandwiched between the water tubes. The fins and

the splitter plate are 0.0254 mm thick. The distance between the water tube and

the splitter plate is 3.16 mm (1 = 3:175 mm 0:0127 mm). The fin density is 2

fins/mm, so that 2 = 0:25 mm. Consider the heat transfer coefficient on the

air side as 120 W/m2 K. Determine f and o for this fin geometry

using the f

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Granges Metallverken Co. of Sweden has developed a compact

fin geometry for a crossflow plate-fin exchanger as a car heater. Two layers of

air centers (fins), as shown in Fig. P4.8, made from copper (thermal

conductivity 380 W/m K) are sandwiched between the water tubes. The fins and

the splitter plate are 0.0254 mm thick. The distance between the water tube and

the splitter plate is 3.16 mm (1 = 3:175 mm 0:0127 mm). The fin density is 2

fins/mm, so that 2 = 0:25 mm. Consider the heat transfer coefficient on the

air side as 120 W/m2 K. Determine f and o for this fin geometry

using the f formula of Problem 4.8. Consider as an approximation only one fin

of the full height 6.40 (3:175 + 3:175 + 2 0:0254) mm and the same fin density.

What is the approximate f? How good is this approximation?

Problem 4.8

A heat exchanger design is generally considered good if ohA

on hot and cold fluid sides are about the same. Because of very low values of

heat transfer coefficients with gas flows compared to those for liquid flows, a

considerable amount of surface area is needed on the gas side. It can be

achieved by increasing either the fin density or the fin height, or both. High

fin height may be structurally very weak. An alternative way is to put two

layers of fins in between liquid tubes as shown in the Fig. P4.8a. Figure P4.8b

represents a general unit fin section. Show that the fin efficiency for this

fin is

Perform the analysis using the solutions presented in the

text for thin fins with (a) an adiabatic fin tip, and (b) finite heat transfer

at the fin tip without solving any

differential equations. Make an appropriate energy balance

at the T point. Mention explicitly any additional assumptions that are needed

for your analysis.

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