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