Page 147 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 127

4.4 Consider the rectangular fin given in Problem 4.3. One of the problems
of practical interest is the determination of the optimum values of B and L to
maximize the heat transfer rate from the fin for a fixed volume, V, and W. Show
that the optimum dimensions are given as

4.5 Consider the rectangular fin given in Problem 4.3. If a laminar flow region
exists over the plate, show that the optimum value of W for the maximum heat
transfer rate from the fin for a fixed volume, V, and thickness, B, is given by

where kf is the thermal conductivity of the fluid.

4.6 A thin aluminum fin (IC = 205 W/ m. K) of length L = 20cm has two ends
attached to two parallel walls which have temperatures To = 100 "C and TL = 90 "C
as shown in the figure below. The fin loses heat by convection to the ambient air
at T, = 30°C with an average heat transfer coefficient of (h) = 120W/m2.K
through the top and bottom surfaces (heat loss from the edges may be considered
negligible).

One of your friends assumes that there is no internal generation of energy within
the fin and determines the steady-state temperature distribution within the fin as

T-T, = eNx - 20 sinh Nz
T* - Tm