In Chapter 3 we assumed that, whenever fins are attached to a base material, the base temperature is unchanged. What in fact happens is that, if the temperature of the base material exceeds the fluid temperature, attachment of a fin depresses the junction temperature below the original temperature of the base, and heat flow from the base material to the fin is two-dimensional.

Consider conditions for which a long aluminum pin fin of diameter D = 5 mm is attached to a base material whose temperature far from the Junction is maintained at Tb = 100°C. Fin convection conditions correspond to h = 50 W/m2 ∙ K and T∞ = 25°C.

(a) What are the fin heat rate and junction temperature when the base material is (i) aluminum (k = 240 W/m. K) and (ii) stainless steel (k = 15 W/m ∙ K)?

(b) Repeat the foregoing calculations if a thermal contact resistance of Rt,j = 3 x 10-5 m2 . K/W is associated with the method of joining the pin fin to the base material.

(c) Considering the thermal contact resistance, plot the heat rate as a function of the convection coefficient over the range 10

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h, Tri D = 0.25 m h, To12 w = 1 m