Consider a rod of diameter D, thermal conductivity k, and

Chapter , Problem 3.119

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Consider a rod of diameter D, thermal conductivity k, and length 2L that is perfectly insulated over one portion of its length, L x 0, and experiences convection with a fluid (T, h) over the other portion, 0 x L. One end is maintained at T1, while the other is separated from a heat sink at T3 by an interfacial thermal contact resistance . T = 20C h = 500 W/m2K Insulation L 0 +L x T1 T2 T3 Rod R"t,c = 4 104 m2K/W D = 5 mm L = 50 mm k = 100 W/mK R (a) Sketch the temperature distribution on T x coordinates and identify its key features. Assume that T1 T3 T. (b) Derive an expression for the midpoint temperature T2 in terms of the thermal and geometric parameters of the system. (c) For T1 200 C, T3 100 C, and the conditions provided in the schematic, calculate T2 and plot the temperature distribution. Describe key features of the distribution and compare it to your sketch of part (a).