Consider a rod of diameter D , thermal conductivity k , and length 2L that is perfectly
Question:
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 R"t.c
(a) Sketch the temperature distribution on T-x coordinates and identify its key features. Assume that T1>T3>Tx.
(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).
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