Solve the folloiwng problem:
Q: 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="" (t8,="" 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="">
(a) Sketch the temperature distribution on T - x coordinates and identify its key features. Assume that T1 > T3 > T8.
(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).
