Question

A thin rod of radius r, length 3L, and thermal conductivity, k is divided into three regions, each of length L. Regions 1 and 2 are surrounded by a perfectly insulating wall, while Region 3 protrudes into ambient air well-insulated. Uniform heat generation, q, occus only in Region 1 Sketch the temperature prolile along the entire length of the rod. For each region, specify why the temperature prolile has the shape you have decided on. Also, specify the nature of the slopes at the start and at the end of the profile, and describe why it is so. Label all regions where temperature changes oceur, and label the overall nature of the profile at each of regions 1,2 and 3. Finally, do not forget to label the axes Derive an expression for the temperature, To where the insulation ends and the protrusion starts, in terms of the variables of the problem, .e., temperature To should solely be obtained as a function of Prove that the efficiency of a fin with an adiabatic tip (Case B in your oquation sheet for fins) will beeome a losing proposition as the length of the fin gets infinitely long insulation o 2r Air h, T region 1 region 2 region 3

Answer 1