2.1 Text Problem 2.16 in 7th Ed. Not in 8th Ed. Steady-state, one-dimensional conduction occurs in a rod of constant thermal conductivity k and variable cross- sectional area A,(x) = ACC, where A, and a are con- stants. The lateral surface of the rod is well insulated. A,(x) = A CAR 96) (a) Write an expression for the conduction heat rate, 9.(x). Use this expression to determine the tempera- ture distribution 7(x) and qualitatively sketch the distribution for T(0) > T(L). (b) Now consider conditions for which thermal energy is generated in the rod at a volumetric rate 9 = , exp(-ax), where g, is a constant. Obtain an expression for 4x(x) when the left face (x = 0) is well insulated. Hint: Start with the following expression: at pCp at k a A(x) @x (A(x) at , + You should get the following: akA,(T. T.) 9x = 1 - exp(-al) and qx(x) = 4o Ax