A metal rod of length 2L, diameter D, and thermal conductivity k is inserted into a perfectly insulating wall, exposing one-half of its length to an air stream that is of temperature T and provides a convection co- efficient h at the surface of the rod. An electro- magnetic field induces volumetric energy generation at a uniform rate q within the embedded portion of the rod. 100 WWm2K Rod, D, k L 50 mm D 5 mm k 25 WNm. K 1 x 106 wm3 (a) Derive an expression for the steady-state tempera- ture Tb at the base of the exposed half of the rod. The exposed region may be approximated as a very long fin. (b) Derive an expression for the steady-state tempera- ture Ta at the end of the embedded half of the rod. (c) Using numerical values provided in the schematic, 3 plot the temperature distribution in the rod and de- scribe key features of the distribution. Does the rod behave as a very long fin?