A cylindrical metal rod (length 2L, radius R, thermal conductivity k) is embedded in a well-insulated wall such that half the rod (along the length) is within the insulated wall and the other half is exposed to a uid stream at a temperature of Tinf . The heat transfer coecient between the uid and the rod is h. The portion of the rod embedded in the insulating wall is exposed to an electromagnetic eld, resulting in a uniform volumetric heat generation rate of q''' in only the embedded half of the rod. You can assume that the
temperature varies only along the length of the rod.
1. Determine an expression for the steady{state temperature Tb at the mid-point of the rod in terms of q''', k, L, R, Tinf . You can treat the portion of the rod exposed to the fuid as a n with adiabatic tip.
2. Determine the highest temperature in the rod.