A thin metallic wire of thermal conductivity K, diameter D, and length 2L is annealed by passing an electriccal current through the wire to induce a uniform volumetric heat generation ËqË. The ambient air around the wire is at a temperature T_infinity, while the ends of the wire at x = ±L are also maintained at T_infinity. Heat transfer from the wire to the air is characterized by the convection coefficient h. Obtain expressions for the following: a. The steady-state temperature distribution T(x) along the wire
b. The maximum wire temperature and
c. The average wire temperature