Consider the base plate of an 800-w household iron with a thickness of l 5 0.6 cm, base area of a 5 160 cm2, and thermal conductivity of k 5 60 w/m·k. the inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. when steady operating conditions are reached, the outer surface temperature of the plate is measured to be 112°c.

a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate,
b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and
c) evaluate the inner surface temperature.

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?