A $4-$mm$-$thick plate $($k$=10$ W$/$mK$)$ which can be assumed to be infinitely$-$long has a volume $4$x$10-5$ m$^3.$ The left and right sides $($surfaces$)$ of the plate are maintained at constant $10$C and $16$C temperatures, respectively. When an electric current is passed through the plate, $2$ kW heat rate is obtained within the plate. Assuming that radiation heat losses from the surfaces could be neglected $($a$)$ Develop the heat conduction equation and the appropriate boundary conditions for the given problem, $($b$)$ solve the heat conduction equation and determine the maximum temperature and its location in the plate.