Consider the $2-$D rectangular region $0xa,0yb$ which is initially at

temperature $F(x,y).$ For $t>0,$ internal energy is generated at a constant

rate $g_0(\frac{W}{m^3})$ and the region is subjected to the following boundary

conditions: the boundaries at $x=0$ is maintained at a prescribed

temperature $f(y),$ the boundary at $x=a$ is subjected to a prescribed heat flux

$q^{\text{'}\text{'}}(y)$ out of the solid, the boundary at $y=0$ are maintained at constant

temperature $T_l,$ and the boundary at $y=b$ dissipates heat by convection into

a medium with fluid temperature $T_{}$ and with a heat transfer coefficient $h.$

Formulate the problem using superposition for solution of $T(x,y,t),$ such

that each sub$-$problem is in a solvable form. Formulation includes the

simplified pde or ode and the corresponding boundary and$/$or initial

conditions. Do not shift the temperature scale for any problems, and do not

actual solve any of the sub$-$problems, only formulate.