Q$1-$a$)$ From the general form solve the energy equation with the following assumptions:

$1-$ Rectangular coordinates

$2-$ Incompressible Solid Media

$3-$ No heat Generation

$4-$ Steady state condition

$5-$ Two$-$dimensional conduction equation $($Laplace form$)$

Find the temperature profile for the following boundary conditions:

$($a$)$ x $=0=0$

$($b$)$ x $=$ W $=$ T$2$ sin $($y$/$H$)$

$($c$)$ y $=0=0$

$($d$)$ y $=$ H $=0$

Given that H $=1\mathrm{.}5$ W$,$

Determine the temperature at the midpoint of the system. Let

T$2=200$C and T$1=100$C$,$ then obtain an equation for the heat flux rate $($q$)$