Question $2(35$ points$)$ : Consider a plane composite wall that is composed of two materials of thermal conductivities $k_A=0\mathrm{.}1\frac{W}{m}.K$ and $k_B=0\mathrm{.}04\frac{W}{m}.K$ and thicknesses $L_A=10mm$ and $L_B=20mm.$ The contact resistance at the interface between the two materials is known to be $0\mathrm{.}30m^2.$K$/$W$.$ Material A adjoins a fluid at $200C$ for which $h=10\frac{W}{m^2}.K$ and material B adjoins a fluid at $40C$ for which $h=20\frac{W}{m^2}.K$

a$.$ What is the rate of heat transfer through a wall that is $2$ m high by $2\mathrm{.}5$ m wide?

b$.$ Sketch the temperature distribition.