B$2.[25$ marks overall$]$ A square composite wall $\backslash ((20\backslash$mathrm$\{$~cm$\}\backslash )$ by $20$ cm$\backslash ()\backslash )$ is insulated on five sides as shown in Fig B$2($note that the front and back are also insulated$).$ A very thin square heater $($negligible thickness$)$ is sandwiched between the copper and alumina sections. The heater delivers $500$ W of heat uniformly across its cross$-$section. Both convection and radiation heat transfer occurs on the open face of the wall. The surface temperature of the open wall is $\backslash (55^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ at steady$-$state. Use the information given on the diagram to determine:

a$)[10$ Marks$]$ The temperature of the thin heater $\backslash (\backslash$left$($T$\_\{2\}\backslash$right$)\backslash ).$

b$)[5$ Marks$]$ The temperature at the copper$-$insulation interface $(\backslash ($ T$\_\{1\}\backslash )).$

c$)[10$ Marks$]$ The convective heat transfer coefficient, $\backslash ($ h $\backslash )$ : Fig. B$2$: Composite wall