A component with thickness L and thermal conductivity k has one side adiabatic and the other exposed to ambient temperature Ti with a heat transfer h$.$ It also generates internal heat q$.$

$-$ Determine T$($x$),$ the temperature distribution across the wall using $1-$D heat conduction. This involves q$,$ L$,$ k$,$ h$,$ and Ti

$-$ Demonstrate how maximum temperature is q$*$L$^2/2$k $+$ q$*$L$/$k $+$ Ti

$-$ Sketch the temperature profile T$($x$)$ along the wall highlighting the point of the maximum temperature