Two large aluminium $($k $=240$ W$/$mK$),$ each $2$ cm thick, with $10$ mm surface roughness are placed in contact at $105$ N$/$m$2$ pressure $($Fig$.)$ with the outside surface temperatures of $390$C and $406$C$.$ The thermal contact resistance is $2\mathrm{.}75104$ m$2$K$/$W$.$ To find: $($i$)$ The heat flux, $($ii$)$ the temperature drop due to contact resistance, and $($iii$)$ the contact temperatures.