Question $4$:

Two large steel plates, one at a temperature of $\backslash (\backslash$mathbf$\{150\}\{\}^\{\backslash$circ$\}\backslash$boldsymbol$\{$C$\}\backslash )$ and the other at $\backslash (100^\{\backslash$circ$\}\backslash$boldsymbol$\{$C$\}\backslash ),$ are separated by a copper rod with a thermal conductivity of $\backslash (\backslash$boldsymbol$\{$k$\}=\backslash$mathbf$\{390\}\backslash$mathbf$\{$W$\}/\backslash$mathbf$\{$m$\}.\backslash$boldsymbol$\{$K$\}\backslash ).$ The rod is $\backslash (\backslash$mathbf$\{300\}\backslash$mathbf$\{$~ m m$\}\backslash )$ long and has a diameter of $\backslash (\backslash$mathbf$\{25$ ~ m m$\}\backslash ).$ It is welded to each plate and insulated on its lateral surface, allowing heat to flow only axially. An electric current flows through the rod, generating heat at a rate of $\backslash (\backslash$mathbf$\{150\}\backslash$boldsymbol$\{$W$\}\backslash ).$ The objective is to find the maximum temperature in the rod and the heat flux at its ends.