PROB $2$: $10$ PTS

The solid rod in the figure is $\backslash (2$ L $\backslash )$ long, and discretized to two elements of equal length. The rod is solid round with radius $\backslash ($ r $\backslash ).$ The rod generates uniform heat internally at the rate of $\backslash ($ Q $\backslash )$ throughout the first element only. The left edge is maintained at a known temperature of $\backslash ($ T$\_\{$L$\}\backslash ).$ The perimeter of the rod is insulated on the left half of the perimeter. The right half and the tip are convective with a convection coefficient of $\backslash ($ h $\backslash ),$ and surrounding temperature of $\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$mathbf$\{$e$\}\}\backslash ).$ The thermal conductivity is $\backslash (\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$x$\}\}\backslash ).$

A$-$ Develop the total combined conduction and convection matrix.

$\backslash ($ B $\backslash )-$ Develop the total global nodal load vector.

C$-$How would the load vector change if the left boundary had specified heat flux?

PLEASE ANSWER ASAP