$5-106$ Consider transient heat conduction in a plane wall whose left surface $($node $0)$ is maintained at $80C$ while the right surface $($node

$6)$ is subjected to a solar heat flux of $600\frac{W}{m^2}.$ The wall is initially at a uniform temperature of $50C.$ Express the explicit finite

difference formulation of the boundary nodes $0$ and $6$ for the case of no heat generation. Also, obtain the finite difference formulation for

the total amount of heat transfer at the left boundary during the first three time steps.