$5-107$ Consider transient heat conduction in a plane wall with variable heat generation and constant thermal conductivity. The nodal

network of the medium consists of nodes $0,1,2,3,$ and $4$ with a uniform nodal spacing of $x.$ The wall is initially at a specified

temperature. Using the energy balance approach, obtain the explicit finite difference formulation of the boundary nodes for the case of

uniform heat flux $q_0^{}$ at the left boundary $($node $0)$ and convection at the right boundary $($node $4)$ with a convection coefficient of $h$ and

an ambient temperature of $T_{}.$ Do not simplify.