Chapter 5, Problem 5.110P

A one-dimensional slab of thickness 2L is initially at a uniform temperature $T_i.$ Suddenly, electric current is passed through the slab causing uniform volumetric heating $\stackrel{.}{q}\left({\text{W/m}}^{\text{3}}\right).$ At the same time, both outer surfaces $\left(x=\pm L\right)$ are subjected to a convection process at $T_{\infty }$ with a heat transfer coefficient h.

Write the finite-difference equation expressing conservation of energy for node 0 located on the outersurface at $x=-L.$ Rearrange your equation and identify any important dimensionless coefficients.