Chapter 4, Problem 4.46P

Derive the nodal finite-difference equations for the followingconfigurations.

1. Node $\left(m,n\right)$ on a diagonal boundary subjected toconvection with a fluid at $T_{\infty }$ and a heat transfercoefficient h. Assume $\Delta x=\Delta y.$

1. Node $\left(m,n\right)$ at the tip of a cutting tool with the uppersurface exposed to a constant heat flux $q_o^{"},$ and thediagonal surface exposed to a convection coolingprocess with the fluid at $T_{\infty }$ and a heat transfercoefficient h. Assume $\Delta x=\Delta y.$