Chapter 4, Problem 4.46P

Derive the nodal finite-difference equations for the following configurations.

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

(b) Node $\left(m,n\right)$ at the tip of a cutting tool with the upper surface exposed to a heat flux $q_o^n,$ and the diagonal surface exposed to a convection cooling process with the fluid at $T_{\infty }$ and a heat transfer coefficient h. Assume $\Delta x=\Delta y.$