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

(a) Node m, n on a diagonal boundary subjected to convection with a fluid at T∞ and a heat transfer coefficient h. Assume ∆x = ∆y.

(b) Node m, n at the tip of a cutting tool with the upper surface exposed to a constant heat flux q"0, and the diagonal surface exposed to a convection cooling process with the fluid at T∞ and a heat transfer coefficient h. Assume ∆x = ∆y.

PART (A) m + 1, n + 1 T, h Ay , m+ 1, n , - 1 -1, - 1 -ar- (PART B) m+ 1, n , 45 Ay FAx- m+ 1, n-1