Table of Nodal Finite Difference Equations

Table 4.2 in textbook, used with nodal networks.

Configuration
Finite-Difference Equation for Δx = Δy
(4.29)
Tm,n+1+Tm,n1+Tm+1,n+Tm1,n4Tm,n=0

Case 1. Interior node

(4.41)
2(Tm1,n+Tm,n+1)+(Tm+1,n+Tm,n1)+2hΔxkT2(3+hΔxk)Tm,n=0

Case 2. Node at an internal corner with convection

(2Tm1,n+Tm,n+1+Tm,n1)+2hΔxkT2(hΔxk+2)Tm,n=0 a

Case 3. Node at a plane surface with convection

(4.43)
(Tm,n1+Tm1,n)+2hΔxkT2(hΔxk+1)Tm,n=0

Case 4. Node at an external corner with convection

(4.44)
(2Tm1,n+Tm,n+1+Tm,n1)+2qΔxk4Tm,n=0 b

Case 5. Node at a plane surface with uniform heat flux