T s given surface temperature
5
4

q s " = 0

h, T ∞
insulated 3
Convection
wall
2
n = 1, ..., 5

y

x
q s
˝ uniform heat flux
m = 1, ..., 5
2
3
4
5
Let T (x, y , z) = T i,j,k , with i = 1, 2, 3, . . . i, j = 1, 2, 3, . . . j, and k = 1, 2, 3, . . . k .
T
T
T
T
1,1,k
2,1,k
3,1,k
i,1,k
1,1,3
T
2,1,3
T
3,1,3
T
i,1,3
T
1,1,2
T
2,1,2
T
3,1,2
T
i ,1,2
T
1,1,1
T
2,1,1
T
3,1,1
T
i ,1,1
T
1,2,k
T
2,2,k
T
3,2,k
T
i,2,k
T
1,2,3
T
2,2,3
T
3,2,3
T
i ,2,3
T
1,2,2
T
2,2,k
T
3,2,2
T
i ,2,2
T
1,2,1
T
2,2,1
T
3,2,1
T
i,2,1
T
1,j,k
T
2,j,k
T
3,j,k
T
i,j,k
T
1,j,3
T
2,j,3
T
3,j,3
T
i,j,3
T
T
T
T
T
1,j,2
2,j,2
3,j,2
i,j,2
112
Analytical Heat Transfer
FIGURE 5.4
Example of using finite difference method to solve 2-D heat conduction problem with various
boundary conditions.