113
Numerical Analysis in Heat Conduction
T (x, y, x)
i = 1,2,3, ..., i
k = 1,2,3, ..., k
j = 1,2,3, ..., j
FIGURE 5.5
Finite difference method to solve 3-D heat conduction problem.
For the case of a curved boundary [3], the interior nodes can be determined as
shown in Figure 5.6.
Given : T i+1,j , T i−1,j , T i,j+1 , T i,j−1
T i−1,j − T i,j
T i+1,j − T i,j
k Δy
+ k Δy
(5.12)
Δx
aΔx
T i,j+1 − T i,j
T i,j−1 − T i,j
+k Δx
+ k Δx
= 0
bΔy
cΔy
Unknown :T i,j
bΔy
cΔy
aΔx
T i+ 1, j
T i, j+ 1
T i, j– 1
Δy
Δx
T i – 1, j
T i , j
FIGURE 5.6
Finite difference method to solve the interior nodes next to the curved boundary.