Unsteady thermal conduction problems in the form of ∂φ/∂θ=α∇
2φ were numerically solved under the Dirichlet condition, by using the explicit finite difference method, and the effect of initial boundary value on the predicted results was studied.
1-dimensional problem was solved by using the scheme;
φ
p, r+1=1/6 [(+1)-(+4)-(+1)] φ
p, rwhere subscript “
p” denotes the spatial point and “
r” the time step. For 2-dimensional problem, the analysis was based on a new scheme :
φ
p, q, r+1=1/36 [(+1)-(+4)-(+1)-(+4)-(+16)-(+4)-(+1)-(+4)-(+1)] φ
p, q, rThe choice of initial boundary values, φ
0, 0 (=φ
N, 0) for 1-dimensional andφ
0, q, 0 (φ
p, 0, 0=φ
N, q, 0=φ
p, N, 0) for 2-dimensional, was of importance, especially for the initial stage, in view of the accuracy of the results.By taking this into account, the same optimal value of 0.5 was found for both 1-dimensional and 2-dimensional problems.
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