Numerical Methods in Transient Heat Conduction : (2nd Report, Methods Using a Digital Computer)

概要

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The following problems concerning numerical solutions of one-dimensional heat conduction are clarified as the first step in applying numerical methods by digital computers. (1) Difference equations corresponding to boundary conditions of, no flux across the surface, prescribed flux across the surface, linear heat transfer at the surface, non-linear heat transfer, contact with a well-stirred fluid or perfect conductor, and the surface of separation of two media of different conductivities, are proposed. The stability conditions for these equations are shown. (2) The conditions necessary to obtain stable numerical solutions of the required accuracy-2〜3% of the maximum temperature change-are discussed. These conditions are shown in a specified region of t_<min>/Δt-at_<min>/(Δx)^2 diagrams for each of the above boundary conditions. From the diagrams, the means sufficient to obtain numerical solutions of the required accuracy are revealed to be t_<min>/Δt≧6 and at_<min>/(Δx)^2≧0.4〜2.6.
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