Numerical Methods in Transient Heat Conduction : (1st Report, Methods Using the Analog Computer)

抄録

One-dimensional unsteady heat conduction problems can usually and easily be solved numerically by use of an analog computer. In this paper, the following problems about linear one-dimensional transient heat conduction are revealed. (1) Computer circuits for boundary conditions of no flux across the surface, prescribed heat 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 given in addition to the well-known circuit for that of prescribed surface temperature. (2) The accuracy of numerical solutions using the analog computer is shown to be governed by the degree of approximation in the ordinary differential equation, which is converted from the original equation of heat conduction. (3) [numerical formula]=0.4∼2.6 is shown to be of sufficient condition to solve the above problems by analog computers, when the required accuracy is within 2∼3% of the maximum temperature change.