Fundamental Studies on the Thermal Properties of Farm Products and those Measurement (I)

Numerical Analysis of Periodic Heat Conduction and Fundamental Experiment

Abstract

The numerical analysis using a weighted average approximation method was examined to obtain solutions of time depedent periodic heat conduction in a semi-infinite solid with adequate accuracy. The results of this study are as follows:
1. A model composed of real and imaginary material was proposed and an approximate condition that numerical solutions can be derived only with one boundary condition at the surface, X=0, was clarified. In this, another boundary condition was unnecessary. Fig. 4 shows the required depth of the model in relation to its Fourier Number.
2. A linear relation was observed between the weight θ and the error of numerical solutions, and the equation (13) was obtained by making use of this results. This equation expressed the optimum value of θ, named the minimum error weight and symbolized by θ₀ in the paper, in terms of R, where R=ΔT/(ΔX)². By use of θ₀, numerical solutions which contained at most 2-3% of error can be obtained.
3. Numerical values were in good agreement with those measured temperatures which were obtained when the surface temperature of material varied periodically but not sinusoidally.