Temperature Distribution along Thin Rod with Radiation Loss from Side Surface

概要

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The paper describes a mathematical approach of solving the temperature distribution along a fine rod whoes one end is highly heated, taking into account the radiation loss from the peripheral surface. A non-linear differential equation of heat conduction has a particular solution only under the special boundary condition, but it has no analytical solution under the arbitrary conditions such as when a cooling terminal is placed at a finite length from the hot end. Then, the authors have applied a method of integration of series to solve the problems under question. Introducing a new parameter θ_c that is related with the temperature gradient or heat flux density at the cooling terminal, one obtains the rigorous solution of the fundamental equation in the infinite series. The effect of cooling terminal is minor if θ_c is less enough than 1, and in such cases the particular solution in analytical function is useful to estimate the thermal field near the hot end.
大阪大学の論文