A Theory of the Envelope Type of Thermal Conductivity Tests

摘要

The well‐known problem of the end effects in a cylinder of finite length has been circumvented by the use of spheroidal rather than cylindrical apparatus. After a general theory of heat flow is given, applications demonstrate the mathematical difficulties caused by discontinuities in the curvature of the surface of the heat conductor. The suitability of the spheroidal shape is demonstrated, and corresponding heat flow equations are derived demonstrating the effects of the variable distance between any two isotherms on the amount of heat crossing any unit area of an isotherm. It is proven that the amount of heat flowing through a slice of a spheroidal isotherm made perpendicular to the axis of the spheroid is proportional to the width of the slice, and independent of the position of the slice with respect to the spheroid. This theorem is applied to find the heat distribution necessary to keep the core of the apparatus at uniform temperature. Because all measurements are made at thermal equilibrium, a rough estimate is given for the time necessary to reach equilibrium.