Deviations from one-dimensional heat flow in guarded hot-plate measurements

Abstract

A theoretical analysis is made of the error in thermal conductivity, measured by the guarded hot-plate apparatus, resulting from a temperature difference, or unbalance, between the test area and guard ring. The solution is obtained by the application of two successive Schwarz transformations, the assumptions having been verified by relaxation calculations. An expression is derived for the error heat flow in the test specimens. The agreement between calculated and measured values of the error heat flow for three different hot plates for which experimental data are available is 5% or better. It is therefore now possible to calculate the maximum tolerable unbalance to achieve any desired accuracy in thermal conductivity measured by the guarded hot plate. © 1957 The American Institute of Physics.