On the Penetration Depth in Fourier Heat Conduction

Abstract

Penetration depth measures the distance or thickness of thermal energy propagating into the surface through conduction. In most heat transfer textbooks and literatures, penetration depth is only dealt with qualitatively for the simple surface boundary condition- a prescribed sur face temperature (i.e. boundary condition of first kind). In this study, the concept of penetration depth is examined and expanded to consider different surface thermal boundary conditions (boundary conditions of second and third kind as well). Penetration depths for all three kinds of thermal boundary conditions are expressed in terms of non-dimensional parameters, Fourier and Biot numbers. The results can be used as a guide for design of thermal systems when there are transient heat conduction processes with different thermal boundary conditions involved.