Analytical solution to heat conduction in finite hollow composite cylinders with a general boundary condition

Abstract

This paper presents a set of classical analytical solutions to heat conduction in a two-layer composite hollow cylindrical medium, which are derived by the method of Laplace transform. The subjected boundary conditions are general and included various combinations of constant temperature, constant flux, zero flux, or convection boundary condition at either surface. The new solution can reduce to Jaeger’s solution to the problems subject to constant-temperature boundary conditions, verifying that our solution is an extension version of his solution. Moreover, the solutions subject to a constant flux and a constant temperature are used to evaluate short-time accuracy of a composite-medium line-source solution. Comparison of these two solutions indicates that the temperature response is always delayed as a result of the line-source assumption. An expression for estimating the minimum threshold, beyond which the line-source solution is acceptable, is suggested for engineering applications.