An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

Abstract

An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at − 1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Theoretical modeling of endovascular drug delivery into a multilayer arterial wall from a drug-coated balloon

“…The following conditions apply at the interfaces to handle, especially in a multilayer geometry [24]. Instead, the problem is solved separately and sequentially, such that the solution at the end of Stage A serves as the initial condition for Stage B.…”

A Numerical Study to Determine the Effect of an Insulator Location on the Transient Heat Transfer

“…A numerical solution is complete for two composite sheets with a trigonometric or exponential function of the heat transfer coefficient with time on the warm surface. Numerical results explained the transitory difference effects in the coefficient of heat transfer on the unsteady temperature range of composite sheets [2]. The unsteady one-dimensional heat transfer pattern was advanced and numerically solved by employing a finite difference method to study the effect of PCMs on the walls of exterior buildings.…”