Non-fourier temperature field in a solid homogeneous finite hollow cylinder

Abstract

Analytical solution of the non-Fourier Axisymmetric temperature field within a finite hollow cylinder is investigated considering the Cattaneo-Vernotte constitutive heat flux relation. The solution is found for the most general linear time-independent boundary conditions. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used. The present solution can be reduced to special problems of interest by choosing appropriate boundary condition parameters. The solution is applied for two special cases including constant heat flux and the Gaussian distribution heating of a cylinder, and their respective non-Fourier thermal behavior is studied.

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

“…The steady-state problem here is a special case of the steady problem in [10]. The steady problem is shown as follows:…”

“…Thus, the solution of the problem with time-independent boundary conditions is a superposition of these two steps according to the below equation [10,13].…”

“…The separation of variables method along with Duhamel's integral theorem is employed to obtain the closed-form solution in a straightforward manner. This solution does not have the difficulties of inverse Laplace determination compared with the Laplace transform method, and because of the generality of the solution procedure, it can be applied to any other boundary conditions shown in work [10]. Finally, the proposed solution is applied to two special cases of harmonic uniform surface heat flux and an exponentially decaying pulse surface heat flux with Gaussian distribution applied to the lateral surface of the cylinder.…”

“…The aim of this research, following the work [10], is to investigate analytically the hyperbolic thermal behavior of a finite hollow cylinder under the influence of periodic boundary heat flux. The separation of variables method along with Duhamel's integral theorem is employed to obtain the closed-form solution in a straightforward manner.…”

“…Sadd and Cha [9] investigated the axisymmetric one-dimensional conduction for regions interior and exterior to a circular cylinder using methods of Laplace transformation and asymptotic analysis. Atefi and Talaee [10] derived an analytical solution for non-Fourier temperature profiles in a finite hollow cylinder under time-independent boundary conditions using separation of variables method.…”