Axisymmetric non-Fourier temperature field in a hollow sphere

Abstract

The non-Fourier axisymmetric (2+1)-dimensional temperature field within a hollow sphere is analytically investigated by the solution of the well-known Cattaneo-Vernotte hyperbolic heat conduction equation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. General linear time-independent boundary conditions are considered. Ultimately, the presented solution is applied to a (1+1)-as well as a (2+1)-dimensional problem, and their respective non-Fourier thermal behavior is studied. The present solution can be reduced to special cases of interest by choosing appropriate boundary conditions parameters.

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

“…TDPL [124,125]. Thermomechanical models [131] Separation of variables [67,69,[132][133][134] Cartesian, Spherical 1-D, 2.5-D, 3-D CV, DPL Spherical coordinates [69]. Solving original DPL model [67].…”

“…The effect of the non-Fourier concept on the dynamic thermal behavior of spherical media, including solid, hollow, and bi-layered composite spheres, due to a sudden temperature change on the surfaces is investigated [68]. The non-Fourier axisymmetric 2.5-D temperature field within a hollow sphere is analytically modeled by the CV heat conduction equation [69]. The analysis of the non-Fourier effect in a hollow sphere exposed to a periodic boundary heat flux is presented [70].…”

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

“…In this research the hyperbolic heat conduction equation in a finite hollow cylinder is analytically solved under the influence of arbitrarily chosen linear time-independent boundary conditions. Similar to the work [16], the method of solution is the well-known separation of variables method. This method does not have the difficulties of inverse Laplace determination compared with the Laplace transform method.…”

“…Jiang [15] used the Laplace transform method for investigating the hyperbolic heat conduction process in a hollow sphere with its two boundary surfaces subjected to sudden temperature changes. The non-Fourier axsymmetric three-dimensional temperature field within a hollow sphere with general linear time-independent boundary conditions was analytically investigated by Moosaie [16]. The method of solution is the standard separation of variables.…”

Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics

“…In cases of time-invariant environments, the response is usually computed by shifting the origin of spatial coordinate to the steady-state response, upon which the dynamics with homogeneous boundary condition can be solved by Separation of Variables [16]. This method can also be extended to time-varying environments by stepwise sampling the temporal continuity as in [17][18] for examples.…”