Numerical Study Of Thermal Behavior Of Anisotropic Medium In Bidirectional Cylindrical Geometry

Rabiâ Idmoussa,Nisrine Hanchi,Abdelaziz Oubarra,Jawad Lahjomri,Hamza Hamza,S Aniss

doi:10.1051/matecconf/201928608009

Rabiâ Idmoussa, Nisrine Hanchi + Show 4 more

Open Access

https://doi.org/10.1051/matecconf/201928608009

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Abstract

In this work, we investigate the transient thermal analysis of two-dimensional cylindrical anisotropic medium subjected to a prescribed temperature at the two end sections and to a heat flux over the whole lateral surface. Due to the complexity of analytically solving the anisotropic heat conduction equation, a numerical solution has been developed. It is based on a coordinate transformation that reduces the anisotropic cylinder heat conduction problem to an equivalent isotropic one, without complicating the boundary conditions but with a more complicated geometry. The equation of heat conduction for this virtual medium is solved by the alternating directions method. The inverse transformation makes it possible to determine the thermal behavior of the anisotropic medium as a function of study parameters: diagonal and cross thermal conductivities, heat flux.

Highlights

Anisotropic materials are present in various industrial applications
The solution in the latter case is limited to the cases of infinite geometries, otherwise there's no analytical solution, the need to use a numerical solution, object of our study
The cylindrical anisotropic medium of length L and radius b is illustrated in Fig.1.The left and right sections of are maintained at temperatures TL,TR ; whereas a radial flux is applied on the surface lateral

Summary

Introduction

Anisotropic materials are present in various industrial applications Such materials exist either in the natural state as wood and quartz, or industrial, like fibrous materials. Thermal conductivity of these kinds of materials varies according to direction. This makes the heat conduction study delicate due to a cross-derivative terms of the temperature with space variables. The case of anisotropic medium has been studied in the context of a permanent [4,5,6,7,8] and a transient conduction regime [9]. The solution in the latter case is limited to the cases of infinite geometries, otherwise there's no analytical solution, the need to use a numerical solution, object of our study

Problem formulation

Numerical solution and Validation

Results and discussion

Conclusion