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Finite element technique applied to heat conduction in solids with temperature dependent thermal conductivity

Finite element technique applied to heat conduction in solids with temperature dependent thermal... Consider a solid heat conductor with a non‐linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is, \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho c\frac{{\partial \theta }}{{\partial t}} = {\rm div}({\rm L}(\theta,{\rm x})({\rm grad}\theta)) + q $$\end{document} Here L(θ, x) (grad θ) is a vector‐valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three‐dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature‐diffusivity curve of the form κ = κ0(l + σT). The resulting system of non‐linear differential equations is integrated numerically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

Finite element technique applied to heat conduction in solids with temperature dependent thermal conductivity

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References (8)

Publisher
Wiley
Copyright
Copyright © 1973 John Wiley & Sons, Ltd
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/nme.1620070311
Publisher site
See Article on Publisher Site

Abstract

Consider a solid heat conductor with a non‐linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is, \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho c\frac{{\partial \theta }}{{\partial t}} = {\rm div}({\rm L}(\theta,{\rm x})({\rm grad}\theta)) + q $$\end{document} Here L(θ, x) (grad θ) is a vector‐valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three‐dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature‐diffusivity curve of the form κ = κ0(l + σT). The resulting system of non‐linear differential equations is integrated numerically.

Journal

International Journal for Numerical Methods in Engineering – Wiley

Published: Jan 1, 1973

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