An Investigation of Numerical Modeling of Transient Heat Conduction in a One-Dimensional Functionally Graded Material
This article presents a closed form analytical solution for one-dimensional transient heat conduction in a material where the thermal conductivity varies linearly through the thickness but the thermal diffusivity is held constant. This solution is used to validate the results from finite-difference and finite-element approximations that account for this variation at the element level. This was motivated by a suggested limitation on the minimum time step used in the commercial finite-element softwar ecode ABAQUS for quadratic elements. Good agreement was found between the analytical and numerical approximations, indicating that conventional numerical techniques may be sufficiently robust to analyze heat conduction problems in functionally graded mate rials without the use of special elements. The minimum time step constraint was found to be unnecessary for a convective boundary condition for the one-dimensional elements and property variation used in this study. Copyright © Taylor and Francis Group, LLC.
L. W. Byrd and V. Birman, "An Investigation of Numerical Modeling of Transient Heat Conduction in a One-Dimensional Functionally Graded Material," Heat Transfer Engineering, Taylor & Francis, Jan 2010.
The definitive version is available at http://dx.doi.org/10.1080/01457630903304384
Mechanical and Aerospace Engineering
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