Approximate Analytical Solution to Temperature Profile in a Solid Composite Heated by a Pulsed Laser

Sani Jibrin, Mohd Maarof Moksin, Mohd Shahril Husin, Mohammed Yusuf Waziri, Azmi Bin Zakaria, Zainal Abidin Bin Talib

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Malaysia.
Department of Physics, Faculty of Science, Universiti Putra Malaysia, Serdang, Malaysia.

DOI: 10.4236/eng.2013.55060                

Abstract

The flash technique of thermal diffusivity measurement applied to composite materials is dependent upon the success at deriving and solving the associated heat diffusion equation for the particular boundary problems of the experiment. Orthogonal expansion technique and the Green’s function approach are easier and straight forward for deriving and solving such equations, but the solutions converge very slowly for small times and hence cannot be used for numerical calculations. The Laplace transformation technique on the other hand has advantage of allowing for the making of small time approximation in order to obtain solutions that are very rapidly convergent. The principle difficulty of this technique is in the inversion of the resulting transform from s to t domain. Inversion by contour integration requires a lot of mastery in integral calculus and the simplest method is therefore to look up for the transform in the standard Laplace conversion table. At first look not all subsidiary equations can be converted using the Laplace transform conversion table; in this work however, we present the mathematical analysis by means of which analytical solutions to heat diffusion problem in composite media; hitherto only transformed via contour integration, is obtained directly from the Laplace transform conversion tables.

Keywords

Laplace Transforms; Subsidiary Equations; Laplace Inversion Theorem; Laser Pulse

Conflicts of Interest

The authors declare no conflicts of interest.

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