Exponential and Binomial Series Expansions in the Analysis of Temperature Profile of Solids Heated by Camera Flash

Publication Issue: 
Volume 37, Issue 1, 2016
Page No: 
Date Received: 
Saturday, June 11, 2016
Authors' Name: 
Sani Jibrin
Mohd Maarof Moksin
Mohd Shahril Husin
Azmi Zakaria
Sirajo L. Bichi
Bashir Ahmed Danzomo
Authors' Affiliation and Address: 

Department of Science Laboratory Technology, College of Science & Technology, Hussaini Adamu Federal Polytechnic, Kazaure, Jigawa State, Nigeria

Physics Department, Faculty of Science, University Putra Malaysia

Physics Department, Faculty of Science, University Putra Malaysia

Physics Department, Faculty of Science, University Putra Malaysia

Department of Mathematical Sciences, Faculty of Science, Bayero University Kano

Department of Mechanical Engineering, College of Engineering, Hussaini Adamu Federal Polytechnic, Kazaure

The solutions of time-dependent heat conduction problems for finite regions such as slabs and cylinders of finite radius are in the form of a series that converge rapidly for large values of diffusion time, t but, converge very slowly for small values of t, and hence are not suitable for numerical computations. Similarly, the solutions of many subsidiary equations resulting from the use of Laplace transform techniques are most often in hyperbolic forms. However, the Laplace transform conversion tables do not give inversion of such hyperbolic functions and, the integral inversion procedure is tedious and mathematically involved. A simple and straightforward procedure of expanding the resulting solution in negative exponentials and binomial series and the subsequent use of the Laplace conversion tables is hereby presented for inverting such solutions back to t domain. This method is supported by experimental determination of the thermal diffusivity of 50 µm thick aluminum, copper, nickel, silver and tungsten metals in one-layer solid configurations. By this analysis, the dual problem of finite pulse-time effects and heat loss from the surfaces of the samples, inherent in thermal diffusivity evaluation by the flash method are significantly minimized. When the experimental values obtained here are compared with other similar values found in literature, the agreement is within about ±3%