Wavelet collocation solution of non-linear Fin problem with temperature dependent thermal conductivity and heat transfer coefficient

Document Type: Research Paper

Authors

1 DST- Centre for Interdisciplinary Mathematical Sciences Banaras Hindu University Varanasi 221005, U.P., India

2 DST- Centre for Interdisciplinary Mathematical Sciences Banaras Hindu University Varanasi 221005, U.P., India

3 Department of Mathematical Science IIT BHU, Varanasi 221005, India

Abstract

In this paper, Wavelet Collocation Method has been used to solve nonlinear fin problem with temperature dependent thermal conductivity and heat transfer coefficient. Thermal conductivity of fin materials varies any type so that we consider thermal conductivity as the general function of temperature.  Here we consider three particular cases, where we assume that thermal conductivity is constant, linear and exponential function of temperature. In each case efficiency of fin is evaluated.  The whole analysis is presented in dimensionless form and the effect of variability of fin parameter, exponent and thermal conductivity parameter on temperature distribution and fin efficiency is shown graphically and discussed in detail.

Keywords