Exact and wavelet collocation solution of fin problem with temperature dependent internal heat generation

Abstract

In this paper, we studied heat transfer in longitudinal fin with temperature dependent internal heat generation and temperature dependent thermal conductivity. It has been observed that solution exists and unique. We consider three particular cases when the thermal conductivity is (1) constant (2) linear and (3) exponential function of temperature. We obtained exact solution in case I and exact solution in explicit integral form is case II and III. The wavelet collocation method has been used in this nonlinear problem. In case I, exact solution is compared with those obtained by wavelet collocation solution and optimal linearization solution. It has been observed that the wavelet collocation solution and exact solution is the same while optimal linearization solutions are having error. In case II, we have compared our results with those obtained by optimal linearization solution and observed that optimal linearization method having similar error as in case I. In case III, the wavelet collocation solution is provided. The whole analysis is provided in dimensionless form. The effect of variability of different parameters on dimensionless fin temperature and on fin efficiency are studied and discussed in detailed. © 2014, Begell House Inc. All rights reserved.