Dual solutions of the nonlinear problem of heat transfer in a straight fin with temperature-dependent heat transfer coefficient

In this paper, a numerical scheme is provided to predict and approximate the multiple solutions for the problem of heat transfer through a straight rectangular fin with temperature-dependent heat transfer coefficient.

The proposed method is based on the two-point Taylor formula as a special case of the Hermite interpolation technique.

An explicit approximate form of the temperature distribution is computed. The convergence analysis is also discussed. Some results are reported to demonstrate the capability of the method in predicting the multiplicity of the solutions for this problem.

The duality of the solution of the problem can be easily predicted by using the presented method. Furthermore, the computational results confirm the acceptable accuracy of the presented numerical scheme even for estimating the unstable lower solution of the problem.