Numerical solution of transient heat conduction equation with variable thermophysical properties by the Tau method

Abstract

In this article, we proposed the operational approach to the Tau method for solving linear and nonlinear one‐dimensional transient heat conduction equations with variable thermophysical properties which can involve heat generation term. To solve heat conduction equation, first we recall the Tau method to obtain a matrix form of the governing differential equation. Then boundary and initial conditions are transformed into a matrix form. Finally the resulting systems of linear or nonlinear algebraic equations are given. Afterwards, efficient error estimation is also introduced for this method. Some numerical examples are given to illustrate the efficiency and high accuracy of the proposed method and also results are compared with solutions obtained by other methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 964–977, 2014

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“…where is the ( + 1)th column of the matrix . For ( ), defined by ( 24), we also have some lemmas [27]:…”

“…In their paper, some numerical examples were given to clarify the efficiency and accuracy of the proposed method. Talati et al [27] proposed the numerical solution of one-dimensional transient heat conduction equation with variable thermophysical properties using the Tau method. Finally, some numerical examples have been solved by the proposed method and the results were compared with solutions obtained by the other methods.…”

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