Abstract
We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i) temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii) cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.
Highlights
Haar wavelet is the lowest member of Daubechies family of wavelets and is convenient for computer implementations due to availability of explicit expression for the Haar scaling and wavelet functions [1]
Haar wavelet-quasilinearization technique [3,4,5,6] is recently developed method for the nonlinear differential equation, which deals with all types of nonlinearities
Our purpose to solve the nonlinear equations arising in heat transfer through Haar waveletquasilinearization technique and show that it is strongly reliable method for heat transfer problems than the other existing methods
Summary
Haar wavelet is the lowest member of Daubechies family of wavelets and is convenient for computer implementations due to availability of explicit expression for the Haar scaling and wavelet functions [1]. Haar wavelet-quasilinearization technique [3,4,5,6] is recently developed method for the nonlinear differential equation, which deals with all types of nonlinearities. In the present work we deal with both initial and boundary value problems In this present work, our purpose to solve the nonlinear equations arising in heat transfer through Haar waveletquasilinearization technique and show that it is strongly reliable method for heat transfer problems than the other existing methods. We use the cubic spline interpolation [7] to get the solution at grid points for the sake of comparison For this purpose we use the MATLAB built-in function yi = interp1(x, y, xi, “spline”), for one-dimensional data interpolation by cubic spline interpolation.
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