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# Numerical Study of Residual Correction Method Applied to Non-linear Heat Transfer Problem

Chia-Yi Cheng, Cha’o-Kuang Chen1, Yue-Tzu Yang
Department of Mechanical Engineering, NCKU, Tainan, Taiwan, R.O.C., 701.Email: ckchen@mail.ncku.edu.tw Tel: +886-62757575 #62140

Computer Modeling in Engineering & Sciences 2009, 44(3), 203-218. https://doi.org/10.3970/cmes.2009.044.203

### Abstract

This paper seeks to utilize the residual correction method in coordination with the evolutionary monotonic iteration technique to obtain upper and lower approximate solutions of non-linear heat transfer problem of the annular hyperbolic profile fins whose thermal conductivity vary with temperature. First, the monotonicity of a non-linear differential equation is reinforced by using the monotone iterative technique. Then, the cubic spline method is applied to discretize and convert the differential equation into the mathematical programming problems. Finally, based on the residual correction concept, the complicated constraint inequality equations can be transferred into the simple iterative equations. As verified by this problem, hereof the method proposed can be efficiently obtained the upper and lower approximate solutions of nonlinear heat transfer problems, and easily identify the error range between mean approximate solutions and exact solutions.

### Keywords

cubic spline, monotone, residual, upper and lower approxiamte solution, mathematical programming

Cheng, C., Chen, C., Yang, Y. (2009). Numerical Study of Residual Correction Method Applied to Non-linear Heat Transfer Problem. CMES-Computer Modeling in Engineering & Sciences, 44(3), 203–218. This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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