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International Heat Transfer Conference 16

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

AN IMPROVED SPACE MARCHING METHOD INCORPORATING FUTURE TEMPERATURES IN LEAST SQUARE MANNER FOR LINEAR AND NONLINEAR IHCP

Ran Li
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR. China

Zhongwei Huang
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, PR. China

DOI: 10.1615/IHTC16.cip.021812
pages 2493-2500


KEY WORDS: Computational methods, Inverse problems, Conduction, Space marching, Nonlinear

Abstract

Based on finite difference algorithm, the space marching (SM) method is especially suitable for nonlinear IHCP with temperature-dependent thermal properties. This paper presents an improved SM method which, comparing to previous SM methods in the literature, can remarkably reduce the oscillation of inverse results by using future temperatures in a least square manner. The algorithm formulations are developed using the concept of sensitivity coefficients. Based on the estimator formulation, the bias error of inverse results is analyzed and several procedures are proposed to improve the inverse results. It was discovered that the present method could improve the estimating accuracy, evaluated through root mean square error (RMSE), by 47% comparing to the method of Raynaud and Bransier. A nonlinear IHCP case was also employed to illustrate the robustness and efficiency of present method. Triangular and sine waves were used to simulate the heat flux history. It was revealed that the present method could well reconstruct different heat flux histories for nonlinear IHCP. Comparing to the method of Raynaud and Bransier, the present method could decrease the RMSE of inverse results by 5 folds when the same number of spatial nodes was used.

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