Numerical solution of the imprecisely defined inverse heat conduction problem

doi:10.1088/1674-1056/24/5/050203

摘要/Abstract

摘要： This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method (VIM). This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. Sci. (2008) 178 1917] along with homotopy perturbation method (HPM) and [Int. Commun. Heat Mass Transfer (2012) 39 30] in the special cases to demonstrate the validity and applicability.

关键词: triangular fuzzy number, double parametric form of fuzzy numbers, uncertain inverse heat conduction, variational iteration method (VIM)

Abstract: This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method (VIM). This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. Sci. (2008) 178 1917] along with homotopy perturbation method (HPM) and [Int. Commun. Heat Mass Transfer (2012) 39 30] in the special cases to demonstrate the validity and applicability.

Key words: triangular fuzzy number, double parametric form of fuzzy numbers, uncertain inverse heat conduction, variational iteration method (VIM)

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.-x (Numerical approximation and analysis) 02.90.+p (Other topics in mathematical methods in physics) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

Smita Tapaswini, S. Chakraverty, Diptiranjan Behera. Numerical solution of the imprecisely defined inverse heat conduction problem[J]. 中国物理B, 2015, 24(5): 50203-050203.

Smita Tapaswini, S. Chakraverty, Diptiranjan Behera. Numerical solution of the imprecisely defined inverse heat conduction problem[J]. Chin. Phys. B, 2015, 24(5): 50203-050203.

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