Numerical solution of the imprecisely defined inverse heat conduction problem

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.