Estimation of Surface Conditions for Nonlinear Inverse Heat Conduction Problems Using the Hybrid Inverse Scheme

Abstract

A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.

Numerical solution of the imprecisely defined inverse heat conduction problem

“…This IHCP equation is analyzed in the literature. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Hetmaniok et al [1] applied the homotopy perturbation method for the solution of inverse heat conduction problem. Moreover, Slota [2] implemented homotopy perturbation method for the solution of one phase.…”

“…Moreover, Slota [2] implemented homotopy perturbation method for the solution of one phase. A hybrid inverse scheme was applied by Chen and Wu [3] for estimation of surface conditions for nonlinear IHCPs. Cialkowski et al [4] used Trefftz non-continuous method for the solution of a stationary inverse heat conduction problem.…”