Estimation of surface heat flux in a one‑ dimensional hyperbolic bio‑ heat conduction problem with temperature‑ dependent properties during thermal therapy

Abstract

In this study, an inverse analysis is presented to determine the time-dependent surface heat flux of a living tissue in a one-dimensional non-Fourier bio-heat conduction problem by using temperature responses measured within the medium. The properties of tissue are assumed to be function of temperature. Therefore, this problem is classified as a nonlinear inverse problem of hyperbolic bio-heat<br><br>conduction. The inverse problem is solved through the minimization of an objective function by the conjugate gradient method. Three examples are presented to show that the proposed method can be implemented to estimate the unknown surface heat flux. In addition, the effects of measurement<br><br>error, measurement location, initial guess, nonlinearity and thermal relation time on the precision of the estimation are investigated. The results show that the proposed method is an accurate and robust method to determine inversely the surface heat flux in hyperbolic bio-heat conduction with temperature-dependent properties.