Tissue Temperature Control in a Bio-Heat Transfer Equation with the Conjugate Gradient Method

Authors

1 Ph.D. Student, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

2 Assoc. Prof., Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

3 Assoc. Prof., Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

The classical conduction heat transfer model which considers infinite thermal propagation speed, named Fourier model and its equations are in elliptic form and has numerous applications. This model is not appropriate for many industrial applications especially in medical applications and thus hyperbolic or non-Fourier model that considers finite heat propagation speed should be used. Temperature control in certain points of such systems obeying these types of equations is an important problem which has been studied in this paper. In this paper, firstly, the validity of the conjugate gradient method is approved using a known heat flux at a system boundary and then the method is used to estimate the boundary condition which leads to a desired temperature distribution in the geometry. Also, the modeling and inverse problem solution are studied for noise in input data and results showed appropriate accuracy and convergence even for considerable noise in input data. Also, the modeling and inverse problem solution are studied for noise in input data and results showed appropriate accuracy and convergence even for considerable noise in input data.

Keywords

Main Subjects

References

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Journal of Solid and Fluid Mechanics
Volume 13, Issue 3
May and June 2023
Pages 159-170

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