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The purpose of this paper is to provide a method for determining the numerical solutions of the thermal damage of cylindrical living tissues using hyperbolic bioheat model. Due to the complex governing equation, the finite element approach has been adopted to solve these problems. To approve the accuracy of the numerical solution, the numerical outcomes obtained by the finite element approach are compared with the existing experimental study. In addition, the comparisons between the numerical outcomes and the existing experimental data displays that the present mathematical models are efficient tools to evaluate the bioheat transfer in the cylindrical living tissue. Numerical computations for temperatures and thermal damage are presented graphically.

In this section, the complex equation of bioheat transfer based upon one relaxation time in cylindrical living tissue is summarized by using the finite element method. This method has been used here to get the solution of equation (8) with initial conditions (9) and boundary conditions (10). The finite element technique is a strong method originally advanced for numerical solutions of complex problems in many fields, and it is the approach of choice for complex systems. Another advantage of this method is that it makes it possible to visualize and quantify the physical effects independently of the experimental limits. Abbas and his colleagues [26-34] have solved several problems under generalized thermoelastic theories.

In this study, the different values of blood perfusion and thermal relaxation time of the dermal part of cylindrical living tissue are used. To verify the accuracy of the numerical solutions, the numerical outcomes obtained by the finite element procedure and the existing experimental study have been compared. This comparison displays that the present mathematical model is an effective tool to evaluate the bioheat transfer in the living tissue.

The validation of the obtained results by using experimental data the numerical solution of hyperbolic bioheat equation is presented. Due to the nonlinearity of the basic equation, the finite element approach is adopted. The effects of thermal relaxation times on the thermal damage and temperature are studied.

The purposes of this study, a generalized model for thermoelastic wave under three-phase lag (TPL) model is used to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimension porous medium.

By using Laplace-Fourier transformations with the eigen values methodologies, the analytical solutions of all physical variables are obtained.

The derived methods are estimated with numerical outcomes which are applied to the porous media in simplified geometry.

Finally, the outcomes are represented graphically to display the difference among the models of the TPL and the Green and Naghdi (GNIII) with and without energy dissipations.

The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimensional (2D) porous medium.

Using Fourier and Laplace transformations with the eigenvalue technique, the exact solutions of all physical quantities are obtained.

The derived method is evaluated with numerical results, which are applied to the porous medium in a simplified geometry.

Finally, the outcomes are graphically represented to show the difference among the models of classical dynamical coupled, the Lord and Shulman and DPL.

The purpose of this paper is to study the wave propagation in a porous medium through the porothermoelastic process using the finite element method (FEM).

One-dimensional (1D) application for a poroelastic half-space is considered. Due to the complex governing equation, the finite element approach has been adopted to solve these problems.

The effect of porosity and thermal relaxation times in a porothermoelastic material was investigated.

The numerical results for stresses, displacements and temperatures for the solid and the fluid are represented graphically. This work will enable future investigators to have the insight of nonsimple porothermoelasticity with different phases in detail.

The purpose of this paper is to study the wave propagation in a non-homogenous semiconducting medium through the photothermal process using the fractional order photo-thermoelastic without neglecting the coupling between the plasma and thermoelastic waves that photogenerated through traction free and loaded thermally by exponentially decaying pulse boundary heat flux.

The analytical solutions in the transformed domain by the eigenvalue approach were observed through the transform techniques of Laplace.

Silicon-like semiconductor was used to achieve the numerical computations.

Some comparisons are shown in the figures to estimate the effects of the fractional order and non-homogeneous parameters.