In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

This study investigates the photo-thermo-elastic interaction in an infinite semi-conductor material with cylindrical cavities. The effect of variable thermal conductivity through the photo-thermo-elastic transport process is studied using the coupled models of thermo-elasticity and plasma waves. The internal surface of the cylindrical cavity is loaded by a thermal shock varying heat. The eigenvalue method, under Laplace transform scheme, is used to get the analytical solution of the studied field distribution as parts of this phenomenon. A detailed analysis of the impacts of the variable thermal conductivity on the physical fields is debated. The numerical outcomes of the studied fields are displayed graphically. According to them, the variable thermal conductivity offers finite speed of the mechanical wave and the thermal wave propagations.

This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia.

This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, normal and strong conductivity.

This paper provides a method for determining a numerical solution of the thermal damage of living tissues using a nonlinear dual phase lag model. Due to the nonlinearity of the basic equations, the finite element approach is adopted to solve such problems. The numerical outcomes obtained by the finite element technique are also compared with the existing experimental study to verify the accuracy of the numerical calculations. Based on the formulation of Arrhenius, the thermal damages to the tissues are estimated by the denatured protein range. Numerical results for temperatures are presented graphically. Also, the comparisons between the numerical outcomes and the existing experimental data show that the present mathematical models are effective tools to evaluate the bioheat transfer in a spherical living tissue.