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.

In the present article, we have presented a theoretical study on the swimming of migratory gyrotactic microorganisms in a non-Newtonian blood-based nanofluid via an anisotropically narrowing artery. Sutterby fluid model is used in order to understand the rheology of the blood as a non-Newtonian fluid model. This fluid pattern has the ability to show Newtonian and non-Newtonian features. The mathematical formulation is performed via continuity, temperature, motile microorganism, momentum, and concentration equation. The series solutions are obtained using the perturbation scheme up to the third-order approximation. The resulting solutions are discussed with the help of graphs for all the leading parameters. The graphical results are also presented for non-tapered, diverging, and converging artery. We further discuss the velocity, temperature, swimming microorganism and temperature distribution. Moreover, the variation of impedance and the impact of wall shear stress are discussed and presented through the graphs.

The present study deals with convective heat transfer performance and fluid flow characteristics of Cu–Ag/water hybrid nanofluids. A geometric model of an inverted cone is used. The mathematical model consists of nonlinear governing equations along with associated boundary conditions reduced to a nondimensional form by using appropriate transformation, Boussinesq and boundary-layer approximations. Analytical solutions are obtained for velocity and temperature profiles. The convergence analysis and error of norm 2 are also presented to check the validity of the results. The effects of nanoparticles volume fraction, hybrid nanoparticles compactness ratio on velocity, temperature, thermophysical properties, convective heat transfer coefficient, and skin friction coefficient are illustrated in graphical and tabular form. A comparison of hybrid nanofluid with single material nanofluids is also made and it is realized that the hybrid nanofluid has greater thermal conductivity and improved convective heat transfer characteristics as compared to the base fluid and nanofluids. The proposed model can help in designing a way to accelerate and mix liquids in the chemical industry.