Nanofluids are extremely useful to investigators due to their greater heat transfer rates, which have significant applications in multiple industries. The primary objective of this article is to look into the effect of viscous dissipation in Sisko nano liquid flow with gold $\left(\mathrm{Au}\right)$ nanoparticles on a porous stenosis artery. Heat transfer properties were explored. Blood was utilized as a base fluid for nanoparticles. To renovate the governing nonlinear PDEs into nonlinear ODEs, appropriate transformations were used. The bvp4c-based shooting method, via MATLAB, was used to determine the numerical results of the nonlinear ODEs. Furthermore, flow forecasts for each physical quantity were explored. To demonstrate the physical influences of flow constraints versus presumed flow fields, physical explanations were used. The findings demonstrated that the velocity contour improved as the volume fraction, curvature, power law index, and material parameter upsurged. For the Prandtl number, the volume fraction of nanoparticles, the index of the power law, and the temperature profile of the nanofluid declined. Furthermore, the drag force and transfer of the heat were also investigated as explanations for influences on blood flow. Further, the Nusselt number reduced and the drag force enhanced as the curvature parameter values increased. The modeling and numerical solutions play an impressive role in predicting the cause of atherosclerosis.

In the current study, since nanofluids have a high thermal resistance, and because non-Newtonian (Ree-Eyring) fluid movement on a stretching sheet by means of suspended nanoparticles $AA7072\text{-}AA7075$ is used, the proposed mathematical model takes into account the influence of magnetic dipoles and the Koo-Kleinstreuer model. The Cattaneo-Christov model is used to calculate heat transfer in a two-dimensional flow of Ree-Eyring nanofluid across a stretching sheet, and viscous dissipation is taken into account. The base liquid water with suspended nanoparticles $AA7072\text{-}AA7075$ is considered in this study. The PDEs are converted into ODEs by exhausting similarity transformations. The numerical solution of the altered equations is then performed utilising the HAM. To examine the performance of velocity, temperature profiles, concentration profiles, skin friction, the Nusselt number, and the Sherwood number, a graphical analysis is carried out for various parameters. The new model’s key conclusions are that the $AA7075$ alloy outperforms the $AA7072$ alloy in terms of thermal performance as the volume fraction and ferro-magnetic interaction constraint rise. Additionally, the rate of heat transmission and the skin friction coefficient improve as the volume fraction rises.

The effect of entropy optimization on an axisymmetric Darcy–Forchheimer Powell–Eyring nanofluid flow caused by a horizontally permeable stretching cylinder, as well as non-linear thermal radiation, was investigated in this research work. The leading equations of the current problem were changed into ODEs by exhausting appropriate transformations. To deduce the reduced system, the numerical method bvp4c was used. The outcome of non-dimensional relevant factors on velocity, entropy, concentration, temperature, Bejan number, drag force, and Nusselt number is discussed and demonstrated using graphs and tables. It is perceived that, with a higher value of volume fraction parameter, the skin friction falls down. Likewise, it is found that the Nusselt number drops with enhancing the value of the volume fraction. Moreover, the result reveals that the entropy generation increases as the volume fraction, curvature parameter, and Brinkman number increase.

The flow of the Ellis fluid in the renal tubule is investigated in this paper. The fluid absorption at the wall is influenced by the pressure gradient across the wall and by the permeability of the wall. The governing equations are considerably simplified if the tubule radius is assumed to be much smaller than its length. Important quantities of interest are computed numerically. The results are compared with available data and are found to be in good agreement.

In this current work, we assume the mathematical modelling of non-Newtonian time-dependent hybrid nanoparticles via a cylindrical stenosis artery. In this work, blood is used as a base fluid, and the nanoparticles (copper and aluminum oxide) of cylindrical shape are inserted inside the artery to combine with blood to form hybrid nanofluid (HNF). The homotopy analysis method (HAM) is deployed for the solution of nonlinear resulting equations. For the validation of this current work, the results of the existing work have been compared with our proposed model results. A comparison of key profiles like velocity, temperature, wall shear stress, and flow rate is also performed at a specific critical height of the stenosis. It is also observed that the thermal conductance of hybrid nanofluids is greater than that of nanofluids. Including the hybrid nanoparticles (copper and aluminum oxide) inside the blood enhances the blood axial velocity. These simulations are applicable to the magnetic targeting treatment of stenosed artery disorders and the diffusion of nanodrugs.