Exploring the movement of blood in a blood vessel has been fascinated by clinicians and biomedical researchers because it is predominant in cell tissue engineering, drug targeting and various treatments like hypothermia, hyperthermia, and cancer. It is noticed that numerous non-Newtonian rheological fluids like Carreau fluid, tangent hyperbolic fluid, Eyring–Powell fluid and viscoelastic fluid manifest the characteristics of blood flow. Further, the investigation of entropy generation can be used to raise the performance of medical equipments. Consequently, the present mathematical model scrutinizes the transport characteristics and entropy generation of the peristaltic Eyring–Powell nanofluid in a permeable vertical divergent channel in the presence of dissipation and linear radiation. The non-similar variables are employed to convert the dimensional partial differential equations into dimensionless form which are tackled by the Homotopy perturbation method. The impacts of emerging parameters like Eyring–Powell parameters, left and right wall amplitudes, thermophoresis, mean flow rate, radiation, permeability parameter, Brownian motion, Eckert number, Hartman number on Eyring–Powell nanofluid axial velocity, temperature, and concentration are manifested. Present results disclose that the thermal Grashof number highly inflates the pressure rise. Eyring–Powell nanofluid temperature reduces for uplifting the linear radiation parameter. Growing values of the non-uniform parameter lead to move the trapping bolus towards the left and right wall. The total entropy generation diminishes for magnifying the temperature difference parameter.

The present study addresses the fluid transport behaviour of the flow of gold (Au)‐copper (Cu)/biomagnetic blood hybrid nanofluid in an inclined irregular stenosis artery as a consequence of varying viscosity and Lorentz force. The nonlinear flow equations are transformed into dimensionless form by using nonsimilar variables. The finite‐difference technique (FTCS) is involved in computing the nonlinear transport dimensionless equations. The significant parameters like angle parameter, the Hartmann number, changing viscosity, constant heat source, the Reynolds number, and nanoparticle volume fraction on the flow field are exhibited through figures. Present results disclose that the Lorentz force strongly lessens the hybrid nanofluid velocity. Elevating the Grashof number values enhances the rate of blood flow. Growing values of the angle parameter cause to reduce the resistance impedance on the wall. Hybrid nanoparticles have a superior wall shear stress than copper nanoparticles. The heat transfer rate is amplifying at the axial direction with the growing values of nanoparticles concentration. The applied Lorentz force significantly reduces the hybrid and unitary nanofluid flow rate in the axial direction. The hybrid nanoparticles expose a supreme rate of heat transfer than the copper nanoparticles in a blood base fluid. Compared to hybrid and copper nanofluid, the blood base fluid has a lower temperature.

Fins, referred to as extended surfaces, play a crucial role in enhancing heat transfer across various industrial sectors. They achieve this by increasing the surface area available for convective heat transfer. These widespread applications span fields such as energy production, mechanical engineering, surface studies, heat recovery processes, and chemical engineering. The broad utility of fins has prompted researchers to enhance their precision through diverse methods, including numerical, experimental, and analytical approaches. Motivated by these practical applications, this study undertakes a theoretical investigation to analyze the effects of varying fin heights on the behavior of a hybrid hydromagnetic nanofluid within a porous square enclosure. The study explores three distinct cases. In the first case, fixed-height heat fins are attached to the upper and lower walls. In the second case, the fin attached to the upper wall remains static, while those on the lower wall are extended from 0.25L to 0.5L. Conversely, the third case involves extending the height of the upper fin from 0.25L to 0.5L. The in-house MATLAB code, coupled with a finite difference method, is employed to solve the governing equations, and its reliability is confirmed through comparison with prior publications. Thorough numerical simulations are conducted, encompassing control parameters such as thermal radiation, Rayleigh number, nanoparticle volume fraction, Hartmann number, heat generation/absorption, and Darcy number. The numerical results are visually presented through streamlines, isotherms, and average Nusselt number plots, elucidating the impact of these parameters across a range of scenarios. It is noticed that case 3 exposes a 96.06% higher heat transfer rate than case 2 with higher values of volume fraction and Rayleigh number. In all three cases, the Rayleigh number and Hartmann number cause a reduction in the entropy generation. For a higher Rayleigh number, employing a hybrid nanofluid containing a volume fraction of 5% causes a 110.41% reduction in heat transfer for the case involving bottom fin height compared to case 1. Similarly, extending the top fin leads to a heat transfer reduction of 100.41%.