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The presence and progression of stenosis disturb the normal circulation of blood through an artery and cause serious consequences. The proposed investigation is aimed to assess non-Newtonian characteristics of blood in an elliptical artery having stenosis. The blood is taken as Sutterby fluid flowing via a multi-stenosed elliptical cross-section artery.

The analytical solution of a mathematical model representing the considered problem is extracted in a non-dimensional form by utilizing the perturbation technique under the mild stenosis assumptions.

The graphical nature of these results is examined and discussed comprehensively for different physical parameters. The height and shape of stenosis are noted to have prominent effects on flow velocity. The wall shear stress and flow velocity attained high values in the stenotic portion of the artery. The non-uniform stenosis is observed to create higher resistance to the flow than the uniform stenosis. Further, a high disorder is noticed in the constricted region of the artery by streamlines analysis.

The manuscript completely comprehends the blood’s non-Newtonian flow in the arteries of elliptical shape having multiple stenoses. The present study is about the properties of non-Newtonian blood flow through an elliptical artery with many stenoses. The Sutterby fluid model is used to describe the blood’s non-Newtonian nature. By utilizing presumptions of mild stenosis, the mathematical model’s non-linearity is decreased, and the perturbation method is applied to generate the resulting equations.

The presence of stenosis can significantly impact the circulation of blood flow. When an artery becomes narrowed, it can create a constriction or obstruction in the flow path of blood, which can lead to several important fluid dynamics phenomena, i.e. increased velocity, shear stress, pressure drop, etc. The presence of stenosis can cause various damages and complications in the affected blood arteries and surrounding tissues, resulting in heart attacks or diseases like atherosclerosis.

The work presented in the manuscript was not published earlier in any form.

This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.

Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.

Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.

Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.

This paper aims to explore dual solutions for the flow of a hybrid nanofluid over a permeable melting stretching/shrinking sheet with nanoparticle shape factor, second-order velocity slip conditions and viscous dissipation. The hybrid nanofluid is formulated by dispersing alumina (Al₂O₃) and copper (Cu) nanoparticles into water (H₂O).

The governing partial differential equations (PDEs) are first reduced to a system of ordinary differential equations (ODEs) using a mathematical method of similarity transformation technique. These ODEs are then numerically solved through MATLAB’s bvp4c solver.

Key parameters such as slip parameter, melting parameter, suction parameter, shrinking parameter and Eckert number are examined. The results reveal the existence of two distinct solutions (upper and lower branches) for the transformed ODEs when considering the shrinking parameter. Increasing value of Cu-volume fraction and the second-order velocity slip enhances boundary layer thicknesses, whereas the heat transfer rate diminishes with rising melting and suction parameters. These numerical results are illustrated through various figures and tables. Additionally, a stability analysis is performed and confirms the upper branch is stable and practical, while the lower branch is unstable.

The analysis of hybrid nanofluid flow over a shrinking surface has practical significance with applications in processes such as solar thermal management systems, automotive cooling systems, sedimentation, microelectronic cooling or centrifugal separation of particles. Both steady and unsteady hybrid nanofluid flows are relevant in these contexts.

While the study of hybrid nanofluid flow is well-documented, research focusing on the shrinking flow case with specific parameters in our study is still relatively scarce. This paper contributes to obtaining dual solutions specifically for the shrinking case, which has been less frequently addressed.

This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous stretched sheet near a stagnation point. Also, the qualities of viscous dissipation, Cattaneo–Christove heat flux and Arrhenius activation energy are taken into account. Thermophoresis, Brownian motion and Joule heating are also considered.

The Navier–Stokes equation, the thermal energy equation and the Solutal concentration equations are the governing mathematical equations that describe the flow and heat and mass transfer phenomena for fluid domains. By using the proper similarity transformations, a set of ordinary differential equationss are retrieved from boundary flow equations. The classical Runge–Kutta fifth-order algorithm along with the shooting technique is implemented to solve the obtained first order differential equations.

The study concludes that the temperature distribution boosting for thermal radiation, magnetic field and Eckert number where as the velocity and entropy generation escalate for the Williamson parameter, diffusion parameter and Brinkman number. The skin-friction and heat and mass transfer rate increases with the fluid injection. In addition, tabulated values of friction drag and rate of heat and mass transfer for various values of constraints are provided.

The comparison of the present results is carried out with the published results and noted a good agreement.