The present paper examines the flow behavior and separation region of a non-Newtonian electrically conducting Casson fluid through a two-dimensional porous channel by using Darcy's law for the steady and pulsatile flows. The vorticity-stream function approach is employed for the numerical solution of the flow equations. The effects of various emerging parameters on wall shear stress and stream-wise velocity are displayed through graphs and discussed in detail. It is noticed the increasing values of the magnetic field parameter (Hartman number) cause vanishing of the flow separation region and flattening of the stream-wise velocity component. The study also reveals that the non-Newtonian character of Casson fluid bears the potential of controlling the flow separation region in both steady and pulsating flow conditions. Non-Newtonian fluids have earned a lot of attention because of a wide range of their applications in science and engineering. Various models such as Jeffery fluid, elastic fluid, micro-polar fluid, and Casson fluid are termed as non-Newtonian fluids. The mechanics of non-Newtonian fluids pose challenges for scientists, engineers, and mathematicians because of their versatility 1-3. Casson fluid is a non-Newtonian fluid introduced by Casson 4. Casson fluid is a shear-thinning liquid that is supposed to have an infinite viscosity at zero shear rate, yield stress below which there is no flow and zero viscosity at an infinite shear rate 5. This means that if the shear stress is lower than the yield stress, it acts like a solid. However, Casson fluid tends to flow as the shear stress surpasses the yield stress. Some examples of Casson fluid are Jelly, salt solutions, ketchup, paints, shampoo, tomato sauce, honey, soup, concentrated fruit juices, etc. Human blood is assumed to have low electric conduction. It is remarkably affected by a magnetic field 6. The phenomenon of blood flow through narrow vessels at low shear rates can be described precisely as a Casson fluid. Numerous studies have been performed regarding blood flow with varying hematocrits, blood temperature, and blood behavior as a Casson fluid 7-9. The findings of such analyses help in the development of models such as for the blood oxygenators and haemodialysers. Sarifuddin 9 analyzed the effects of stenosis and mass transfer on arterial flow. Siddiqui et al. 10 studied blood pulsation within the stenotic artery by modeling blood as a Casson fluid and discussed how the blood flow is affected by the pulsation, stenosis, and non-Newtonian behavior. Priyadharshini and Ponalagusamy 11 studied the influence of MHD on blood parameters with magnetic nanoparticles in a stenosed artery. Fredrickson 12 discussed the steady flow of a Casson fluid. Dash et al. 5 investigated Casson fluid moving in a porous vessel. Mustafa et al. 13 analyzed an unsteady boundary layer flow and heat transfer of a Casson fluid. They used the Homotopy Analysis Method in the study. Hayat et al. 14 studied non-Newtonian fluid boundary layer flows caused by a stretching sheet....

This article presents a numerical investigation of the pulsatile flow of non-Newtonian Casson fluid through a rectangular channel with symmetrical local constriction on the walls. The objective is to study the heat transfer characteristics of the said fluid flow under an applied magnetic field and thermal radiation. Such a study may find its application in devising treatments for stenosis in blood arteries, designing biomechanical devices, and controlling industrial processes with flow pulsation. Using the finite difference approach, the mathematical model is solved and is converted into the vorticity-stream function form. The impacts of the Hartman number, Strouhal number, Casson fluid parameter, porosity parameter, Prandtl number, and thermal radiation parameter on the flow profiles are argued. The effects on the axial velocity and temperature profiles are observed and argued. Some plots of the streamlines, vorticity, and temperature distribution are also shown. On increasing the values of the magnetic field parameter, the axial flow velocity increases, whereas the temperature decreases. The flow profiles for the Casson fluid parameter have a similar trend, and the profiles for the porosity parameter have an opposite trend to the flow profiles for the magnetic field parameter. The temperature decreases with an increase in the Prandtl number. The temperature increases with an increase in the thermal radiation parameter. The profile patterns are not perfectly uniform downstream of the constriction.

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The use of experimental relations to approximate the efficient thermophysical properties of a nanofluid (NF) with Cu nanoparticles (NPs) and hybrid nanofluid (HNF) with Cu-SWCNT NPs and subsequently model the two-dimensional pulsatile Casson fluid flow under the impact of the magnetic field and thermal radiation is a novelty of the current study. Heat and mass transfer analysis of the pulsatile flow of non-Newtonian Casson HNF via a Darcy–Forchheimer porous channel with compliant walls is presented. Such a problem offers a prospective model to study the blood flow via stenosed arteries. A finite-difference flow solver is used to numerically solve the system obtained using the vorticity stream function formulation on the time-dependent governing equations. The behavior of Cu-based NF and Cu-SWCNT-based HNF on the wall shear stress (WSS), velocity, temperature, and concentration profiles are analyzed graphically. The influence of the Casson parameter, radiation parameter, Hartmann number, Darcy number, Soret number, Reynolds number, Strouhal number, and Peclet number on the flow profiles are analyzed. Furthermore, the influence of the flow parameters on the non-dimensional numbers such as the skin friction coefficient, Nusselt number, and Sherwood number is also discussed. These quantities escalate as the Reynolds number is enhanced and reduce by escalating the porosity parameter. The Peclet number shows a high impact on the microorganism’s density in a blood NF. The HNF has been shown to have superior thermal properties to the traditional one. These results could help in devising hydraulic treatments for blood flow in highly stenosed arteries, biomechanical system design, and industrial plants in which flow pulsation is essential.

This work aimed to analyze the heat transfer of micropolar fluid flow in a constricted channel influenced by thermal radiation and the Lorentz force. A finite difference-based flow solver, on a Cartesian grid, was used for the numerical solution after transforming the governing equations into the vorticity-stream function form. The impact of various emerging parameters on the wall shear stress, axial velocity, micro-rotation velocity and temperature profiles is discussed in this paper. The temperature profile is observed to have an inciting trend towards the thermal radiation, whereas it has a declining trend towards the Hartman and Prandtl numbers. The axial velocity profile has an inciting trend towards the Hartman number, whereas it has a declining trend towards the micropolar parameter and Reynolds number. The micro-rotation velocity escalates with the micropolar parameter and Hartman number, whereas it de-escalates with the Reynolds number. The Nusselt number is observed to have a direct relationship with the Prandtl and Reynolds numbers.