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.

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.

Heat transfer analysis of the pulsatile flow of a hybrid nanofluid through a constricted channel under the impact of a magnetic field and thermal radiation is presented. Hybrid nanofluids form a new class of nanofluids, distinguished by the thermal properties and functional utilities for improving the heat transfer rate. The behaviors of a water-based copper nanofluid and water-based copper plus a single-wall carbon nanotube, i.e., ($Cu–SWCNT$/water), hybrid nanofluid over each of velocity, wall shear stress, and temperature profiles, are visualized graphically. The time-dependent governing equations of the incompressible fluid flow are transformed to the vorticity-stream function formulation and solved numerically using the finite difference method. The laminar flow simulations are carried out in 2D for simplicity as the flow profiles are assumed to vary only in the 2D plane represented by the 2D Cartesian geometry. The streamlines and vorticity contours are also shown to demonstrate the flow behviour along the channel. For comparison of the flow characteristics and heat transfer rate, the impacts of variations in Hartmann number, Strouhal number, Prandtl number, and the thermal radiation parameter are analyzed. The effects of the emerging parameters on the skin friction coefficient and Nusselt number are also examined. The hybrid nanofluid is demonstrated to have better thermal characteristics than the traditional one.

This article concerns heat transfer analysis in pulsating flow in a channel with walls having multiple symmetric constrictions. The flow is influenced by Lorentz force and thermal radiation. The unsteady governing equations, simplified for low conducting fluids, are solved by the finite difference method using the stream–vorticity function formulation. The effects of the emerging parameters, including the magnetic field parameter (Hartman number), Reynolds number, Prandtl number, and radiation parameter on various flow profiles, are studied. The profiles of dimensionless axial velocity, temperature, wall shear stress (WSS), skin friction coefficient, and local Nusselt number are discussed graphically. The profiles are examined at various prominent axial locations and time instants of the pulse cycle. The WSS has a direct relation with the Hartmann and Strouhal numbers. The WSS generated at the first constriction is higher than that at the second constriction. The WSS increases with an increase in the Strouhal number in the accelerating phase and decreases in the decelerating phase on both the constrictions. The temperature decreases with an increase in the Hartman and Prandtl numbers at the constricted portion of the channel. The radiation parameter directly affects the temperature and inversely affects the Nusselt number at the constricted part of the channel. However, in general, the flow profiles exhibit irregular patterns downstream of the constriction. The Nusselt profiles are higher at the first encountered constriction bump than that at the next bumps.

This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid under Lorentz force’s effect in a channel with symmetrical constrictions on the walls. The governing equations were first converted into the vorticity–stream function form, and a finite difference-based solver was used to solve it numerically on a Cartesian grid. The impacts of different flow controlling parameters, including the Hartman number, Strouhal number, Reynolds number, and MP parameter on the flow profiles, were studied. The wall shear stress (WSS), axial, and micro-rotation velocity profiles were depicted visually. The streamlines and vorticity patterns of the flow were also sketched. It is evident from the numerical results that the flow separation region near constriction as well as flattening of the axial velocity component is effectively controlled by the Hartmann number. At the maximum flow rate, the WSS attained its peak. The WSS increased in both the Hartmann number and Reynolds number, whereas it declined with the higher values of the MP parameter. The micro-rotation velocity increased in the Reynolds number, and it declined with increment in the MP parameter.

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, is 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.