This study explores the magnetohydrodynamic (MHD) flow of a Jeffrey-Hamel fluid within a convergent/divergent channel, a scenario relevant to both physical and biological sciences. The flow dynamics between nonparallel inclined walls are governed by highly nonlinear differential equations derived through conservation laws and similarity transformations. By applying similarity transformations, the governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs). The NDSolve approach is then utilized to obtain numerical solutions for these equations. A comparison with existing methods in the literature confirms the accuracy and reliability of the results. Additionally, the impact of various dimensionless physical parameters, such as the influence of the magnetic parameter, angle alpha, and the Deborah number on the velocity profile is investigated. The parameters angle alpha, Eckert number, and volume friction are examined on the temperature profile, followed by a detailed discussion of the findings.

This study aims to provide a thorough mathematical simulation of the effects of heat radiation and thermocapillarity on the time-dependent flow of couple stress ternary hybrid nanofluid across a stretching parallel surface in magneto-hydrodynamics. The ternary hybrid nanofluid consists of Ag, TiO2, Al2O3 nanoparticles dispersed within a base fluid, blood, enhancing its thermal performance. The governing partial differential equations are converted into a system of nonlinear ordinary differential equations by applying the proper similarity transformations to model the flow’s unstable behavior. After that, the Homotopy Analysis Method is used to solve these equations semi-analytically. The intricate interactions between radiative heat transport, thermocapillary forces induced by surface tension gradients, Lorentz force from the applied magnetic field, and couple stress effects are all captured in the simulation. The influence of main dimensionless parameters, including the magnetic parameter, couple stress parameter, nanoparticle volume fractions, dimensionless film thickness, unsteady parameter, thermal radiation parameter and Eckert number, on velocity profile, temperature profile, skin friction and Nusselt number in the form of graphs. According to the results, radiation improves the properties of heat transmission, whereas thermocapillarity dramatically changes the flow and thermal boundary layers. Furthermore, the fluid velocity is suppressed by the occurrence of magnetic fields and couple stress, providing information about possible control mechanisms in thermal management systems. The results’ graphical and tabular representations demonstrate how sensitive the temperature and velocity fields are to the physical parameters at play. These findings offer significant new insights into thermal management technologies and energy systems that employ complex nanofluid compositions.

This study examines the unsteady free convection flow of Casson dusty fluid within an inclined microchannel under the influence of wall shear stress and an inclined magnetic field. The fluid is assumed to contain uniformly dispersed electrically conductive dust particles, and heat is applied via Newtonian heating at one boundary. The governing partial differential equations representing the motion of both fluid and dust phases are derived and solved using the Poincaré-Lighthill Perturbation Technique (PLPT). Key physical parameters such as the Casson fluid parameter, Grashof number, magnetic field inclination, radiation, and dusty fluid interaction parameter are varied to analyze their effect on velocity and temperature profiles. Results reveal that increasing the Casson parameter reduces fluid velocity, while higher Grashof numbers and radiation levels enhance it. The magnetic field generates Lorentz forces that oppose the motion, thereby reducing both fluid and dust particle velocities. The inclined magnetic field and Newtonian heating significantly influence thermal and flow behavior. These findings have practical implications in microfluidics, industrial coatings, biomedical flows, and heat management systems, where controlling dusty fluid dynamics under external fields is crucial.

In this research, we investigate the flow of ternary nanofluids under the influence of magnetic field in converging/diverging channel. The fluid assumed to be viscous, incompressible, and electrically conducting. The effect of Lorentz force on fluid motion is systematically examined. For practical applications, stretching and shrinking channel are considered. Using similarity transformation, the governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs), which are then solved numerically with the ND-Solve technique. This method effectively handles the highly nonlinear equations and provides accurate results. The velocity and temperature profiles are presented graphically for various physical parameters, while skin friction and Nusselt number are analyzed. The results reveal that an increase in the magnetic parameter reduces the fluid velocity and enhances the temperature in both convergent/divergent channels. Furthermore, ternary nanofluids exhibit a stronger impact compared to nano and hybrid nanofluids.