The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

This article explores the impact of a magnetic dipole on the heat transfer phenomena of different nano-particles Fe (ferromagnetic) and Fe₃O₄ (Ferrimagnetic) dispersed in a base fluid ( $60\%$ water + $40\%$ ethylene glycol) on micro-polar fluid flow over a stretching sheet. A magnetic dipole in the presence of the ferrities of nano-particles plays an important role in controlling the thermal and momentum boundary layers. The use of magnetic nano-particles is to control the flow and heat transfer process through an external magnetic field. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations by using appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The impact of different physical parameters on the velocity, the temperature, the Nusselt number, and the skin friction coefficient is shown. The velocity profile decreases in the order Fe (ferromagnetic fluid) and Fe₃O₄ (ferrimagnetic fluid). Furthermore, it was observed that the Nusselt number is decreasing with the increasing values of boundary parameter $(\delta )$ , while there is controversy with respect to the increasing values of radiation parameter $(N)$ . Additionally, it was observed that the ferromagnetic case gained maximum thermal conductivity, as compared to ferrimagnetic case. In the end, the convergence of the finite element solution was observed; the calculations were found by reducing the mesh size.

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid’s viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.