The aim of this study is to analyze the effects of activation energy and thermal diffusion an unsteady MHD reactive Maxwell fluid flow past a porous stretching sheet in the presence of Brownian motion, Thermophoresis and nonlinear thermal. The non-linear partial differential equations that govern the fluid flow have been transformed into a two-point boundary value problem using similarity variables and then solved numerically by fourth order Runge–Kutta method with shooting technique. Graphical results are discussed for non-dimensional velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system. The present study is compared with the previous literature and found to be in good agreement.

This study investigates the influence of Hall current diffusion, thermo-activation energy, and other parameters on the flow characteristics of an electrically conducting Jeffrey nanofluid. The Jeffrey nanofluid flow occurs across a continually expanding surface, and additional factors like thermal radiation, heat generation/absorption, and inclined plates are included in the analysis. A vertically installed transverse magnetic field is assumed to have a modest Reynolds number. The controlling partial differential equations are transformed into nonlinear ordinary differential equations using appropriate similarity transformations. These equations are then numerically solved using the Matlab bvp4c module. This study aims to analyze the impact of many factors, including the Hall current factor, the thermal radiation factor, the heat source/sink factor, the Brownian motion factor, the thermophoresis parameter, and the magnetization, on the velocity, concentration, and temperature. To do this, graphical representations will be used as a means of visualizing and discussing the impacts, as mentioned earlier. To get a deeper understanding of the internal dynamics of the emerging parameters, a numerical computation is conducted to determine the local Nusselt number, Sherwood number, and skin friction coefficient along the x and z axes. Research findings have shown that the flow velocity exhibits a decreasing trend as the linear and nonlinear thermal radiation components rise. Furthermore, augmenting the values of the Brownian motion parameter will lead to a reduction in the concentration profile of the nanoparticle.

We explore the impact of the aligned magnetic field, buoyant force, and thermal radiation on the unsteady MHD-free convection of momentum and energy transmission in a viscous, incompressible, electrically conducting water-based Cu and TiO\(_2\) Jeffrey nanofluid. We consider radiation absorption and thermo diffusion. The flow occurs along permeable objects with isothermal inclined plates, with Cu and TiO\(_2\) in water being the focus. Analytic solutions for the governing equations of fluid velocity, temperature, and species concentration are derived using the perturbation method, considering initial and boundary conditions. Results for shear stress and the heat and mass transfer rates at the plate are presented graphically, along with tables for various flow characteristics.