In this paper, we explored the impact of thermally radiative MHD flow of Williamson nanofluid over a stretchy plate. The flow in a stretchy plate is saturated via Darcy–Forchheimer relation. Cattaneo–Christov heat-mass flux theory is adopted to frame the energy and nanoparticle concentration equations. Additionally, the mass transfer analysis is made by activation energy and binary chemical reaction. Activation energy is invoked through the modified Arrhenius function. The intention of the current investigation is to enhance the heat transfer rate in industrial processes. The non-Newtonian nanofluids have more prominent thermal characteristics compared to ordinary working fluids. The governing models are altered into ODE models, and these models are numerically solved by applying the MATLAB bvp4c algorithm. The graphical and tabular interpretations have scrutinized the impact of sundry distinct parameters. The fluid speed escalates for enhancing the Richardson number, and it falls off for higher values of the Weissenberg number. It is noticed that the fluid temperature declines for higher values of the Brownian motion parameter and it grows for larger values of the thermophoresis parameter. The activation energy enriches the heat transfer gradient and suppresses the local Sherwood number. Additionally, the more significant heat transfer gradient occurs in heat-absorbing nonradiative viscous nanofluid and a smaller heat transfer gradient occurs in heat-generating radiative Williamson nanofluid. Also, we noticed that a higher heat transfer gradient appears in the Fourier model than in the Catteneo–Christov model. In addition, the comparative results are confirmed and reached an outstanding accord.

This study explains the impression of MHD Maxwell fluid with the presence of thermal radiation on a heated surface. The heat and mass transmission analysis is carried out with the available of Cattaneo–Christov dual diffusion. The derived PDE equations are renovated into ODE equations with the use of similarity variables. HAM technique is implemented for finding the solution. The importance of physical parameters of fluid velocity, temperature, concentration, skin friction, and heat and mass transfer rates are illustrated in graphs. We found that the fluid velocity declines with the presence of the magnetic field parameter. On the contrary, the liquid temperature enhances by increasing the radiation parameter. In addition, the fluid velocity is low, and temperature and concentration are high in Maxwell fluid compared to the viscous liquid.

The magneto-hydrodynamic dual convection stagnation flow pattern behavior of a Tangent Hyperbolic (TH) fluid has been reported in this study. The radiation, Joule heating, and heat generation/absorption impacts have also been analyzed. The flow-narrating differential equations, which are constrained by a thermal and solutal stratified porous medium, are transmuted into a system of nonlinear differential equations. To provide a numerical solution to the flow problem, a computational model is created. Numerical solutions are obtained using the fifth-order exactness program (Bvp5c), and for validation of the results, a comparison is also made with the methodology of the Runge–Kutta fourth order. The physical implications are appraised and depicted using diagrams or tables against flow-controlling parameters, such as Hartmann number, porosity parameter, solutal stratification, the parameter of curvature, temperature stratification, local Weissenberg number, Schmidt number, etc. It has been observed that in the appearance of Joule heating phenomena, the fluid temperature is a lowering function of thermal stratification. The findings are compared to the existing literature and found to be consistent with earlier research.

The aim of this study is to examine the Darcy–Forchheimer flow = of $H_{2}O$-based $Al-A{l}_2{O}_3/$$Cu-A{l}_2{O}_3$ hybrid nanofluid past a heated stretchable plate including heat consumption/ generation and non-linear radiation impacts. The governing flow equations are formulated using the Naiver–Stokes equation. These flow equations are re-framed by using the befitted transformations. The MATLAB bvp4c scheme is utilized to compute the converted flow equations numerically. The graphs, tables, and charts display the vicissitudes in the hybrid nanofluid velocity, hybrid nanofluid temperature, skin friction coefficient, and local Nusselt number via relevant flow factors. It can be seen that the hybrid nanofluid velocity decreased as the magnetic field parameter was increased. The hybrid nanofluid temperature tended to rise as the heat absorption/generation, nanoparticle volume friction, and nonlinear radiation parameters were increased. The surface drag force decreased when the quantity of the magnetic parameter increased. The larger size of the radiation parameter led to enrichment of the heat transmission gradient.