In this numerical examination, the thermal stability of an electrically conducting nanofluid is deliberated comprehensively by considering the presence of an externally applied magnetic field along with an imposed vertical throughflow. Additionally, this thin nanofluidic layer is supposed to have a Newtonian rheological behavior, heated from below, and confined horizontally between two permeable rigid plates of infinite extension. Herein, the governing conservation equations are strengthened realistically by the revised version of the Buongiorno's mathematical model, in which the vertical component of the mass flux of solid nanoparticles is presumed to vanish entirely at the horizontal permeable boundaries. After specifying the basic state of the present nanofluid problem, the linear stability theory and normal mode analysis technique are applied properly to obtain the principal stability equations. Finally, the eigenvalue problem derived analytically is tackled thereafter numerically via the Chebyshev-Gauss-Lobatto Spectral Method (CGLSM), in which the thermal Rayleigh number is chosen as an eigenvalue. As a main result, it was demonstrated that the throughflow effect exhibits a dual behavior on the complex dynamics of the system. However, the excreted magnetic field has always a stabilizing impact on the nanofluidic medium.

This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

Deliberation on the dynamics of non-Newtonian fluids, most especially Powell-Eyring fluid flow can be described as an open question. In this investigation, the flow and heat transfer characteristics are examined numerically by means of similarity analysis for a Powell-Eyring fluid moving over an isothermal stretched surface along the horizontal direction, whose velocity varies nonlinearly as a function of and follows a specified power-law degree formula. In order to solve the problem under consideration, the resulting system of coupled nonlinear partial differential equations with their corresponding boundary conditions is transformed into a correct similar form by utilizing appropriate similarity transformations, which are exceptionally acceptable for a particular form of the power-law stretching velocity, whose exponent is equal to . From the mathematical point of view, the similar equations of the studied flow cannot be obtained for any form of the power-law surface stretching velocity. As a result, it was found that the use of a general power-law stretching velocity results in non-similar equations. Also, appropriate numerical methods for similar and non-similar equations are used to discuss the results of engineering significance. Furthermore, correlation expressions for the skin friction and Nusselt number have been derived by applying the linear regression on the data outputted from the used computational methods.On the contrary to the heat transfer rate, it was found that the local skin friction coefficient is a decreasing property of power-law stretching.