The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro‐annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev‐based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence.

The problem of coupled heat and mass transfer by free convection of a chemically reacting viscous incompressible and electrically conducting fluid confined in a vertical channel bounded by wavy wall and flat wall in the presence of diffusion-thermo (Dufour), thermal-diffusion (Soret) and internal heat source or sink is studied. The walls are maintained at constant but different temperatures and species concentrations. A uniform magnetic field β 0 is acting transversely to the walls which are assumed to be electrically non-conducting. The dimensionless governing equations are perturbed into mean part (zeroth-order) and perturbed part (first-order), using amplitude as a perturbation parameter. The first-order quantities are obtained by long wave approximation. The resulting set of coupled ordinary differential equations are solved numerically using the Adomian decomposition method. Some of the results indicating the influence of various parameters on the zeroth-order and first-order fluid flow, heat and mass transfer characteristics are presented graphically.

In this study, various fluid physical quantities effects such as diffusion-thermo, thermal-diffusion, thermal radiation, viscous dissipation, inclined magnetic field on unsteady MHD slip flow over a permeable vertical plate are considered. The coupled and nonlinear partial differential governing equations consisting of momentum, energy and species equations are reduced to ordinary differential equations using perturbation technique. The resulted coupled, nonlinear ordinary differential equations are solved by using collocation method with the aid of assumed Legendre polynomial. The impacts of different physical parameters on fluid properties are discussed and presented both graphically and tabularly. Both Dufour and Soret have the tendency of enhancing velocity profiles.

Investigation of the effect of slip on natural convective flow and heat transfer of a viscous incompressible fluid confined within a channel made up of a long vertical wavy wall and a parallel flat wall is carried out in this article. It is assumed that at the flat wall, there exists the slip condition. The coupled non-linear differential equations governing the fluid flow subjected to the relevant boundary conditions were perturbed and the resulting zero- and first-order set of equations were solved, using Adomian decomposition technique with the MAPLE 18 software. A comparison between the present study and an earlier one not involving a slip parameter and for which a different solution technique was used is carried out and the results are found consistent. The effects of various parameters involved in the problem viz Grashof number, slip parameter, heat source parameter, and wavelength parameter on the zero- and first-order temperature profile, velocity profile, skin friction, and Nusselt number at the walls are presented graphically and discussed quantitatively.

This study investigates the boundary layer motion of Williamson fluid over an electromagnetic with thermophoretic movement, variable thermal conductivity and viscosity, nonlinear radiation, and ± $\pm $Soret‐Dufour influences. The real prediction of regional movement and temperature‐dependent properties of the non‐Newtonian fluids in real space (three‐dimensional [3D]) becomes imperative due to their numerous industrial, engineering, and biomedical use. This flow motion is induced as a result of the introduced mechanism (Riga plate) capable of controlling a weakly hydromagnetic flow. To actualize the aim of this study, the formulated governing partial differential equations conveying the flow model of Williamson fluid in a 3D sense are transformed to systems of ordinary differential equations (ODEs) via applicable similarity variables. The reduced systems of ODEs are solved numerically by the collocation approach. Therein, the Riga surface is seen preventing the heat source/sink impact on the flow fields, the thermophoretic impact indicates a more accumulation of Williamson fluid particles in the cold region thus resulting in higher fluid concentration. Thermal variability energizes the energy field positively, momentum boundary layer reduction prevails for higher Williamson number while heat source dominates the temperature field and heat sink showcases its ability to enhance the fluid concentration in contrast to the heat source.