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This research study discusses the flow of a magnetohydrodynamic Casson fluid under the influence of Soret, Dufour, and thermal radiation. Nonlinear partial differential equation (PDE) of governing equations is transformed into a dimensionless version of the modified PDEs presented in terms of dimensionless parameters. The solution of coupled PDEs is obtained by the finite difference method with a combination of the quasilinearization technique. The effects of various dimensionless parameters are shown graphically, such as buoyancy force (λ $\lambda $), concentration buoyancy force (λC) $({\lambda }_{{\rm{C}}})$, Casson parameter (β $\beta $), magnetic parameter (H $H$), thermal radiation (Rd $Rd$), Darcy parameter (K0 ${K}_{0}$), Forchheimer (fr), Dufour (Df ${D}_{f}$), Soret (Sor), Brownian motion (Nb $Nb$), thermopohersis (Nt $Nt$), and Lewis number (Le $Le$). Prevention of heat transfer in the industrial system is critical, the velocity behavior (F $F$), thermal variation (θ $\theta $), and concentration profile (ϕ $\phi $) are more prominent in the roles of coal, gas, and solar thermal collectors. [ABSTRACT FROM AUTHOR]

The flow of micropolar nanofluids affected by the phenomena of MHD and thermal radiation through a regular and irregular vertical plate is examined in the present study. The primary goal of the research is to investigate the influence of boundary irregularities on the flow and heat transfer phenomena while considering the phenomena of Brownian motion, MHD, thermal radiation, and thermophoresis. The similarity transformation is applied to the flow’s governing momentum and energy nonlinear coupled partial differential equations, converting them into linear coupled ordinary differential equations. The coupled ODEs are numerically solved using a quasilinearization technique and finite difference schemes. The physical effects of Brownian motion, MHD, heat radiation, and thermophoresis are explored through data and illustrations. The importance of MHD in controlling flow and boundary layer thickness is demonstrated in particular by showing the impact of crucial physical parameters such as the buoyancy force and the Brownian motion parameter. Also, more significant effects on velocity, temperature profiles, and heat transfer rate are observed in irregular boundaries than in regular boundaries. [ABSTRACT FROM AUTHOR]

Objective: The objective of the current study is to deal with magnetohydrodynamic (MHD) nanoliquid flow over moving vertical plate with variable Prandtl numbers and viscosities. This analysis also includes the influence of thermal radiation. Quite significant variation in viscosity and Prandtl number in highrange temperature is observed. Thus, Prandtl number and viscosity are surmised to vary as an inversely proportional linear function of temperature. Problem definition: The MHD nanoliquid flow is considered along with the semi-infinite plate with the velocity Uw toward the x-direction, which is also the direction for free-stream velocity (U∞). The geometrical sketch of the physical problem with the coordinate system is shown in Figure 1. The coordinate system has two coordinate axes: the ξ-coordinate (x) and η-coordinate (y). They are perpendicular to each other. The mathematical modeling of physical problem has been formulated by incorporating viscous terms into the governing equation related to thermal radiation, buoyant force, Brownian motion, thermophoresis, and magnetic parameter. Methodology: The mathematical modeling of current physical problem consists of highly nonlinear partial differential equations which have been solved numerically using quasilinearization technique along with finite difference method. The present outcome during numerical simulation is outlined in terms of velocity, temperature, and concentration profiles and they are analyzed with suitable physical reasons. Main results: The impact of various parameters on the velocity, temperature, and concentration profiles has been discussed with physical explanation. Velocity profile (F) of the fluid enhances and concentration (ϕ) reduces with escalating buoyancy parameter (λ). In particular, 13% increment in velocity profile is observed as λ increases by 0.9 scale [0.9 → 1.8], whereas 17% reduction in concentration profiles is noticed as λ increases by 0.5 scale [1.5 → 2.0] at other fixed parameters. It is observed that magnetic parameter (H) increases the temperature (θ) and concentration profiles (ϕ), whereas it works as deduction parameter for velocity profile (F). The increasing value of thermophoresis (Nt) and Lewis number (Le) works as catalyst for velocity, temperature, and concentration profiles. As thermophoresis (Nt) increases from 0.5 to 2.0, temperature profile approximately increases 65% at other fixed parameters. As Lewis number (Le) increases from 0.5 to 4.0, then the temperature increases approximately 75% at other fixed parameters. [ABSTRACT FROM AUTHOR]