In this article, numerical investigation is carried out for the unsteady MHD mixed convection flow of radiating and chemically reacting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion. The transport model employed includes the Hall current. A uniform magnetic field is applied transversely to the direction of the fluid flow. The flow consideration is subject to small magnetic Reynolds number. The Rosseland approximation is used to describe the radiation heat flux in the energy equation. The dimensionless governing system of partial differential equations of the flow has been solved numerically by employing the finite element method. The influence of pertinent parameters on primary velocity, secondary velocity, temperature and concentration are presented graphically whereas primary skin friction, secondary skin friction, Nusselt number and Sherwood number are presented in tabular form. A comparison of the present method was madewith the exact solution obtained by Rajput and Kanaujia (2016) by considering primary and secondary skin frictions, it was noticed that a very good agreement.
 Keywords: MHD, radiation parameter, chemical reaction parameter, magnetic parameter, Hall current.
A finite element numerical simulation is undertaken to explore the aspects of angled magnetic field and thermo-diffusion on an unsteady reacting mixed convection flow of hydro-magnetic Casson dissipating fluid with thermal radiation. The fluid streams across an oscillating tilted plate ingrained in a porous medium including time-altering temperature and concentration. The dimensionless flow, guiding partial differential equations along their associated initial and boundary conditions, are handled, enforcing an efficient finite element scheme. The key parameters affecting the velocity, temperature, and concentration profiles are comprehensively interpreted through graphical representations while the skin friction, heat transfer, and mass transfer rates are outlined via tables. The ultimate results of this study posted that the plate inclination angle, Casson parameter, and applied magnetic strengths are compelled to impede the fluid velocity and local skin friction, whereas the porosity parameter displays a reverse effect. The thermo-diffusion effect amplifies the fluid velocity and species concentration. It also supports that the Eckert number and heat source boost up the velocity and temperature profiles. Moreover, increasing radiation parameter and time crusade results in an upsurge in the Nusselt number. The chemical reaction quickens the Sherwood number, but it decays with the thermo-diffusion parameter. A comparative analysis between the current findings and existing research works in the literature demonstrates the results' precision and exactitude.
This effects of viscous dissipation, angled magnetic field, Joule heating, and buoyancy forces on the conjugate heat and mass transport mixed convection stream of heat consuming hydro-magnetic Casson fluid from a permeable oscillating plate in a porous medium with suction/blowing in the existence of chemical reaction and radiation have been studied. The heat and mass transmission aspect are interpreted through the processes of conjugate heat and mass transport. This kind of study has not been analyzed earlier; hence the results of this study are novel. The model elucidatory coupled nonlinear PDEs are incurred and numerically tackled via the intense Galerkin finite element numerical scheme. Computational results showing disposition of the velocity, concentration, and the temperature profiles owing to the emerging parameters variation are displayed via graphic representations, whereas the skin-friction, Sherwood and Nusselt numbers are in tables. The study reveals that an expanding thermal radiation, heat dissipation, and conjugate heat transfer magnifies the temperature and velocity distributions, but heat consumption has shown contrary impact. An accentuating chemical reaction compresses the concentration and velocity distributions, but conjugate mass transfer impact witnessed an opposite trend. The rising Casson parameter and magnetic parameter slackens the fluid velocity, whereas porosity parameter displays the adverse effect. The fluid velocity is lessened by escalating phase angle but it upsurges with inclination angle of magnetic field. Further, it is acclaimed that the activity of suction slenderizes the fluid velocity, concentration, and temperature, while blowing has shown contrary nature. Comparative analysis reveals that our findings are in agreement with the one factual in the literature.
In this article, numerical investigation is carried out for the unsteady MHD mixed convection flow of radiating and chemically reacting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion. The transport model employed includes the Hall current. A uniform magnetic field is applied transversely to the direction of the fluid flow. The flow consideration is subject to small magnetic Reynolds number. The Rosseland approximation is used to describe the radiation heat flux in the energy equation. The dimensionless governing system of partial differential equations of the flow has been solved numerically by employing the FEM. The influence of pertinent parameters on primary velocity, secondary velocity, temperature and concentration are presented graphically whereas primary skin friction, secondary skin friction, Nusselt number and Sherwood number are presented in tabular form. The findings of the present study are in good agreement with the earlier reported studies.
This study examines the diffusive–bioconvective magnetohydrodynamic (MHD) flow of a hybrid nanofluid past an exponentially stretching sheet embedded in a porous medium, incorporating thermal radiation, viscous dissipation, Soret–Dufour effects, and gyrotactic microorganisms. The hybrid nanofluid, consisting of nanoparticles (Ag + TiO 2 ) suspended in water, is employed to enhance thermal conductivity and overall heat transfer performance. The governing nonlinear partial differential equations for the incompressible, steady, and two‐dimensional flow are transformed into a system of ordinary differential equations via appropriate similarity variables and solved numerically using the finite element method (FEM). Comprehensive parametric analyses reveal that the fluid velocity decreases with increasing magnetic field strength and suction parameter, while it rises under the influence of viscous dissipation, thermal radiation, and the Dufour effect. The temperature field is significantly augmented by thermal radiation, viscous dissipation, and coupled Soret–Dufour mechanisms. The concentration field diminishes with stronger chemical reactions and higher Lewis numbers but grows with the Soret effect. Furthermore, skin friction coefficient increases notably with magnetic field intensity, viscous dissipation, and Soret–Dufour parameters. Both the local Nusselt number and Sherwood number exhibit declining trends with rising heat generation and chemical reaction rate, respectively. The computed results demonstrate excellent agreement with established benchmark solutions.
This study investigates the consequence of thermal radiation on the fractional magnetohydrodynamic (MHD) Couette flow of a Jeffrey fluid in a vertical channel, incorporating the influences of activation energy and Joule heating. The mathematical model is derived using appropriate governing equations that account for the non-Newtonian behavior of the Jeffrey fluid, combined with the impacts of thermal radiation, magnetic field, and activation energy mechanisms. The classical mathematical framework has been transformed into a system of fractal fractional-order derivatives using the Caputo–Fabrizio derivative operator. To solve these systems, the finite difference technique was employed. The behavior of fluid flow fields in response to several significant parameters was analyzed and represented graphically. It is ascertained that velocity distribution upsurges as Hall current parameter rises, while a more substantial effect from the Jeffrey fluid parameter results in a decrease in the velocity field. Additionally, thermal field profiles exhibited higher values in response to increased thermal radiation and Joule heating parameters, whereas the temperature distribution showed a decline with improving in Hall current parameter values. The concentration field improved with higher activation energy parameter values, in contrast to the opposite trend observed with temperature difference and chemical reaction parameters. Furthermore, it is remarked that fractal fractional-order derivatives operator produced a more pronounced boundary layer compared to both fractional and classical models. It is ascertained that the Nusselt number showing a 15.7% improvement in thermal efficiency as thermal radiation varied from 2 to 4. These findings are important for applications in geothermal energy extraction, and biomedical engineering.
Abstract The current investigation is purported on viscous heating dissipation and Hall consequences on mixed convection magneto‐hydrodynamic heat captivating fluid transmitting from an impulsively starting vertical porous plate with ramp surface temperature and concentration in the existence of chemical reaction and radiation. The dimensional flow dominating partial differential equations is translated into a non‐dimensional partial differential form by adopting appropriate variables and parameters. A finite element approach is driven to simplify the resulting dimensionless nonlinear linked partial differential equations with initial and boundary stipulates. The after‐effects of flow commanding parameters on the velocity components, temperature and concentration are broadly analysed graphically, whereas both primary and secondary shear stresses, heat and mass transferral rates close to the surface area of the plate are discussed in tables. The ultimate results of this research revealed that viscous heating dissipation, Hall current, and thermal and mass buoyancy responses intensify both velocity components, whereas the efficacy of magnetic fields and radiation degrade both velocity components. The temperature distribution devalues with increasing heat absorption and Prandtl number, but a contrary impulse was noted with viscous heating dissipation. Likewise, concentration distribution expands with time progress but decays with chemical reaction parameters. A comparative analysis among the current results and certain research studies in the literature manifests the results’ precision and correctness.
ABSTRACT This study investigated the dissipative effects on time‐dependent Casson nanofluid motion over a cone, considering variable heat source/absorption and higher‐order reacting species. Water ethylene glycol was employed as the Casson base fluid. The dimensional PDEs were transformed into dimensionless PDEs by fitting non‐dimensional parameters and solved using an effectual Galerkin finite element method (GFEM). The impact of physical parameters on momentum, energy, and concentration profiles is analyzed via graphical representations. The wall friction, thermal, and solutal transport rates are tabularly detailed. It was detected that increasing the absorbency parameter, Eckert number, thermal radiation, and thermal generation improves fluid velocity. Conversely, intensifying the magnetic field, Prandtl number and inclination angle reduces fluid velocity. The nanofluid temperature declines with a mounted Prandtl number and nanoparticle volume fraction, and the opposite effect is perceived with increased Eckert, Dufour, and Soret numbers. Wall friction intensifies with rising porosity, magnetic field strength, Casson parameter, and diffusive parameters, while it diminishes with higher nanoparticle volume fraction. The findings distinctly indicate that nanofluid exhibits superior effectiveness in enhancing thermal and mass exchanges compared to nanofluid. Furthermore, a comparative analysis agrees with earlier findings. This current model problem finds application across various scientific, engineering, and technological domains, including energy production, space exploration, food preservation, agricultural product manufacturing, materials processing, astrophysical phenomena, biomedical procedures, and enhanced oil recovery.
