Transient magnetohydrodynamic flow over a rotating vertical porous surface incorporating thermal radiation, hall and ion-slip effects: Using finite element method

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented. A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy. The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity. The governing equations are solved by the perturbation technique and a numerical method. The analytical expressions for the velocity field, the temperature field, the induced magnetic field, the skin-friction, and the rate of heat transfer at the plate are obtained. The numerical results are demonstrated graphically for various values of the parameters involved in the problem. The effects of the Hartmann number, the chemical reaction parameter, the magnetic Prandtl number, and the other parameters involved in the velocity field, the temperature field, the concentration field, and the induced magnetic field from the plate to the fluid are discussed. An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values. The induced magnetic field along the x-direction increases with the increase in the Hartmann number, the magnetic Prandtl number, the heat source/sink, and the viscous dissipation. It is found that the flow velocity, the fluid temperature, and the induced magnetic field decrease with the increase in the destructive chemical reaction. Applications of the study arise in the thermal plasma reactor modelling, the electromagnetic induction, the magnetohydrodynamic transport phenomena in chromatographic systems, and the magnetic field control of materials processing.

In this study, the heat and mass transfer rates in electrically conducting Casson ternary hybrid nanofluid flows () were investigated, considering various factors such as variable thermal conductivity, Joule heating, viscous dissipation, chemical reactions, Darcy–Forchheimer flow, and nonlinear thermal radiation. The use of ternary hybrid nanofluids, combining aluminum oxide, copper nanoparticles, and titanium oxide in blood, can significantly improve thermal conductivity and heat transfer efficiency, making them useful in engineering fields such as heat exchangers, aerospace, renewable energy, and electronic cooling. The study focuses on the effects of nonlinear thermal radiation, viscous dissipation, Joule heating, Soret number, chemical reactions, Darcy–Forchheimer effect, and curvature on the flow of Casson fluid over a stretching cylinder. The partial differential equations governing the system are transformed into ordinary differential equations using a similarity variable and solved using the Sixth‐Order Runge–Kutta (RK6) method in MATLAB, validated against previous studies for accuracy. The analysis includes the impact of physical parameters on velocity, temperature, and concentration profiles, as well as skin friction coefficient, local Nusselt number, and Sherwood number. A higher Casson parameter leads to an increased yield stress, resulting in greater resistance and a reduction in the velocity distribution. Variable thermal conductivity, nonlinear thermal radiation, Eckert number, and nanoparticle volume fraction improve heat transfer. Higher nanoparticle concentrations increase thermal conductivity, leading to improved heat transfer and higher Nusselt numbers.

This research investigates the simultaneous effects of thermal diffusion and diffusion thermo on incompressible, viscous, electrically conducting non-Newtonian Casson fluid flow past a vertically inclined surface through a porous medium in the presence of the uniform transverse magnetic field, chemical reaction, viscous dissipation, and constant heat flux. The action of thermal radiation and viscous dissipation is scrutinized. The fundamental governing equations determining the flow condition are transfigured as nonlinear coupled partial differential equations through self-similarity transmutations. The finite element technique is implemented to acquire the solution to the problem. Graphs are plotted to inspect the influence of sundry physical quantities on the three routine profiles of the flow field. Further, expressions are procured for friction factor and the rate of heat and mass transfers and discussed comprehensively through tabular forms. Favorable comparisons with previously published work on various exceptional cases of the problem are obtained. This research shows that the Soret number increases both the velocity and concentration fields, and the Dufour number increases the velocity and temperature fields. It is also observed that concentration and velocity fields reduce toward chemical reaction parameter. Furthermore, the Schmidt number decreases the velocity and concentration profiles. It is also noteworthy that velocity decays for the magnetic variable. An improvement in radiation declines the velocity and temperature profiles.

This research investigation explores the effects of viscous dissipation, radiation, Hall current, ion slip condition and nanofluid properties of Ag and TiO2 on magnetohydrodynamic (MHD) rotating, free convection flow of a permeable rotating vertical plate with a constant heat source. Governing equations describing the model are converted to dimensionless form, advocating appropriate non-dimensional variables. The study aims at understanding the impact of Hall current, ion slip effect, radiation and viscous dissipation on thermal energy transfer aspects, velocity, temperature and concentration profiles. Implementing Galerkin FEM and MATLAB, graphical representations of temperature, velocity and concentration distributions are obtained. Skin friction and Nusselt & Sherwood numbers are also tabulated for varying values of different heat transfer characteristics. The findings reveal that the velocity decreases with the increasing values of the rotation parameter but escalates with Eckert number, Hall parameter, ion slip parameter and radiation parameter. Additionally, the temperature boundary layer expands with an increase in Eckert number. The study also shows that the Sherwood number increments with the chemical reaction parameter, while the effect is reversed for the Nusselt number for the suction parameter. The results obtained are in good agreement with the available research. The results showcase potential highlights into the responses of MHD flows of nanofluids in rotating systems. The outcomes of the research can be applied in the fields of energy systems, chemical processes, environmental engineering and various other industrial processes.

Nonlinear dissipative slip flow of Jeffrey nanomaterial towards a curved surface with entropy generation and activation energy

Heat transfer analysis of steady laminar 2D flow of CNTs-blood-based nanofluid over a moving permeable plate with viscous dissipation and thermal radiation

The unsteady simulation of hydromagnetic radiative polar fluid, including thermophoresis, Brownian motion, and higher-order chemical reactions across a perpendicular permeable plate with heat radiation, is performed numerically. The nonlinear PDEs are solved by the explicit finite difference technique and studio developer FORTRAN. The stability and convergence of the present model and a comparison are done to obtain accuracy. The effects of various parameters such as Brownian motion, thermophoresis, radiative heat transfer, and higher-order chemical reactions on the velocity, temperature, and concentration fields are investigated. It is found that the parameters have a significant influence on velocity and temperature profiles, angular velocity, concentration, shear stress, angular momentum density, and Nusselt and Sherwood numbers. In addition, the local share stress rises with the chemical reaction, Eckert number, and thermophoresis, whereas it decreases with the magnetic field and porous medium. In addition, the Nu (local) intensifies with higher order chemical reactions and porous mediums, whereas it falls with Eckert number, Brownian effects, micro-rotation, and thermophoresis. The concentration profile decreases with higher radiation, and the Lewis number whereas it augments with higher radiation. With an Eckert number and thermophoresis, the temperature and velocity increase. Additionally, the higher order of chemical reaction and Brownian motion augment the Sherwood number, whereas the chemical reaction, magnetic field, and porous medium reduce it. Moreover, the study may help to understand the dynamics of flow and heat transfer for the design and optimization of various engineering applications such as heat exchangers, pollutant dispersion models, energy systems, biomedical, and so on.

The effects of chemical reactions on heat and mass transfer with radiation are extremely important in hydrometallurgical industries and chemical technology, such as polymer synthesis and food processing. A mathematical model for a viscous, incompressible, mixed convective, and MHD slip flow over a moving vertical plate is proposed in the present research. On account of physical relevance, the combined effect of radiation and chemical reaction on MHD nanofluid is studied. Using the similarity transformation method, the governing equations are converted into a system of ODEs. The transformed equations are then numerically solved by the Galerkin finite element method (GFEM). To analyse the characteristics of flow and heat transfer, a number of parameters are examined, including the slip, magnetic, radiation, and chemical reaction parameters, as well as the Schmidt, Grashof, Eckert, and Prandtl numbers. The coefficient of skin friction, Nusselt number, and Sherwood numbers for selected parameters are numerically presented. Graphs are used to determine and study the effects of magnetic fields, slip conditions, radiation, and chemical reactions on the temperature, concentration, and velocity profiles of nanofluids. This study shows that the presence of chemical reactions and radiation causes an increase in the velocity profile and temperature profile, respectively. Additionally, it is discovered that the temperature profile grows with increasing velocity slip, and concentration increases with increasing thermal slip. The current work has broad applications in various fields and can lead to the development of more efficient and effective systems in different industries, such as heat exchangers, energy production, environmental engineering, and biomedical engineering.

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

An analytical investigation is conducted to study the unsteady free convection heat and mass transfer flow through a non-homogeneous porous medium with variable permeability bounded by an infinite porous vertical plate in slip flow regime while taking into account the thermal radiation, chemical reaction, the Soret number, and temperature gradient dependent heat source. The flow is considered under the influence of magnetic field applied normal to the flow. Approximate solutions for velocity, temperature, and concentration fields are obtained using perturbation technique. The expressions for skin-friction, rate of heat transfer, and rate of mass transfer are also derived. The effects of various physical parameters, encountered in the problem, on the velocity field, temperature field, and concentration field are numerically shown through graphs, while the effects on skin-friction, rate of heat, and mass transfer are numerically discussed by tables.

The current investigations are carried out to study the influence of the Darcy–Forchheimer relation on third-grade fluid flow and heat transfer over an angled exponentially stretching sheet embedded in a porous medium. In the current study, the applied magnetic field, Joule heating, thermaldiffusion, viscous dissipation, and diffusion-thermo effects are incorporated. The proposed model in terms of partial differential equations is transformed into ordinary differential equations using suitable similarity transformation. The reduced model is then solved numerically with the help of MATLAB built-in function bvp4c.The numerical solutions for velocity profile, temperature profile, and mass concentration under the effects of pertinent parameters involved in the model are determined and portrayed in graphical form. The graphical effects of the skin friction coefficient, the Nusselt number, and the Sherwood number are also shown. From the displayed results, we conclude that when the Joule heating parameter is enlarged, the velocity and the temperature of the fluid are increased. We observed that while enhancing the viscous dissipation parameter (Eckert number) the fluid’s velocity and temperature increase but decreases the mass concentration. By increasing the values of the thermal-diffusion parameter, the velocity distribution, the temperature field, and the mass concentration increase. When the diffusion–thermo parameter rises, the velocity field and the temperature distribution increase, and the reverse scenario is seen in the mass concentration. The results of the current study are compared with already published results, and a good agreement is noted to validate the current study.

The present article investigates the collective influence of chemical reaction, viscous dissipation and Hall current magnetic effects on timedependent radiative magnetohydrodynamic flow, heat and mass transfer from an inclined wall embedded in a homogenous, isotropic highpermeability porous medium. The model developed is relevant to near wall magnetohydrodynamic energy generator transport phenomena in which chemical corrosion effects may arise during operations. The governing non-linear partial differential equations for mass, momentum, energy and species conservation are transformed into a system of coupled non-linear dimensionless partial differential equations with appropriate similarity variables. The normalized conservation equations are then solved with a robust finite element method (MATLABFEM) subject to corresponding initial and boundary conditions. Important dimensionless parameters emerging are Eckert number, thermal Grashof number, solutal Grashof number, magnetic body force parameter, Hall parameter, permeability parameter, Dufour number, Soret number, time, radiation-conduction parameter, chemical reaction parameter, heat absorption parameter, Prandtl number, Schmidt number and wall angle. Primary velocity is enhanced with Eckert number, thermal Grashof number, solutal Grashof number, Hall parameter, permeability parameter, Dufour number, Soret number, radiation-conduction parameter and time whereas it is reduced with first order chemical reaction parameter, heat absorption, magnetic body force parameter, Prandtl number, Schmidt number and wall inclination. Secondary velocity is elevated with Eckert number, solutal Grashof number, thermal Grashof number, magnetic body force parameter, Hall parameter, radiation-conduction parameter, Dufour number, Soret number and time whereas it is suppressed with reaction parameter, heat absorption, Prandtl number, Schmidt number and wall inclination. Temperature is enhanced with Eckert number, Dufour number, heat absorption, radiation-conduction parameter and time whereas it is depressed with Prandtl number. Species concentration is reduced with increasing chemical reaction parameter (destructive homogenous reaction) and Schmidt number whereas it is elevated with Soret number and time. Extensive discussion of the finite element formulation, convergence and validation is provided Skin friction, Nusselt number and Sherwood number distributions are also provided for selected parameter variation. Validation of solutions with published literature is also included for several special cases, namely non-reactive, non-dissipative flow in the absence of heat generation or absorption. Further validation is included using a multi-step differential transform method (MS-DTM). The present simulations provide an interesting insight into complex fluid/thermal/species diffusion characteristics in the boundary layer region of relevance to working MHD generator systems.

This work analyzed numerically the impacts of viscous dissipation, Joule heating and inclined magnetic field on reactive-diffusion magneto-hydrodynamic radiative mixed convection oscillatory non-Newtonian Casson fluid (CF) fluxing across a slanted semi-infinite vertical plate inserted in a porous medium. The framed dimensional flow controlling partial differential equations were modified to dimensionless partial differential equations by bringing in applicable scaling variables and then numerically solved by imposing the finite difference scheme. The outcomes are established with graphical representations to inspect the flow fields’ performance for diverse flow parameters. At the same time, numerical data of skin friction and heat and mass transferal rates near the surface area are presented in a tabular format. This research study discovered that the viscous dissipation and radiation effects intensify the temperature and velocity fields while heat ingestion has a contrary effect. Both velocity and concentration distributions are diminished by the chemical reaction and Schmidt number while the converse trend was noted with thermo-diffusion effect. The velocity distribution was narrowed by the angled magnetic field, Casson parameter, and magnetic field but the porosity parameter exposed the opposite impact. The influence of the magnetic field and Casson parameters incited to decline the friction. Heat absorption in the flow makes the Nusselt number rise but improving viscous dissipation and radiation effects have pointed to an opposite trend. The chemical reaction parameter increases the Sherwood number but thermo-diffusion decreases it. Further, validation with already published results is accomplished and an excellent agreement is realized.

An analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperaturedependent viscosity and thermal radiation on an unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate by taking into account the viscous dissipation effects. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations, which are solved numerically by using implicit finite difference scheme with shooting method. Numerical results for the non-dimensional velocity, temperature and concentration profiles as well as the local skin-friction coefficient, the local Nusselt number and the local Stanton number are presented for different physical parameters. The results show that variable viscosity significantly increases viscous drag and rate of heat transfer. The results also show that higher order chemical reaction induces the concentration of the particles for a destructive reaction and reduces for a generative reaction.

The heat transfer between ambient medium and moving material can be examined by the fluid flow past an impulsively started vertical plate (ISVP). In manufacturing processes such as wire/fiber drawing, hot rolling, continuous casting, and hot extrusion can be related to the hot moving material and heat transfer to the ambient medium. Also, a similar type of study addresses the understanding of aerospace engineering applications. This present study considers a mathematical model which describes the hybrid nanofluid past the ISVP by considering the transient term as a fractional derivative. The fractional order of flow governing equations is derived to enhance the heat transfer predictions with real-world problems by considering viscous dissipation, applied magnetic field, and radiation effects. Such a mathematical model is discretized by a finite difference technique and solved by a computational algorithm using FORTRAN. The findings of the study are illustrated using the velocity and temperature profiles. Also, the heat transfer and fluid friction against the boundary are interpreted using the Nusselt number and skin-friction coefficient, respectively. The results are examined under the variation of dimensionless parameters such as Eckert number, time-fractional order, Grashof number, the fraction of nanoparticles, suction, magnetic, and radiation parameters. It is observed that the heat transfer and fluid flows are affected by changing the time-fractional order. Also, a transition in the distribution of velocity and temperature is detected with varying time-fractional order.