Radiation and Hall effects on a 3D flow of MHD Williamson fluid over a stretchable surface

Magnetohydrodynamics (MHD) three-dimensional flow of an unsteady Williamson fluid on an enlarging surface with Hall current, radiation, heat source/sink, and chemical reaction is investigated in this article. The basic governing equations are transformed into a system of ordinary differential equations by using an appropriate similarity transformation. The system is deciphered using the shooting method. The properties of influential parameters such as parameters of magnetic field, Hall current, radiation, and so forth, on the flow are discussed with the help of graphs and tables. We noticed that the increase in the magnetic field reduces the velocity in x-direction and the rate of heat and mass transfer. We also acknowledged that the growing values of Hall current parameter boost the velocity in z-direction but it reduce the temperature and concentration distributions, respectively. The results of this study represent many applications in biomedical engineering and these results are helpful for further study of non-Newtonian fluids in various circumstances.     

MHD boundary layer bionanoconvective non‐Newtonian flow past a needle with Stefan blowing

The purpose of the article is to present a transport model for magnetohydrodynamics‐forced convective non‐Newtonian boundary flow from a thin needle in a nanofluid in the presence of microorganisms and Stefan blowing. The governing equations are reduced to ordinary differential equations with the help of similarity transformations and then numerically solved by using the Matlab bvp4c function. The effect of various emerging parameters on the flow field, heat, mass, and density of motile microorganisms transfer was computed and studied. It was found that some of the parameters have an important effect on the boundary layer thickness. Justification with earlier simpler model in the absence of magnetic field is included. The model finds applications in various transdermal delivery system, biomedical electromagnetic treatments and to design new medical devices for cell delivery to the central nervous system.     

Heat and mass transfer of MHD Jeffrey nanofluid flow through a porous media past an inclined plate with chemical reaction,radiation, and Soret effects

This paper investigates the heat and mass transfer of an unsteady, magnetohydrodynamic incompressible water-based nanofluid (Cu and TiO₂) flow over a stretching sheet in a transverse magnetic field with thermal radiation Soret effects in the presence of heat source and chemical reaction. The governing differential equations are transformed into a set of nonlinear ordinary differential equations and solved using a regular perturbation technique with appropriate boundary conditions for various physical parameters. The effects of different physical parameters on the dimensionless velocity, temperature, and concentration profiles are depicted graphically and analyzed in detail. Finally, numerical values of the physical quantities, such as the local skin-friction coefficient, the Nusselt number, and the Sherwood number, are presented in tabular form. It is concluded that the resultant velocity reduces with increasing Jeffrey parameter and magnetic field parameter. Results describe that the velocity and temperature diminish with enhancing the thermal radiation. Both velocity and concentration are enhanced with increases of the Soret parameter. Also, it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameters. This is because chemical molecular diffusivity reduces for higher values of chemical reaction parameter. Also, water-based TiO₂ nanofluids possess higher velocity than water-based Cu nanofluids. Comparisons with previously published work performed and the results are found to be in excellent agreement. This fluid flow model has several industrial applications in the field of chemical, polymer, medical science, and so forth.     

Thermal diffusion and diffusion thermo effects of Eyring‐Powell nanofluid flow with gyrotactic microorganisms through the boundary layer

In this article, the effects of thermal diffusion and diffusion thermo on the motion of a non‐Newtonian Eyring Powell nanofluid with gyrotactic microorganisms in the boundary layer are investigated. The system is stressed with a uniform external magnetic field. The problem is modulated mathematically by a system of a nonlinear partial differential equation, which governs the equations of motion, temperature, the concentration of solute, nanoparticles, and microorganisms. This system is converted to nonlinear ordinary differential equations by using suitable similarity transformations with the appropriate boundary conditions. These equations are solved numerically by using the Rung‐Kutta‐Merson method with a shooting technique. The velocity, temperature, concentration of solute, nanoparticles, and microorganisms are obtained as functions of the physical parameters of the problem. The effects of these parameters on these solutions are discussed numerically and illustrated graphically through figures. It is found that the velocity decreases with the increase in the non‐Newtonian parameter and the magnetic field, whereas, the velocity increases with a rise in thermophoresis and Brownian motion. Also, the temperature increases with an increase in the non‐Newtonian parameter, magnetic field, thermophoresis, and Brownian motion. These parameters play an important role and help in understanding the mechanics of complicated physiological flows.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature-dependent thermophysical properties

This paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature-dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.     

Radiative CNT-based hybrid magneto-nanoliquid flow over an extending curved surface with slippage and convective heating

This study concentrates on the hydrothermal prominence of a mixed convective flow of a hybrid nanoliquid over a convectively heated extending curved surface under the influence of a uniform transverse magnetic field. Two types of carbon nanotubes (CNTs), namely single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), and magnetite nanoparticles are dispersed in the host liquid (water) to simulate the hybrid nanoliquid flow model. First- and second-order velocity slip conditions and nonlinear radiative heat flux are incorporated in this model. First, the system of governing partial differential equations is changed into nonlinear ordinary differential equations through the utilization of appropriate transformations and computed numerically via MATLAB built-in function bvp4c based on the three-stage Lobatto IIIA technique. The consequences of physical and geometrical parameters pertinent to this analysis on the dimensionless physical quantities of interest are deliberated using requisite graphs and tables. Our simulation communicates that the first-order velocity slip parameter decreases the velocity profile, whereas the second-order velocity slip parameter is found to be augmented. The suspension of CNTs in the magnetite nanoliquid improves the local surface drag force but diminishes the local heat flux. Moreover, it is examined that SWCNTs have greater impacts than MWCNTs.     

Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

Variable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time-dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.     

Entropy optimized flow of Darcy-Forchheimer viscous fluid with cubic autocatalysis chemical reactions

Background and objectiveThe dynamic of entropy generation phenomenon is important in industrial and engineering process and thermal polymer processing. In order to improve the thermal efficiency of industrial and systems, the main concern of scientists is to reduce the entropy generation. The optimized frame for the Darcy-Forchheimer flow accounted by curved surface has been worked out this continuation. The applications of the chemically reactive material are focused via heterogeneous and homogeneous chemical utilizations. The thermal and velocity slip constraints are imposed for investigating the flow phenomenon. Additionally, the determination of heating phenomenon is investigated by incorporating the heat source features. The importance of entropy generation and Bejan number is also signified.MethodologyNonlinear partial systems are reduced to dimensionless differential system through suitable variables. The problem consists of highly nonlinear equations are numerically worked out with appliances of ND-solve procedure.ResultsInfluence of fluid flow, thermal field, entropy rate, concentration and Bejan number via influential variables are examined. A slower velocity change due to implementation of slip is noticed. The applications of Brinkman number offer resistance to fluid particles while an enhancement in the Bejan number is claimed.ConclusionsFor an augmentation in curvature variable, the concentration and velocity show reverse effect. There is an increase in temperature distribution against heat generation parameter. Velocity field is reduced against higher porosity and slip parameters. Temperature has revers trends against radiation and thermal slip parameters. Larger Schmidt number decreases concentration distribution. Entropy rate is augmented versus larger radiation parameters. An augmentation in Brinkman number leads to improve the velocity filed whereas it reduces the Bejan number. Brinkman number influence on Bejan number is similar to that of homogenous reaction parameter on concentration. The comparative simulations against the reported results are performed.     

Impact of the magnetic dipole on stagnation point flow of ferromagnetic Walters-B liquid: A passive control approach with Buongiorno's model

The properties of ferromagnetic fluids make them suitable for a wide range of applications, including loudspeakers, magnetic resonance imaging, computer hard drives, magnetic drug delivery, and magnetic hyperthermia. Owing to all such potential applications, the present research work is established to explain the stagnation point flow, heat, and mass transfer of Walters-B liquid in the presence of magnetic dipole, Brownian diffusion, and thermophoresis. To control the nanoparticles concentration at the surface, a passive control condition is employed. Using suitable similarity transformations, the governing equations are converted into nonlinear ordinary differential equations. Noticeable behavior of significant parameters on flow fields is studied graphically. The significant outcomes of the present study are that the increased values of viscoelastic parameter decline the velocity but an inverse trend is seen in heat transfer. The increased values of the Brownian motion parameter decline the heat transfer but a contrary trend is seen for augmented values of the thermophoresis parameter. The heat transfer rate is increased for rising values of radiation parameter and Biot number. The upward values of the thermophoresis parameter decline the rate of mass transfer. The escalating values of ferromagnetic interaction and velocity ratio parameters improve the skin friction.     

Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity

In this paper we have analyzed the combined effects of magnetic field and convective diffusion of species through a non-Darcy porous medium over a vertical stretching sheet with temperature dependent viscosity and non-uniform heat source/sink. The boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge–Kutta Fehlberg method with shooting technique for various values of the governing parameters. The effects of electric field parameter, non-uniform heat source/sink parameters and Schmidt number on concentration profiles are analyzed and discussed graphically. Favorable comparisons with previously published work on various special cases of the problem are obtained.     

The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet

The influence of temperature-dependent fluid properties on the hydro-magnetic flow and heat transfer over a stretching surface is studied. The stretching velocity and the transverse magnetic field are assumed to vary as a power of the distance from the origin. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. Using the similarity transformation, the governing coupled non-linear partial differential equations are transformed into coupled non-linear ordinary differential equations and are solved numerically by the Keller–Box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on five parameters, namely the stretching parameter, viscosity parameter, magnetic parameter, variable thermal conductivity parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are discussed.     

Electromagnetohydrodynamic boundary layer flow in hybrid nanofluid with thermal radiation effect: Numerical simulation

Hybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self-similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction.     

Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition

The investigations on the flow of non-Newtonian fluids are becoming one of the major topics in the research field. These liquids have substantial applications in industrial and engineering fields such as drilling rigs, food processing, paint and adhesives, nuclear reactors and cooling systems. On the other hand, hybrid nanofluids play a major role in the heat transfer process. Keeping this in mind, the motion of Casson hybrid nanofluid squeezing flow between two parallel plates with the effect of heat source and thermophoretic particle deposition is examined here. The partial differential equations that govern fluid flow are converted into ordinary differential equations using appropriate similarity variables and those equations are numerically solved using the Runge–Kutta–Fehlberg fourth–fifth-order method by implementing the shooting scheme. The graphs depict the effects of a number of key parameters on fluid profiles in the absence and presence of the Casson parameter. These graphs show that fluid velocity enhances with the augmentation of the local porosity parameter. Thermal dispersal upsurges for enhancement of heat source/sink parameter and the concentration profile escalates for an upsurge of the thermophoretic parameter. Skin friction enhances with enhancement in the local porosity parameter.     

Nonlinear magnetohydrodynamic flow of nanofluids across a porous matrix over an extending sheet with mass transpiration and bioconvection

The consequences of the nonlinear magnetic field and radiative thermal energy are evaluated for bioconvective viscous flow across a porous matrix over a nonlinearly stretching sheet. The rationale of the study is to attain enhanced thermal transportation. The dilute dispersion of nanoentities and bioconvection of swimming microorganisms are taken into consideration. The coupled partial differential system of field equations is transformed into ordinary differential form. Finally, the numeric solution is obtained by utilizing the fourth-order Runge–Kutta method shooting technique, and results are validated through an acceptable accord with existing studies. The variation of influential parameters such as combined magnetic parameter, mass transpiration parameter, thermophoresis, Brownian motion, bioconvection Lewis numbers made notable impacts on fluid velocity, temperature, concentration of nanoentities, and distribution of microorganisms.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions

The present paper investigates heat and mass transfer over a moving porous plate with hydrodynamic slip and thermal convective boundary conditions and concentration dependent diffusivity. The similarity representation of the system of partial differential equations of the problem is obtained through Lie group analysis. The resulting equations are solved numerically by Maple with Runge–Kutta–Fehlberg fourth–fifth order method. A representative set of results for the physical problem is displayed to illustrate the influence of parameters (velocity slip parameter, convective heat transfer parameter, concentration diffusivity parameter, Prandtl number and Schmidt number) on the dimensionless axial velocity, temperature and concentration field as well as the wall shear stress, the rate of heat transfer and the rate of mass transfer. The analytical solutions for velocity and temperature are obtained. Very good agreements are found between the analytical and numerical results of the present paper with published results.     

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating

Thermo-diffusion (Soret effect) and diffusion-thermo (Dufour effect) effects on combined heat and mass transfer of a steady hydromagnetic convective and slip flow due to a rotating disk in the presence of viscous dissipation and Ohmic heating is investigated. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically by applying the shooting method. For fluids of medium molecular weight (H₂, air), profiles of the dimensionless velocity, temperature and concentration distributions are shown graphically for various values of slip parameter γ, magnetic field parameter M, Eckert Ec, Schmidt Sc, Dufour Du and Soret Sr numbers. Finally, numerical values of physical quantities, such as the local skin friction coefficient, the local Nusselt number and the local Sherwood number are presented in tabular form.     

Thermal radiation effects on oscillatory squeeze flow with a particle-fluid suspension

The study of squeezing flow has attracted considerable interest in recent years for its important applications in industrial, biomedical and engineering domains such as fibre-reinforced, cell squeeze technology. The aim of this study is to analyze the flow and heat transfer of a squeezed particle fluid with thermal radiation effects between parallel plates. The governing partial differentials are reduced to ordinary differential equations by a similarity transformation and solved numerically using the finite difference method. The effects of different physical parameters on the velocity and temperature profiles are discussed with the help of graphs coupled with comprehensive discussions. The results indicate that the thermal radiation parameter enhanced the fluid and particle temperature distribution and for the plate oscillation case, reverse flow is observed. To show the biological relevance of the analysis, the results obtained analyzed the influence of the squeezed artery wall on the suspension blood flow for normal and diseased blood using the experimental data from the published literature. Finally, a comparison between the present similarity solutions and previously published results shows the accuracy of the current results.