Transient electromagnetohydrodynamic radiative squeezing flow between two parallel Riga plates using a spectral local linearization approach

This article addresses transient electromagnetohydrodynamic radiative squeezing flow due to convectively heated electromagnetic actuator. The transport analysis of heat and mass is explored considering the heat generation/absorption and destructive species homogeneous reaction. Suitable transformations are applied on the mathematical model developed to convert governing partial differential equations to ordinary differential equations (ODEs). Spectral local linearization method (SLLM) is employed on the resultant nonlinear coupled ODEs to compute the numerical results. Influence of sundry physical quantities on heat mass transfer of squeezing flow characteristics are determined using graphs and tabular results. SLLM results exhibit that momentum and temperature improved with rise in squeezing and heat source parameters correspondingly. Momentum enhances at lower plate and detracts with rise in modified Hartmann number. For improved heat source parameter, the rate of heat transfer diminishes and is more significant for higher Prandtl number values. This investigation has relevance in disk style magnetic clutches, rolling elements, food processing, bearings, squeezing film pressure sensors, and flow rheostats.     

Flow of three-dimensional radiative Williamson fluid over an inclined stretching sheet with Hall current and nth-order chemical reaction

In the current communication, three-dimensional Williamson fluid flow past a bidirectional inclined stretching plate with novel Hall current, nonuniform heat source/sink, and nth-order chemical reaction features are investigated. Rosseland's diffusion model is defined for the radiation heat transfer. The nonlinear governing derivative equations satisfying the flow are transmuted to the coupled derivative equations by employing the local similarity quantities and then solved numerically through the Runge–Kutta–Fehlberg method utilizing the shooting quadrature. An inclusive analysis is reported via graphs for the flow rate field, temperature, and concentration distributions for different evolving terms of immense concern. Wall dragging effect and wall heat gradient and wall concentration gradient have been examined, plotted, and described. The detailed geometry reveals that dimensionless velocity field is monotonically rising as the Hall parameter rises. The chemical reaction concentration for the Williamson fluid is enhanced with expanding values of the magnetic field parameter. Transitional values of wall stress components upturn with an increase in Hall parameter while the Williamson term is boosted. Nusselt number is reduced as the Williamson term rises and the Sherwood number enhances with a rising chemical reaction term. The results are verified for limiting cases by comparing with various investigations and found to have excellent accuracy.     

Study of chemically reactive and thermally radiative Casson nanofluid flow past a stretching sheet with a heat source

Nanoparticle (NP) delivery is an exciting and rapidly developing field that adequately takes care of thermal radiation in blood flow and is likely to have bearing on the therapeutic procedure of hyperthermia, blood flow, and heat transfer in capillaries. The NP parameters such as size, shape, and surface characteristics can be regulated to improve nano-drug delivery efficiency in biological systems. The NPs outperform traditional drug delivery processes in drug carrying capacity and controlled release. The current article investigates the boundary layer flow and heat transfer of thermally radiative Casson nanofluid (NF) over a stretching sheet with chemical reaction and internal heat source. In our study, Cu and Al₂O₃ are taken as NPs in a suitable base fluid. The problem is analyzed by using similarity transformations and is solved with MATLAB's built-in solver bvp4c. The effects of pertinent parameters characterizing the flow model are presented through graphs and tables. The important findings of the investigation are noted as: the use of metallic oxide is more beneficial to attain higher temperature within a few layers close to the bounding surface; the appearance of convexity and concavity in the concentration profile attributed to flow instability, and the constructive and destructive heterogeneous reactions at the bounding surface have distinct roles to modify the NF flow in the boundary layer.     

Second law analysis in radiative mixed convective squeezing flow of Casson fluid between parallel disks with Soret and Dufour effects

The present communication deals the entropy generation by cause of heat and mass transform in an unsteady mixed convective radiative squeezing flow of a Casson fluid confined between two parallel disks in the presence of diffusion‐thermo and thermal‐diffusion effects and temperature jump. The lower disk is taken to be porous and the upper one is impermeable. The governing PDE is converted as nonlinear ordinary differential equations (ODE) by using well‐established similarity transformations; then, the reduced nonlinear ODE are solved by shooting method with Runge‐Kutta fourth‐order approach. The influence of distinct nondimensional fluid and geometric‐related parameters on the velocity profiles, temperature, concentration, entropy generation number, and Bejan number are studied in detail and represented in the form of graphs. The entropy of the Casson fluid is increased with the Eckert number, whereas the concentration profile is decreased by squeezing Reynolds number. The current results are correlated with existing results for the viscous case and found to be in better agreement.     

Exploration of radiative heat on magnetohydrodynamic rotating fluid flow through a vertical sheet

An analysis is built up for the exploration of radiative heat transport on the magnetohydrodynamic flow of rotating fluid over a vertical sheet. The inclusion of thermal radiation in conjunction with the reacting species enhances the energy as well as the solutal profiles respectively. In an advance, external heat source and applied magnetic field effects are considered for further improvement. As the magnetic Reynolds number is low, the influence of the induced magnetic field is neglected. The transformation of governing nonlinear partial differential equations into coupled nonlinear ordinary differential equations is attained with a proper supposition of similarity variables. Moreover, the solution of these transformed equations is scheduled using the “Runge–Kutta fourth-order” method numerically in association with the “shooting technique.” The simulation or various illustrating parameters affecting the flow phenomena are obtained and displayed through graphs and for numerical validation with earlier published work shows the convergence process of the methodology applied. The main findings of the study are; the Dufour number is favorable to enhance the fluid temperature throughout the domain and the destructive chemical reaction also encourages the solutal profile significantly.     

Unsteady thermally radiative and chemically reactive viscoelastic fluid flow past a vertical porous plate with a heat source

An analytical study is performed to investigate the thermal radiation effect on the unsteady two-dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters $B\prime$ fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis-à-vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.     

Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

In the current study, a mathematical formulation is developed by combining the non-Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge-Kutta-Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank-Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.     

Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity,Brownian moment,and thermophoresis aspects

The improvement of heat transport is a very important phenomenon in nuclear reactors, solar collectors, heat exchangers, and coolers, which can be achieved by choosing the nanofluid as the functional fluid. Nanofluids improve thermophysical properties; as a result, they have made great progress in engineering, biomedical, and industrial applications. Therefore, a numerical study has been proposed to analyze the flow and heat transport of nanoliquids over an extendable surface near a stagnation point with variable thermal conductivity under the influence of the magnetic field, due to their importance in the engineering field. Nanoliquid attributes explain the Brownian motion and the diffusion of thermophoresis. The effects of the chemical reaction and the uniform internal heat source/heat sink are also considered. The Nachtsheim‐Swigert shooting procedure based on the Runge‐Kutta scheme is used for numerical calculation. The impact of effective parameters on velocity, temperature, and volume fraction of the nanoparticles is shown in the graphs and reported in detail. The surface criteria are also estimated with respect to the shear stress and the rate of heat and mass transfer. The aspects of the Brownian moment and Lorentz force are positively correlated to the thermal field of the nanoliquid. Also, the variable thermal conductivity aspect favors the growth of the thermal boundary layer.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Unsteady squeezing flow of magnetic hybrid nanofluids within parallel plates and entropy generation

Nowadays, due to the novel thermal effectiveness, a new class of fluid, named “hybrid nanofluid,” is used. It has significant applications in domestic and industrial fields. In this study, we investigated the entropy generation and heat transfer of unsteady squeezing magnetic hybrid nanofluid flow between parallel plates by considering heat source/sink and thermal radiation. In this analysis, carbon nanotubes (CNTs) (single‐walled carbon nanotube and multiwalled carbon nanotube) are considered as nanoparticles that are dispersed in water‐ethylene glycol (EG) mixtures (ie, 70%W + 30%EG and 50%W + 50%EG). For the analysis of the physical behavior of hybrid nanofluids, new models related to hybrid nanofluids are incorporated. From this study, it has been observed that as the hybrid nanofluids moved away from the surface, the entropy generation outlines accelerated with an increase in magnetic field values. Moreover, an increase in the volume fraction of CNTs, the thermal conductivity of 50%W + 50%EG + CNTs hybrid nanofluid is greater than 70%W + 30%EG + CNTs hybrid nanofluid.     

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.     

Unsteady squeezing flow of water‐based nanofluid between two parallel disks with slip effects: Analytical approach

The squeezing flow of an unsteady water‐based nanofluid between two parallel disks has been analyzed in the current study. Thermal and solutal buoyancy along with heat source enhance the flow phenomena of free convective flow through a porous medium. In addition to that velocity slip and temperature slip are also accounted for in the boundary conditions. The similarity transformation is adopted to formulate the governing equations that convert the complex partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). These transformed equations are handled analytically by using the variation parameter method (VPM). For computational purposes, the fixed numeric values of physical parameters are used and their behaviors are shown by means of graphs. The calculated results for the physical quantities of interest are shown in tables. The conformity of the solution is obtained in comparison to an earlier study in a particular case. The major findings are (i) the velocity profile has distinct variations, which are separated by the middle layer of the channel and (ii) enhancement in the heat transfer coefficient is noted due to the interaction of buoyancy parameter.     

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

Heat transport subject to nonlinear thermal radiation has multiple applications in physics, industry, engineering field, and space technology, such as aerodynamic rockets, solar power technology, large open water reservoirs, and gas-cooled nuclear reactors. This effort studies the magnetohydrodynamic flow of cross fluid, which is a type of non-Newtonian, along a heated surface. Furthermore, the transportation of heat in the fluid is induced by  thermal radiation. Furthermore, the behavior of opposing/assisting flow and impact of nonuniform heat sink/source is scrutinized. The reserved suitable transformations are carried out to shift the ruling equations into nondimensional class. Through reserved transformations, two nonlinear partial differential equations are altered into corresponding nonlinear ordinary differential equations. Then a scheme of integration referred to as Runge–Kutta–Fehlberg is imposed to get a numerical solution of these. The impact of parameters are mentioned concisely on temperature and velocity profiles in the absence and presence of a magnetic parameter. It is proved that the presence of a magnetic field steps up the velocity and temperature as well.     

Effect of viscous dissipation on Cu‐water and Cu‐kerosene nanofluids of axisymmetric radiative squeezing flow

This paper analyzes the axisymmetric squeezing current phenomena of Cu‐water and Cu‐kerosene for two dimensional nanofluid between two parallel plates. The effects of thermal radiation with velocity slip are also enhancing the subject as well. The similarity approach has been adopted to obtain the ordinary differential equations from partial differential equations. The solution of these complex coupled nonlinear equations is obtained analytically using the variation parameter method. For the corroboration of the current result, we have matched with prior results in particular cases and concluded that both the results coincide with each other. Computations are obtained for velocity and temperature profiles for different pertinent parameters along with skin friction and Nusselt number and presented via graphs and tables.     

Buoyancy-motivated dissipative free convection flow of Walters-B fluid along a stretching sheet under the Soret effect and Lorentz force influence

A two-dimensional numerical model has been framed to investigate the effect of buoyancy forces on magnetized free convective Walters-B fluid flow over a stretching sheet with Soret effect, heat radiation, thermal source/sink, and viscous dissipation. The current physical model is developed based on the stretching sheet geometry. The impact of Lorentz force on the nonlinear system is investigated and considered in the velocity equation. The influence of thermal radiation, heat source/sink, viscous dissipation, and Joule heating is considered in the energy equation. The effect of Soret parameter and chemical reaction on mass transfer is accounted in the concentration equation. The current physical model is governed by the highly coupled nonlinear system of partial differential equations. Owing to the inadequacy in the analytical techniques, the obtained governing equations are solved by using the bvp4c Matlab function via similarity transformations approach. Numerical computations are performed for the varying values of physical parameters, which are expressed in terms of tables and graphs. Magnifying viscoelastic parameter decays the velocity profile and enhances the thermal and concentration fields. Enhancing free convection parameters diminishe the velocity fields and magnifies the thermal profile. Thermal field magnifies with enhancing thermal radiation parameter and Eckert number. Enhancing the Soret number raises the concentration field. Also, the bvp4c Matlab function adequately simplifies the highly nonlinear coupled system of equations occurring in nature. The present similarity solutions presented in this paper coincides with previously published results in the literature.     

Numerical simulation of laminar flow development with heat and mass transfer in PEM fuel cell flow channels having oxygen and hydrogen suction at one channel wall

Numerical simulation has been carried out of the fluid flow, heat and mass transfer for the developing laminar flow in polymer electrolyte membrane (PEM) fuel cell cathode and anode flow channels, respectively. Each flow channel is considered to be composed of two parallel walls, one porous (simulating electrode surface) and one non‐porous, or impermeable, wall (simulating bipolar plate surface). Various flow situations have been analyzed, and the local and the averaged friction coefficient, Nusselt number for heat transfer and Sherwood number for mass transfer are determined for various flow conditions corresponding to different stoichiometries, operating current densities and operating pressures of the cell. The effect of suction or injection (blowing) wall boundary condition has also been investigated, corresponding to the oxygen consumption in the cathode and hydrogen consumption in the anode. Correlations for the averaged friction coefficient, Nusselt and Sherwood numbers are developed, which can be useful for PEM fuel cell modeling and design calculations. Copyright © 2010 John Wiley & Sons, Ltd.     

Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing

A similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet in a porous medium subject to suction/blowing and in the presence of internal heat generation/absorption. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. Boundary layer velocity and temperature profiles are determined numerically for various values of the ratio of free stream velocity and stretching velocity, the permeability parameter, suction/blowing parameter, heat source/sink parameter, Prandtl number. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (cx). The temperature decreases in this case. At a particular point of the porous stretching sheet, the non-dimensional fluid velocity decreases with the increase of the permeability of the porous medium and also with the increasing suction parameter when the free stream velocity is less than stretching velocity whereas fluid velocity increases with the increasing injection parameter. But when the free stream velocity is greater than the stretching velocity the opposite behaviour of horizontal velocity is noticed. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The temperature at a point is found to decrease with the increasing Prandtl number.     

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

The present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first-order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first-order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.     

Significance of heat source/sink on the radiative flow of Cross nanofluid across an exponentially stretching surface towards a stagnation point with chemical reaction

A numerical review on magnetohydrodynamics radiative motion of Cross nanofluid across an exponentially stretchable surface near stagnation point with varying heat source/sink is addressed. Brownian movement and thermophoretic impacts are assumed. The governing equations for this study are first altered as a system of ordinary differential equations by similarity transformation. With an aid of the Runge–Kutta 4th order mechanism together with the shooting procedure, the impacts of several pertinent parameters including chemical reaction on regular profiles (velocity, temperature, and concentration) are explicated. The consequences of the same parameters on surface drag force, transfer rates of heat, and mass are visualized in tables. From the analysis, it was noticed that the magnetic field parameter enhances the temperature and decreases the velocity of the Cross nanofluid. Also, fluid temperature is an increasing function with thermal radiation and nonuniform heat source/sink. The rate of heat transfer is increased with thermophoresis and diminished with Brownian motion. Sherwood's number is diminished with Brownian motion but it was boosted up with thermophoresis. The present results are compared with published results and those are in agreement.