Magnetohydrodynamic Squeezing Flow Research Articles

Combined Effects of Chemical Reaction and Radiation on MHD Squeezing Flow of Casson Fluid

The impacts of chemical reaction on the magnetohydrodynamic (MHD) squeezing Casson fluid flow through a porous medium under the slip condition with viscous dissipation the presence of radiation parameter have been discussed. The flow is produced when two plates are compressed together in close proximity to one another. Using similarity variables may successfully convert partial differential equations (PDEs) to ordinary differential equations (ODEs). The shooting technique was used to perform the numerical analysis, which entailed solving the competent governing equations with dominating parameters for a thin liquid layer. This was done to determine the results of the study. It is essential to evaluate the numerical results in light of previously conducted research to validate the current answers. According to the results, an increase in the distance between the two plates leads to a rise in the velocity and the wall shear stress. The gas's velocity, temperature, and concentration all drop due to an increase in the Hartmann and Casson parameters. Both the temperature and the rate of heat transfer rise in direct proportion to the amount of viscous dissipation. In addition, it has been shown that the rate of mass transfer rises during destructive chemical interactions, but during constructive chemical reactions, the contrary occurs, which results in adverse effects.

Unsteady MHD Squeezing Flow of Casson Fluid Over Horizontal Channel in Presence of Chemical Reaction

The fluid flow with chemical reaction is one of well-known research areas in the field of computational fluid dynamic. It has been acknowledged by many researchers due to its industrial applications in the modelling of flow on a nuclear reactor. Motivated by the implementation of the flow in the industry problems, the aim of this study is to explore the impacts of chemical reaction on magnetohydrodynamic (MHD) squeeze flow of Casson fluid over a permeable medium in the slip condition with viscous dissipation. The flow is induced due to compress of two plates. Transformation of the partial differential equations (PDEs) to ordinary differential equations (ODEs) is performed by imposing similarity variables. The numerical procedure of Keller-box is used to solve the dimensionless equations. Comparison of the numerical results with former studies to validate the current solutions is conducted. It is shown to be in proper agreement. The results show that the velocity and wall shear stress enhance as both plates moving nearer. Moreover, increase in Hartmann and Casson parameters reducing the velocity, temperature and concentration. The temperature and the rate of thermal transfer boosts with the existence of viscous dissipation. Furthermore, the mass transfer rate is discovered boosts in destructive chemical reaction and adverse outcome is noted in constructive chemical reaction.

Optimization through the Levenberg—Marquardt Backpropagation Method for a Magnetohydrodynamic Squeezing Flow System

The present study introduced the unsteady squeezing flow of two-dimensional viscous fluid with nanoparticles between two disks by using the Levenberg–Marquardt backpropagated neural network (LMB-NN). Conversion of the partial differential equations (PDEs) into equivalent ordinary differential equations (ODEs) is performed by suitable similarity transformation. The data collection for suggested (LMB-NN) is made for various magnetohydrodynamic squeezing flow (MHDSF) scenarios in terms of the squeezing parameter, Prandtl number, Brownian motion parameter, and the thermophoresis parameter by employing the Runge–Kutta technique with the help of Mathematica software. The worth of the proposed methodology has been established for the proposed solver (LMB-NN) with different scenarios and cases, and the outcomes are compared through the effectiveness and reliability of mean square error (MSE) for the squeezing flow problem MHDSF. Moreover, the state transition, Fitness outline, histogram error, and regression presentation also endorse the strength and reliability of the solver LMB-NN. The high convergence between the reference solutions and the solutions obtained by incorporating the efficacy of a designed solver LMB-NN indicates the strength of the proposed methodology, where the accuracy level is achieved in the ranges from 10−6 to 10−12.

Effects of viscous dissipation and chemical reaction on MHD squeezing flow of Casson nanofluid between parallel plates in a porous medium with slip boundary condition

The present numerical study investigates magnetohydrodynamic squeezing flow of Casson nanofluid embedded in a porous medium with velocity slip under the influence of viscous dissipation and chemical reaction. Buongiorno’s nanofluid model is considered in this study. Suitable similarity transformations are used to convert the governing nonlinear partial differential equations into the system of nonlinear ordinary differential equations. Then, the equations are solved using an implicit finite difference scheme known as Keller-box method. The present method is validated by comparing the numerical results of skin friction coefficient, Nusselt and Sherwood numbers with previous published results and found to be in good agreement. Graphical results for velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are examined with pertinent parameters. Findings reveal that fluid velocity and wall shear stress increase when the plates move closer. Also, increment of Casson and Hartmann number reduce the fluid velocity, temperature and nanoparticles concentration. The presence of viscous dissipation and thermophoresis enhance the fluid temperature and the convective heat transfer rate. Moreover, the rate of convective mass transfer decrease when Brownian motions of nanoparticles occurs, while it rises with increase in chemical reaction and thermophoresis.

MHD Squeezing Flow of Casson Nanofluid with Chemical Reaction, Thermal Radiation and Heat Generation/Absorption

The heat and mass transfer characteristics on unsteady squeezing flow of magnetohydrodynamic (MHD) Casson nanofluid with chemical reaction, thermal radiation and heat generation/absorption effects is investigated in this study. The influences of viscous and joule dissipation are also examined. The flow is caused by squeezing between two parallel plates embedded in a porous medium. The highly coupled nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations via similarity transformations. The transformed equations are solved using numerical scheme of Keller-box method. The accuracy of present method is validated through comparison of skin friction coefficient, Nusselt and Sherwood numbers with previously published results. Comparisons reveal that good agreements are achieved. Graphical results for velocity, temperature and nanoparticles concentration are analysed with various parameters. Findings demonstrate that the fluid velocity and temperature enhance when the plates move closer. Besides, increase in Hartmann number suppressed the fluid velocity and concentration due to the presence of strong Lorentz forces. The Brownian motion boosts the fluid temperature and concentration. Moreover, nanoparticles concentration is found to be higher in constructive chemical reaction and opposite effect is observed in destructive chemical reaction.

Evaluation of entropy generation in cubic autocatalytic unsteady squeezing flow of nanofluid between two parallel plates

BackgroundNanomaterials have advanced behaviors that make them possibly beneficial in various applications in mass and heat transports such as engine cooling, pharmaceutical processes, fuel cells, engine cooling and domestic refrigerator etc. Therefore here we deliberated the entropy generation in unsteady magnetohydrodynamic squeezing flow of viscous nanomaterials between two parallel plates. The upper plate is squeezing towards lower plate. The lower plate exhibits porous character. Energy attributes are discussed through heat flux, dissipation and Joule heating. Furthermore the irreversibility analysis with cubic autocatalysis chemical reaction is also accounted. MethodsNonlinear differential systems are converted to ordinary differential system by transformations. For convergent series solution the given system are solved by homotopy analysis method (HAM). ResultsCharacteristics of various interesting variables on velocity, Bejan number, concentration, entropy optimization and temperature are deliberated through graphs. Gradient of velocity (Cfx) and Nusselt number (Nux) are numerically computed against various physical variables. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter. For larger squeezing parameter the velocity and temperature field are increased. ConclusionsThe obtained results show that for larger squeezing parameter the velocity field boosts up. Velocity have opposite impact For larger magnetic and porosity parameters. Temperature is decreased for higher values of radiation parameter and Prandtl number. Temperature and concentration have same outcome for thermophoresis parameter. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter, while reverse is hold for Brinkman number.

Combined effect of viscous dissipation and Joule heating on MHD flow past a Riga plate with Cattaneo–Christov heat flux

The present work is committed to study the influence of dissipation and Joule heating on the magnetohydrodynamic squeezing flow between two Riga plates with Cattaneo–Christov heat flux. Riga plate is known as an electromagnetic actuator which comprises of permanent magnets and alternating electrodes placed on a plane surface. A non-Fourier (Cattaneo–Christov) heat flux by considering thermal relaxation time to Fourier’s law is implemented to analyse the features of heat transfer. The resulting system of nonlinear ordinary differential equations together with the boundary conditions is solved numerically by the RK Fehlberg method with shooting technique. The effects of diverse parameters on the flow, energy and concentrations are discussed and displayed graphically. Additionally, the influence of selected parameters on reduced skin friction, Nusselt number and Sherwood number is also graphically illustrated. It is noticed that there is a significant increase in temperature of the fluid with rising viscous dissipation and Joule dissipation. In addition, increasing squeezing parameter and magnetic field parameter results a strong reduction in skin friction at the upper Riga plate. A consistent growth in Nusselt number is observed with rising Eckert number, length parameter, radiation parameter and thermal Biot number.

Viscous Dissipation and Joule Heating Effects in Non-Fourier MHD Squeezing Flow, Heat and Mass Transfer Between Riga Plates with Thermal Radiation: Variational Parameter Method Solutions

A Riga plate is an electromagnetic actuator which comprises permanent magnets and alternating electrodes placed on a plane surface. The present article investigates the influence of viscous and Joule heating (Ohmic dissipation) in the magnetohydrodynamic squeezing flow, heat and mass transfer between two Riga plates. A non-Fourier (Cattaneo–Christov) heat flux model is employed which generalizes the classical Fourier law to incorporate thermal relaxation time. Via suitable transformations, the governing partial differential conservation equations and boundary conditions are non-dimensionalized. The resulting nonlinear ordinary differential boundary value problem is well posed and is solved analytically by the variational parameter method (VPM). Validation of the solutions is included for the special case of non-dissipative flow. Extensive graphical illustrations are presented for the effects of squeeze parameter, magnetic field parameter, modified Hartmann number, radiative parameter, thermal Biot number, concentration Biot number, Eckert number, length parameter, Schmidt number and chemical reaction parameter on the velocity, temperature and concentration distributions. Additionally, the influence of selected parameters on reduced skin friction, Nusselt number and Sherwood number are tabulated. An error analysis is also included for the VPM solutions. Detailed interpretation of the results is provided. The study is relevant to smart lubrication systems in biomechanical engineering and sensor design.

Thermal-diffusion and diffusion-thermo effects on squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates with thermal radiation

Present numerical study examines the heat and mass transfer characteristics of unsteady magneto-hydrodynamic squeezing flow of Casson fluid between two parallel plates with viscous and Joule dissipation effects in the presence of chemical reaction. The influence of Soret and Dufour parameters on squeezing flow is investigated along with thermal radiation and heat source/sink effects. The heat and mass transfer behaviour of squeezing flow is analysed by considering the rheological Casson fluid model. The present physical problem is governed by the set of nonlinear coupled time-dependent partial differential equations (PDEs). The method of similarity transformation approach is used to reduce the system of PDEs to a system of nonlinear ordinary differential equations (ODEs). Further, the Runge–Kutta fourth order integration scheme with shooting method (RK-SM) is used to solve the reduced ODEs. Numerical computations are performed for different sets of control parameters. The non-Newtonian flow behaviour of Casson fluid is presented in terms of graphs and tables. It is remarked that the temperature field is enhanced for increasing values of Hartmann number. Also, increasing Casson fluid parameter increases the velocity field. Concentration field is diminished for enhancing values of Soret parameter. Finally, the comparison between present similarity solutions and previously published results shows the accuracy of the current results.

Effect of Aligned Magnetic Field on MHD Squeezing Flow of Casson Fluid between Parallel Plates

The two-dimensional unsteady magnetohydrodynamic squeezing flow and heat transfer of Casson fluid between two parallel plates with aligned magnetic field and nonlinear thermal radiation is investigated theoretically. The resulting governing equations are transformed as set of ODEs and solved numerically by using bvp4c Matlab package. The influence of various pertinent parameters on the flow and temperature fields are discussed with the assistance of graphical illustrations. The reduced Nusselt number are presented through graphs. It is seen that increasing values of squeeze number depreciate the flow and temperature fields.

Magnetohydrodynamic squeezing two-phase flow of particulate suspension in a rotating channel with transpiration cooling

This article addresses the time-dependent two-phase magnetohydrodynamic squeezing flow of dusty liquid. The fluid flow is considered in a rotating channel. The flow is constructed by squeezing of an upper plate and stretching of the lower plate and relevant equations are obtained. Numerical results are computed by utilizing shooting method along with the RK–Fehlberg scheme. The obtained solutions are validated by comparison with the existing analytical solutions. The effects of pertinent parameters on velocities of both phases are comprehensively discussed through graphical results. The numerical values of shear stress of both phases at lower and upper walls are also tabulated. Furthermore, the slope of the linear regression line through data points is determined in order to quantify the increase/decrease. Numerical simulations disclosed that the normal and transverse velocities are decreased due to stronger Coriolis force. It is also established that the velocities of the fluid phase are higher than that of the dust phase

Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method

In this paper, two-dimensional squeezing flow of nanofluid under the effects of a uniform transverse magnetic field and slip boundary conditions is analyzed using variation of parameter method. The approximate analytical solutions of the variation of parameter method show excellent agreement and accuracy with the solutions of numerical method using shooting method coupled with Runge–Kutta coupled. Therefore, the developed analytical solutions are used to investigate the effects of fluid properties, magnetic field and slip parameters on the squeezing flow of nanofluid. From the results, it is observed that the velocity of the fluid increases with increase in the magnetic field parameter under the influence of slip condition while under no-slip condition, the velocity of the fluid decreases with increase in the magnetic field parameter. Also, the fluid velocity increases as the slip parameter increases but it decreases with increase in the magnetic field parameter and Reynolds number under the no-slip condition. It is hoped that this study will enhance the understanding of squeezing flow process such as found in various biological and industrial applications.

Magnetohydrodynamic squeezing flow of casson nanofluid between two parallel plates in a porous medium using method of matched asymptotic expansion

In this paper, unsteady squeezing flow of Casson nanofluid between two parallel plates embedded in a porous medium and subjected to magnetic field is analyzed. The developed systems of partial differential equations for the fluid flow models are converted to ordinary differential equations through suitable similarity variables. The obtained ordinary differential equation is solved using method of matched asymptotic expansion. The accuracies of the approximate analytical method for the small and large values of squeezing numbers are investigated. Good agreements are established between the results of the approximate analytical method and the results numerical method using fourth-fifth order Runge-Kutta-Fehlberg method. Thereafter, the developed approximate analytical solutions are used to investigate the effects of pertinent flow parameters on the squeezing flow phenomena of the nanofluids between the two moving parallel plates. The results established that the as the squeezing number and magnetic field parameters decreases, the flow velocity increases when the plates come together. Also, the velocity of the nanofluids further decreases as the magnetic field parameter increases when the plates move apart. However, the velocity is found to be directly proportional to the nanoparticle concentration during the squeezing flow i.e. when the plates are coming together and an inverse variation between the velocity and nanoparticle concentration is recorded when the plates are moving apart. It is hope that this study will enhance the understanding the phenomena of squeezing flow in various applications.

Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems

ABSTRACTAn analysis was performed in this paper to study the problem of magnetohydrodynamic squeezing flow of nanofluid between parallel disks. This paper also proposed a reproducing kernel method for solving fourth-order four-point boundary value problems. In order to eliminate the singularity of the equation, a transform was used. Convergence analysis and error estimation for the present method in -space were also discussed. The exact solution was represented in the form of series in the reproducing kernel Hilbert space which proved higher accuracy in numerical computation. The algorithm derived from this approach can be easily implemented. The ideas and techniques presented in this paper will be useful for solving many other problems.

MHD squeezing flow between two parallel disks with suction or injection via Legendre wavelet-quasilinearization technique

PurposeThis paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more accurate results.Design/methodology/approachTo test the significance of the proposed scheme, the authors applied the method on the model representing magneto-hydrodynamic squeezing flow of a viscous fluid between two parallel infinite disks, where one disk is impermeable and the other is porous with either suction or injection of the fluid. For the sake of comparison, numerical solution by using RK-4 is also computed. From the graphs and tables, it is evident that the proposed method shows an excellent accordance with the numerical solution.FindingsThe solution converges to the numerical solution when the degree of Legendre polynomials m is increased. For m = 20 in all the three cases, for different values of S, M and A, the graphs of solutions obtained by Legendre wavelet quasilinearization technique show an excellent agreement with numerical solution. Also, it is evident from figures that suction and injection affects the velocity profile in opposite way. For suction, maximum velocity is seen to be at the center of the channel. Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.Originality/valueMagnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Double diffusive magnetohydrodynamic squeezing flow of nanofluid between two parallel disks with slip and temperature jump boundary conditions

In this paper, double diffusive squeezing unsteady flow of electrically conducting nanofluid between two parallel disks under slip and temperature jump condition is analyzed using the homotopy perturbation method. The obtained solutions from the analysis are used to investigate the effects of the Brownian motion parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip and temperature jump boundary conditions on the behavior of the nanofluid. Also, the results of the homotopy perturbation method are compared to the results in the literature and good agreements are established. This study is significant to the advancements of nanofluidics such as energy conservation, friction reduction and micro mixing biological samples.

Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method

Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium.

Homotopy Analysis Solution for Magnetohydrodynamic Squeezing Flow in Porous Medium

The aim of the present work is to analyze the magnetohydrodynamic (MHD) squeezing flow through porous medium using homotopy analysis method (HAM). Fourth-order boundary value problem is modeled through stream functionψ(r,z)and transformationψ(r,z)=r2f(z). Absolute residuals are used to check the efficiency and consistency of HAM. Other analytical techniques are compared with the present work. It is shown that results of good agreement can be obtained by choosing a suitable value of convergence control parameterhin the valid regionRh. The influence of different parameters on the flow is argued theoretically as well as graphically.

Analyzing magneto-hydrodynamic squeezing flow between two parallel disks with suction or injection by a new hybrid method based on the Tau method and the homotopy analysis method

In this paper an algorithm based on the homotopy analysis method (HAM) is introduced to study the magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid in the presence of an applied magnetic field. The continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation via similarity transformations. In addition, by using the Tau method the problem converts to the algebraic equations to obtain the solution iteratively. The combined effect of inertia, electromagnetic forces for both suction and blowing cases is discussed. Additionally, the convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. The applicability, accuracy and efficiency of this new Tau modification of the HAM is demonstrated via the accomplished comparison.

MHD squeezing flow between two infinite plates

Magneto hydrodynamic (MHD) squeezing flow of a viscous fluid has been discussed. Conservation laws combined with similarity transformations have been used to formulate the flow mathematically that leads to a highly nonlinear ordinary differential equation. Analytical solution to the resulting differential equation is determined by employing Variation of Parameters Method (VPM). Runge–Kutta order-4 method is also used to solve the same problem for the sake of comparison. It is found that solution using VPM reduces the computational work yet maintains a very high level of accuracy. The influence of different parameters is also discussed and demonstrated graphically.