Hydromagnetic Boundary Layer Flow Research Articles

Investigating the magnetohydrodynamics non-Newtonian fluid movement on a tensile plate affected by variable thickness with dufour and soret effects: Akbari Ganji and finite element methods

Significant progress in the investigation of non-Newtonian Williamson and Casson boundary layer flow has led us to explore the extension of non-Newtonian Williamson and Casson hydromagnetic boundary layer flow in an electrically conductive fluid subjected to a strong magnetic field and a uniform thermal field. This study is divided into two interconnected parts. The first part converts the nonlinear system governing the Partial Differential Equations into a simpler, nonlinear, ordinary differential equation. It is then analyzed using the Akbari Ganji method (AGM). The output data from the first part, solved using AGM, is compared and evaluated with the output data from the second part, solved with the assistance of finite element (FEM) methods. This research validates previous works with current methodologies. Subsequently, changes in temperature and concentration parameters, influenced by variations in magnetic parameters, are obtained and analyzed through three-dimensional charts. Upon reviewing the results, it is observed that the distribution of concentration and temperature is dependent on the distribution of the magnetic parameter, with an increase in concentration and temperature being influenced by the rise in the magnetic parameter. Other parameters are also examined, each of which is elaborated upon below. The effects of Bi1, Sr, and Sc parameters on temperature are investigated, and design points for achieving optimal and effective design are presented in the graph. Some applications of magnetohydrodynamics and non-Newtonian fluids include improving fluid pumping technologies. Using magnetohydrodynamics in non-Newtonian fluid pumping systems can help improve efficiency and reduce energy costs. Additionally, enhancing the efficiency of heat transfer systems using magnetohydrodynamics can help improve efficiency and reduce energy losses in these systems.

Thermodynamics of hydromagnetic boundary layer flow of Prandtl nanofluid past a heated stretching cylindrical surface with interface slip

BackgroundThe mathematical modelling of a non-Newtonian fluid in the backdrop of applied magnetic field against an electrically conducting liquid is recognized as magnetohydrodynamics (MHD), which has important implications in chemical engineering and the biological sciences. Illustrations of such magneto-fluids include molten metals, electrolytes, blood plasma, and salty water. The applications of flowing liquids over cylindrical geometries is a fascinating due to its wide range importance in engineering. The aforementioned uses of MHD encourage scientists and analysts to establish new mathematical modelling in the area of fluid dynamics. Therefore, we considered the Prandtl fluid flow with loaded nanoparticles over a cylindrical tube with slip triggered by wall shear stress. The transport equation involving thermophoresis and Brownian diffusions are modelled using the Buongiorno model. The modelling of energy and entropy are established considering the effects of frictional dissipation, non-uniform heat source, thermal stratification, and Ohmic heating. MethodsThe formulated mathematical model leading to a complex system of partial differential equations with numerous integrated parameters. Using numerical algorithm RK-45 with a tolerance limit of 10−6, the system of resultant ordinary differential equations is simulated. The solver is used repeatedly to select the parameters that best meet the intended boundary conditions. Significant findingThe results of the current study revealed that the influence of heat source and thermal stratification on fluid temperature are conflicting. Additionally, the magnetic variable and Brinkman parameter have an escalating relationship with the rate of entropy development. The Bejan number detract with the magnetic variable. For distinct estimations of slip factors, heat and mass transport behave identically. However, the effect of slip is higher as compared to no slip scenario. The effect of Lewis number against nanoparticles concentration is opposite.

Effect of Porosity on Hydromagnetic Boundary Layer Flow with Forced Convective Heat Transfer

Effect of Porosity on Hydromagnetic Boundary Layer Flow with Forced Convective Heat Transfer

MHD Nanofluid boundary layer flow over a stretching sheet with viscous, ohmic dissipation

The objective of this research is to examine the steady incompressible two-dimensional hydromagnetic boundary layer flow of nanofluid passing through a stretched sheet in the influence of viscous and ohmic dissipations. The present problem is obtained with the help of an analytical technique called DTM-Pade Approximation. The mathematical modeling of the flow is considered in the form of the partial differential equation and is transformed into a differential equation through suitable similarity transformation. The force of fixed parameters like thermophoresis number Nt, Brownian motion number Nb, Prandtl number Pr, Lewis number Le, Magnetic field M, suction/injection S and Eckart number Ec are displayed with the aid of Figures. Our outcomes showed a greater trend in the velocity profile for the parameters of magnetics M, suction S, and nonlinear stretching parameter n. While the reverse trend is found against the temperature profile when the Prandtl number increases. Lewis number and other parameters have shown increasing behavior in the concentration profile.

Heat source and sink effects on periodic mixed convection flow along the electrically conducting cone inserted in porous medium.

The system of partial differential equations governing the unsteady hydromagnetic boundary-layer flow along an electrically conducting cone embedded in porous medium in the presence of thermal buoyancy, magnetic field, heat source and sink effects are formulated. These equations are solved numerically by using an implicit Finite-Difference Method. The effects of the various parameters that are source/sink parameter, porous medium parameter, Prandtl number, mixed convection parameter and magnetic Prandtl number on the velocity, temperature profiles, transverse magnetic field are predicted. The effects of heat source and sink parameter on the time-mean value as well as on transient skin friction; heat transfer and current density rate are delineated especially in each plot. The extensive results reveal the existence of periodicity and show that periodicity becomes more distinctive for source and sink in the case of the electrically conducting cone. As the source and sink contrast increases, the periodic convective motion is invigorated to the amplitude and phase angle as reflect in the each plot. The dimensionless forms of the set of partial differential equations is transform into primitive form by using primitive variable formulation and then are solved numerically by using Finite Difference Scheme which has given in literature frequently. Physical interpretations of the overall flow and heat transfer along with current density are highlighted with detail in results and discussion section. The main novelty of the obtained numerical results is that first we retain numerical results for steady part and then used in unsteady part to obtain transient skin friction, rate of heat transfer and current density. The intensity of velocity profile is increased for increasing values of porosity parameter Ω, the temperature and mass concentration intensities are reduced due heat source effects.

Unsteady magnetohydrodynamic couple stress fluid flow from a shrinking porous sheet: Variational iteration method study

AbstractMotivated by magnetic polymer manufacturing applications, the present research article examines theoretically the hydromagnetic boundary layer flow of an electrically conducting non‐Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into a fifth‐order nonlinear ordinary differential equation via similarity transformations with associated boundary conditions. A semi‐analytical/numerical scheme employing Lagrangian multipliers and known as the variational iteration method (VIM) is implemented to solve the ordinary differential boundary value problem. Validation of the solutions is conducted by benchmarking against earlier Newtonian studies and very good agreement is achieved. A detailed assessment of the impact of couple stress (rheological), unsteadiness, magnetic body force parameter, and wall transpiration (suction/injection) parameter on flow characteristics is conducted with the aid of graphs. A significant deceleration in the flow is computed with increasing injection (acceleration is caused with greater suction) and acceleration is induced with higher unsteadiness parameter values. Increasing magnetic field (higher magnetic number) generates flow acceleration, rather than the customary deceleration, due to the shrinking sheet dynamics. A stronger couple stress effect manifests in strong retardation in the boundary layer flow and an increase in momentum (hydrodynamic|) boundary layer thickness. VIM demonstrates excellent convergence and accuracy and shows significant promise in studying further magnetic polymer fabrication flow problems.

Numerical study on MHD radiating and reacting unsteady slip flow past a vertical permeable plate in a porous medium

This paper examines the unsteady hydro-magnetic boundary layer flow of a reacting and radiating electrically conducting fluid past a slippery permeable vertical plate embedded in a porous medium. The governing partial differential equations are obtained and tackled numerically via Galerkin finite element method. Pertinent results with respect to the effects of emerging thermo physical parameters on the velocity, temperature and concentration fields together with skin-friction, Nusselt number and Sherwood number are elucidated graphically and in tabular form. Numerical validation of the present work special case results with the one already in the literature shows an excellent agreement. It is found that buoyancy forces enhanced the momentum boundary layer while magnetic field and radiative heat absorption lessen it. Both heat and mass transfer rates diminished with a rise in the rate of chemical reaction.

Time-Dependent Hydromagnetic Boundary Layer Flow across a Porous Vertical Surface with Internal Heat Generation

The time-dependent hydromagnetic boundary layer flow across a vertical surface with internal heat regeneration in porous media is investigated. The flow problem has been modelled mathematically in partial differential equations along with appropriate defined boundary conditions. These equations were expressed in dimensionless form using suitable similarity variables. The resulting dimensionless equations along with the conditions defined at the boundaries are solved by means of the Laplace transform methods. Results of the study are graphically illustrated for various quantities of practical importance. It was concluded that time positively influence the flow as a reduced skin friction coefficient was observed. Furthermore, the magnetic parameter, the radiation parameter, the heat absorption parameter and the permeability of the porous media can be used to influence the characteristics of a flow in porous media.

Hydromagnetic boundary layer flow with heat transfer past a rotating disc embedded in a porous medium

AbstractIn this study, the effect of Coriolis force along with the Darcy parameter has been analyzed on time‐dependent forced convective boundary layer flow of conducting fluids over a rotating disc embedded in a porous medium. The modeled system is solved by power series approximations in the Mathematica environment shooted values. The significant impact of the rheological properties, such as Darcy parameter and Prandtl number , of water, hydrocarbon, and kerosene‐based conducting fluids for the deviation of parameter (Karman) has been noted and then analyzed qualitatively and quantitatively with graphs and tables.

Analytical ADM study of time-dependent hydromagnetic flow of biofluid over a wedge

In this research work, we consider the two-dimensional time-dependent laminar hydromagnetic boundary-layer flow of a bio-magnetic fluid over a wedge using a micropolar fluid model with convective boundary conditions and taking into account the action of a transversely magnetic field. The partial differential equations that govern velocity, temperature and micro-rotation are transformed into nonlinear ordinary differential equations with similarity transformations. The findings are analytically analyzed afterward through the Adomian decomposition method (ADM) and numerically through the shooting technique based on Runge–Kutta–Fehlberg. In this study, we have considered the effect of the unsteadiness parameter $$K$$ , wedge angle parameter $$\beta$$ , Reynolds number Re, magnetic field parameter $$M$$ and induced magnetic field $$h$$ on the evolution of dimensionless velocity, temperature and micro-rotation of the bio-magnetic flow throughout the boundary layer. It is found that the flow separation may occur with the increase in unsteadiness parameter $$K$$ and is prevented as the wedge angle parameter $$\beta$$ rises. Also, results indicate that in the vicinity of the wedge surface, increasing K parameter leads to a reduction in fluid temperature and grows the micro-rotation of the blood corpuscles. Finally, comparisons between analytical and numerical data clearly show the effectiveness of the adopted analytical ADM technique.

Stability of hydromagnetic boundary layer flow of non-Newtonian power-law fluid flow over a moving wedge

We consider the two-dimensional laminar boundary-layer flow of power-law fluid over a moving wedge in which the uniform magnetic field is applied normally to the flow. The motion of the mainstream and wedge is approximated in terms of the power of the distance from leading boundary-layer edge which helps to reduce the governing partial differential equations to an ordinary differential equation. No analytic solution is feasible due to high nonlinearity; therefore, the numerical simulations are sought by Chebyshev collocation and shooting techniques. These techniques provide a means to assess physical insights into the hydrodynamics of complex flows and particularly the Chebyshev collocation method enables the construction of efficient tools suitable for nonlinear problems. This method often leads to a matrix-based analysis and an iterative technique needs to be employed to solve the problem. The various results on the physical parameters show that the shear-thinning and shear-thickening solutions are demarcated by the Newtonian fluid. It is also noticed that the system yielded a non-unique solution structure for a given set of parameters. However, the non-uniqueness of the solutions disappears for increasing the magnetic field. To assess the nature of the non-unique solutions, it is important to perform the linear stability using large-time asymptotics. This analysis gives as to which of these solutions is practically feasible and models the flow. Eigensolution-based analysis reveals that the first solution is always stable while the other one leading to unstable mode. The results further show that an increase in the magnetic field stabilizes the fluid flow over the moving wedge and promotes the unique solution to the problem. Further, the obtained numerical results are compared by examining the large λ asymptotics. It is observed that there is a qualitative comparison between solutions. The hydrodynamics behind the magnetic field and non-Newtonian fluid are discussed in detail.

Hydromagnetic free convective flow of Walters’-B fluid over a vertical surface with time varying surface conditions

Purpose In the present investigation, hydromagnetic boundary layer flow of Walters’-B fluid over a vertical porous surface implanted in a porous material under the action of a strong external applied magnetic field and rotation is presented. In several industrial applications, the external applied magnetic field is strong enough to produce Hall and ion-slip currents. Thus, the influence of Hall and ion-slip currents is also considered in this analysis. The flow through configuration is generated because of time varying motion of the free-stream and buoyancy action. Design/methodology/approach Regular perturbation scheme is used to obtain the solution of the system of coupled partial differential equations representing the mathematical model of the problem. Numerical computation has been performed to notice the change in flow behavior and the numerical results for velocity field, temperature field, species concentration, skin friction, rate of heat and mass transfer are presented through graphs and tables. Findings An important fact noticed that the exponential time varying motion of the free-stream induces reverse flow in the direction perpendicular to the main flow. Rising values of the strength of the applied magnetic field give increment in the fluid velocity in the neighbourhood of the vertical surface, this may cause because of the exponential motion of the free-stream. The behaviour of the Darcian drag force is similar as magnetic field on fluid flow. Originality/value In literature, very less research works are available on Walters’-B fluid where unsteadiness in the system occurs because of time varying motion of the free-stream. In this paper, the authors have made an attempt to study the action of Hall and ion-slip currents, rotation and external applied magnetic field on hydromagnetic boundary layer flow of Walters’-B fluid over a vertical surface implanted in a porous material.

A new improved generalized decomposition method (improved-GDM) for hydromagnetic boundary layer flow

Purpose The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring shooting technique and analytically via a new modified analytical technique called improved generalized Adomian decomposition method (improved-GDM). Design/methodology/approach It is well established that the generalized decomposition method (GDM) (Yong-Chang et al., 2008), which uses a new kind of decomposition strategy for the nonlinear function, has proved its efficiency and superiority when compared to the standard ADM method. In this investigation, based on the idea of improved-ADM method developed by Lina and Song (Song and Wang, 2013), the authors proposed a new analytical algorithm of computation named improved-GDM. Thereafter, the proposed algorithm is tested by solving the nonlinear problem of the hydro-magnetic boundary layer flow over a flat plate. Findings The proposed improved generalized decomposition method (I-GDM) introduces a convergence-control parameter “ω’’ into the GDM, which accelerates the convergence of solution and reduces considerably the computation time. In fact, the key of this method is mainly based on the best selection of the convergence-control parameter ω. Originality/value The paper presents a new efficient algorithm of computation that can be considered as an alternative for solving the nonlinear initial boundary layer value problems. Obtained results show clearly the accuracy of the proposed method.

Impacts of viscous dissipation and Joule heating on hydromagnetic boundary layer flow of nanofluids over a flat surface subjected to Newtonian heating

Main concern in this analysis is to study the two-dimensional, steady boundary layer flow of viscous, incompressible, electrically conducting nanofluids past a flat plate in the presence of magnetic field with heat being transferred by Newtonian heating way. Influences of viscous dissipation and Joule heating are considered also. Nonlinear partial differential equations are reduced into nonlinear ordinary differential equations by formulating similarity transformations. Numerical solutions of transformed boundary layer equations are clarified by applying the Keller-Box method. Effects of several types of nanofluids and various specified parameters such as solid volume fraction, magnetic parameter, Brinkmann number and local Biot number on velocity and temperature fields have been plotted graphically, while values of surface shear stress and surface heat flux are presented via table. Further, comparison of obtained computational values has been made with earlier published results for non-magnetic case.

Entropy generation in hydromagnetic nanofluid flow over a non-linear stretching sheet with Navier’s velocity slip and convective heat transfer

The intention behind carrying out this research work is to investigate the unsteady hydromagnetic boundary layer flow of a thermally radiating nanofluid past a non-linear stretching sheet embedded in a porous medium in the presence of an externally applied magnetic field along with Navier’s velocity slip. The governing partial differential equations, defining the flow regime, are transformed into a system of ordinary differential equations by employing suitable similarity transformation. Optimal Homotopy Analysis Method has been incorporated in order to solve the converted non-linear coupled equations. The impact of several regulatory flow parameters on the temperature, velocity, and nanoparticle concentration are explained via graphs, while the variation of some useful engineering quantities such as the Nusselt number, skin friction co-efficient, and Sherwood number are interpreted through tabular values. An analysis regarding entropy generation of the system is also presented. Furthermore, on the numeric data of the skin friction coefficient and Nusselt number, a linear and quadratic multiple linear regression analysis has also been performed. The findings of the present analysis reveal that the velocity slip, unsteadiness and the nonlinearity of the stretching velocity lead to a fall in the velocity profile of the nanofluid.

MHD Flow of a Carreau Fluid Past a Stretching Cylinder with Cattaneo-Christov Heat Flux Using Spectral Relaxation Method

A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temperature distributions are sketched as well as analyzed physically. The result indicates that the temperature distribution decay for higher temperature jump and thermal relaxation parameters respectively.

Entropy Analysis in MHD Flow with Heat Source and Thermal Radiation Past a Stretching Sheet in a Porous Medium

In this paper, we conducted the thermodynamics first and second laws analyses on hydromagnetic boundary layer flow of an incompressible electrically conducting viscous fluid past a vertically stretching sheet embedded in a porous medium with heat source and thermal radiation. The governing equations describing the problem are converted to a system of nonlinear ordinary differential equations using appropriate similarity variables. Using shooting technique coupled with Runge-Kutta-Ferhlberg integration scheme, the model boundary value problem is numerically tackled. The parametric effects on fluid velocity, temperature, skin friction, Nusselt number, entropy generation rate and the Bejan number are presented graphically and discussed quantitatively. Our results revealed among others, that the entropy generation is enhanced by magnetic field, thermal radiation and heat source but lessened by increasing porous medium permeability and buoyancy force.

MHD heat transfer flow of Casson fluid past a stretching wedge subject to suction and injection

The steady two dimensional incompressible hydromagnetic boundary layer flow caused by stretching wedge immersed in Casson fluid with heat transfer and suction/injection is investigated numerically. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. Numerical results for local skin friction coefficient are compared with the existing literature and observed in closed agreement with those results. The effects of pertinent parameters on flow fields are displayed graphically and discussed. It is found that velocity decreases with increase of Casson parameter and wedge angle parameter when the wedge is stretching faster than free stream. It is also observed that rate of heat transfer at surface increases with the increase of Prandtl number and Casson fluid parameter. Moreover, with increase of suction parameter the fluid velocity decreases and rate of shear stress increases.

Unsteady MHD free convective boundary layer flow of a nanofluid past a moving vertical plate

An investigation on hydromagnetic boundary layer flow over a past an exponentially accelerated vertical plate of a nanofluid in presence of the transverse magnetic field. The fluid considered here is a non-scattering medium and the Boussinesq’s approximation is used to describe pressure gradient and radiative heat flux in the energy equation. We have considered three types of nanofluids containing Cu- water, TiO2- water and Al2O3 - water. The governing partial differential equations are transformed to dimensionless with suitable dimensional quantities and then employed Laplace transform technique in order to a closed form solution for velocity, temperature and concentration fields without any restriction. The numerical values of nanofluids on the temperature, transverse velocity, skin-friction, and Nusselt number are studies through graphs.

MHD three dimensional double diffusive flow of Casson nanofluid with buoyancy forces and nonlinear thermal radiation over a stretching surface

Purpose This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface. The combined effects of nonlinear thermal radiation, magnetic field, buoyancy forces, thermophoresis and Brownian motion are taken into consideration with convective boundary conditions. Design/methodology/approach Similarity transformations are used to reduce the governing partial differential equations into a set of nonlinear ordinary differential equations. The reduced equations were numerically solved using Runge–Kutta–Fehlberg fourth-fifth-order method along with shooting technique. Findings The impact of several existing physical parameters such as Casson parameter, mixed convection parameter, regular buoyancy ratio parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, temperature ratio parameter on velocity, temperature, solutal and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that the solutal component increases for Dufour Lewis number, whereas it decreases for nanofluid Lewis number. Moreover, velocity profiles decrease for Casson parameter, while the Nusselt number increases for Biot number, radiation and temperature ratio parameter. Originality/value This paper is a new work related to three-dimensional double-diffusive flow of Casson nanofluid with buoyancy and nonlinear thermal radiation effect.