Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

The present paper is concerned with a class of ex- act solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angu- lar speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form veloc- ity equations. Making use of this solution, analytical formu- las for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is fur- ther analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condi- tion of suction or injection imposed on the wall.

Slip effects on shearing flows in a porous medium

This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.

Three-dimensional unsteady squeezing flow with irreversibility

This exploration examines unsteady magnetohydrodynamic(MHD) three-dimensional flow of viscous material between rotating plates subject to radiation,Joule heating and chemical reaction.The non-linear partial differential system is re-structured into the ordinary differential expressions by the implication of appropriate transformations.The developed differential equations are computed by homotopy analysis technique.Numerical consequences have been accomplished by various values of emerging parameters.Coefficients of skin friction and heat and mass transfer rates have been scrutinized.Irreversibility analysis is carried out.Influence of various prominent variables on entropy generation is presented.Moreover,the temperature increases for higher Dufour number and concentration distribution reduces against Soret number.Higher squeezing parameter enhances velocity while concentration reduces with an increment in squeezing parameter.Both entropy rate and Bejan number increase against higher diffusion parameter.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field: Considerations about the Forces and Wall Shear Stresses

The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several biomedical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Exact solutions of MHD second Stokes flow of generalized Burgers fluid

This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.

Stratified magnetohydrodynamic flow of tangent hyperbolic nanofluid induced by inclined sheet

This paper studies stratified magnetohydrodynamic （MHD） flow of tan- gent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indi- cate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.

Hydromagnetic rotating flow of third grade fluid

This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.

Approximate solutions to MHD Falkner-Skan flow over permeable wall

The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

The aim of this paper is two-dimensional magnetohydrodynamic viscous fluid bounded by infinite sheets to examine the Dufour and Soret effects on the （MHD） steady flow of an electrically conducting An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method （HAM）. The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.

Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid

This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.

EXACT SOLUTIONS FOR MAGNETOHYDRODYNAMIC FLOW IN A ROTATING FLUID

An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.

Soret and Dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation

The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.

Magnetohydrodynamic flow over a moving plate in a parallel stream with an induced magnetic field

A viscous boundary layer flow of an electrically-conducting fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate was investigated. The goveming system of partial differential equations was transformed to ordinary differential equations using a similarity transformation. The similarity equations were then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results of the skin friction coefficient, velocity profiles, and the induced magnetic field profiles were obtained for some values of the moving parameter, magnetic parameter, and reciprocal magnetic Prandtl number. The results indicate that dual solutions exist when the plate and the fluid move in the opposite directions up to a critical value of the moving parameter, whose value depends on the value of the magnetic parameter.

MAGNETOHYDRODYNAMIC PIPE FLOW IN DUCTS WITH PARTIAL CIRCULAR RING CROSS SECTION AND ANNULAR CROSS SECTION

In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross sec- tion and one with annular cross section, in the presence of an applied transverse uniform magnetic field, We ob- tain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnet- ic field.

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

An unsteady magnetohydrodynamic （MHD） boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTM- BF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.