MHD flow and heat transfer over a radially stretching/shrinking disk

A steady magnetohydrodynamic (MHD) flow past a radially stretching or shrinking disk is investigated. The governing partial differential equations are transformed into a set of ordinary (similarity) differential equations by a similarity transformation. These equations along with the corresponding boundary conditions are solved numerically using the boundary value problem solver (bvp4c) in Matlab. The effects of magnetic field and suction on the shear stress and the heat transfer are analyzed and discussed. It is found that both parameters affect more in the shrinking region. The increase in the magnetic parameter results in the increase of the skin friction coefficient but decrease in the local Nusselt number.The skin friction coefficient and the local Nusselt number increase as suction increases.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

MHD Double-Diffusive Carreau Fluid Flow through a Porous Medium with Variable Thermal Conductivity and Suction/Injection

In this article, we consider the effects of double diffusion on magnetohydrodynamics (MHD) Carreau fluid flow through a porous medium along a stretching sheet. Variable thermal conductivity and suction/injection parameter effects are also taken into the consideration. Similarity transformations are utilized to transform the equations governing the Carreau fluid flow model to dimensionless non-linear ordinary differential equations. Maple software is utilized for the numerical solution. These solutions are then presented through graphs. The velocity, concentration, temperature profile, skin friction coefficient, and the Nusselt and Sherwood numbers under the impact of different parameters are studied. The fluid flow is analyzed for both suction and injection cases. From the analysis carried out, it is observed that the velocity profile reduces by increasing the porosity parameter while it enhances both the temperature and concentration profile. The temperature field enhances with increasing the variable thermal conductivity and the Nusselt number exhibits opposite behavior.     

Free convective MHD flow of visco-elastic fluid past a vertical porous plate in the presence of heat source and chemical reaction

Magnetohydrodynamics flow of a visco-elastic incompressible fluid (Walter’s B′ model) past an infinite porous plate in porous medium under the action of transverse uniform magnetic field in the presence of heat source and chemical reaction is investigated. The governing equations of the motion, energy and concentration are solved by a successive perturbation technique. The flow phenomenon is characterized by suction parameter, magnetic parameter, porosity parameter, Grashoff number, modified Grashoff number, Prandtl number, heat source parameter, chemical reaction parameter and Schmidt number. The expressions for skin friction coefficient, Nusselt number, and Sherwood number on the surface are also discussed.     

Heat transfer analysis for stretching flow over a curved surface with magnetic field

The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.     

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.     

Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications.     

Comparative study on electroosmosis modulated flow of MHD viscoelastic fluid in the presence of modified Darcy’s law

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the high field magnets are extremely important to create 3D images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present work is to explore the impact of an external magnetic field on the viscoelastic fluid flow in the existence of electroosmosis, porous medium and slip boundary conditions. The governing equation is modified under the suitable dimensionless quantities. The resulting non-dimensional differential equation is evaluated by analytical as well as numerical (finite difference and cubic B-spline) methods. The convergence analysis is also presented for the numerical methods. The variations of sundry parameters on velocity, volume flow rate and skin friction are presented through graphical representations. The current analysis depicts that, the higher velocities are noticed in viscoelastic fluid as compared with Newtonian fluid. The velocity enhances with rising of slip and Darcy parameters. Volume flow rate rises with the slip and viscoelastic parameters. Skin friction is a decreasing function of zeta potential, Darcy number and Hall current parameter. The limiting solutions can be captured for the Newtonian fluid model by setting the viscoelastic parameter to zero.     

Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics

In this study, the effects of variable fluid properties on heat transfer in MHD Casson fluid melts over a moving surface in a porous medium in the presence of the radiation are examined. The relevant similarity transformations are used to reduce the governing equations into a system of highly nonlinear ordinary differential equations and those are then solved numerically using the Runge–Kutta–Fehlbergmethod. The effects of different controlling parameters, namely, the Casson parameter,melting and radiation parameters, Prandtl number,magnetic field, porosity, viscosity and the thermal conductivity parameters on flow and heat transfer are investigated. The numerical results for the dimensionless velocity and temperature as well as friction factor and reducedNusselt number are presented graphically and discussed. It is found that the rate of heat transfer increases as the Casson parameter increases.     

MHD free convection flow over an isothermal vertical cone with temperature dependent viscosity

Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity and MHD is studied in this paper. Using appropriate variables, the basic equations are transformed into the non-dimensional boundary-layer equations. These equations are then solved numerically using a very efficient implicit finite-difference method known as Crankl-Nicolson scheme. Detailed results for the velocity, temperature, skin friction, and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, magnetic field parameter, and Prandtl number are discussed. In order to validate our numerical results, the present results are compared with the available work in the literature and are found to be in an excellent agreement.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Free convection effects on HMD horizontal channel flow with Hallcurrents

An exact solution of MHD channel flow between two horizontal parallel plates taking into account free convection currents and the Hall currents is presented. Solutions for the primary and secondary velocity, the induced magnetic field, the skin friction, and the temperature are derived. The velocity field and magnetic field are shown on graphs, and the values of the skin friction and the rate of heat transfer are indicated on tables. The results are discussed in terms of the hall parameter, the Hartmann number, and the Grashof number     

Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.     

Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition

This paper presents a numerical solution for the steady mixed convection magnetohydrodynamic (MHD) flow of an electrically conducting micropolar fluid over a porous shrinking sheet. The velocity of shrinking sheet and magnetic field are assumed to vary as power functions of the distance from the origin. A convective boundary condition is used rather than the customary conditions for temperature, i.e., constant surface temperature or constant heat flux. With the aid of similarity transformations, the governing partial differential equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically, using the variational finite element method (FEM). The influence of various emerging thermophysical parameters, namely suction parameter, convective heat transfer parameter, magnetic parameter and power index on velocity, microrotation and temperature functions is studied extensively and is shown graphically. Additionally the skin friction and rate of heat transfer, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, have also been computed for these parameters. Under the limiting case an analytical solution of the flow velocity is compared with the present numerical results. An excellent agreement between the two sets of solutions is observed. Also, in order to check the convergence of numerical solution, the calculations are carried out by reducing the mesh size. The present study finds applications in materials processing and demonstrates excellent stability and convergence characteristics for the variational FEM code.     

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].      

Theoretical solution of impulsively started vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation

An analysis is performed to study the free convective flow over a moving vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation. The fluid considered here is a gray, absorbing-emitting radiation, but a nonscattering medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature, skin friction and Nusselt number are studied for different parameters like the radiation parameter, Grashof number, Prandtl number, magnetic field parameter, permeability parameter, and time. It is observed that the velocity decreases with increasing radiation parameter.     

Study of graphene Maxwell nanofluid flow past a linearly stretched sheet: A numerical and statistical approach

This study aims to unfold the significance of numerous physical parameters such as magnetic field, heat absorption, thermal radiation, viscous and Joule dissipations, etc. on the flow of graphene Maxwell nanofluid over a linearly stretched sheet with considerations of momentum and thermal slip conditions. The prevailing mathematical equations are reformed into extremely nonlinear coupled ordinary differential equations (ODE) utilizing similarity variables and then the equations are solved numerically by the scheme of Runge-Kutta Fehlberg method along with the shooting technique. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters are shown via numerous graphs whereas numerical values of skin friction coefficients and Nusselt numbers are illustrated and reported in different tables. In addition, statistical approach is followed for the multiple regression estimation analysis on the numerical findings of wall velocity gradient and local Nusselt number and are reported in tabular form to demonstrate the relationship among the heat transfer rate and physical parameters. Our results reveal that the graphene Maxwell nanofluid velocity gets reduced owing to enhancement in magnetic field, angle of inclination of magnetic field, porosity and unsteadiness parameters whereas behavior of nanofluid velocity is reversed due to Maxwell parameter. Further, it is noticed that the heat transfer rate of nanofluid is augmented owing to heat absorption, radiation and thermal slip parameters while it is reduced due to increase in viscous dissipation and unsteadiness parameters. The numerical results of the paper are validated by making comparisons with the earlier published paper under the restricted conditions and we found an excellent agreement with those results. A careful review of research papers reported in literature reveals that none of the authors has attempted this problem earlier although the thoughts and methodology explained in this paper can be anticipated to lead to enormously prolific connections across disciplines.     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.