Hydromagnetic Boundary Layer Flow Research Articles

Hydromagnetic boundary layer flow of a dusty fluid in a porous medium over a stretching sheet with slip effect

This paper investigated the problem of hydromagnetic boundary layer flow and heat transfer of a dusty fluid over a stretching sheet through a porous medium. The velocity slip was considered instead of the no-slip condition at the boundary. The governing partial equations were reduced into a set of non-linear ordinary differential equations by using the suitable similarity transformation. The transformed equations were numerically integrated using bvp4c in Matlab. The effects of various physical parameters on the velocity and temperature profiles of both phases, such as fluid-particle interaction parameter, magnetic parameter, mass concentration parameter, porosity parameter and Prandtl number were obtained and analyzed through several plots. Useful discussions were carried out with the help of plotted graphs and tables. Under the limiting cases, the obtained numerical results were compared and found to be in good agreement with previously published results.

Entropy generation in hydromagnetic boundary flow under the effects of frictional and Joule heating: Exact solutions

The objective of the present article is to discuss the effects of viscous dissipation and Joule heating on entropy generation in a hydromagnetic boundary layer flow. Governing equations are reduced to self-similar equations via suitable similarity transformations. The expressions for the volumetric entropy generation rate and the Bejan number are also obtained using similarity transformations. The exact solution of the transformed energy equation is computed using the Laplace transform treatment. The obtained exact solutions are utilized to calculate the entropy generation number and the Bejan number. The impacts of Prandtl number, viscous dissipation parameter (Eckert number), magnetic parameter, mass suction and temperature difference parameter on entropy generation and Bejan number are discussed graphically. The increasing value of the temperature difference parameter reduces the entropy generation. The entropy generation increases with the increasing values of the magnetic parameter, the Eckert number, the mass suction parameter and the Prandtl number.

Double stratification effects on heat and mass transfer in unsteady MHD nanofluid flow over a flat surface

The focus of this work is to theoretically investigate the problem of double stratification on heat and mass transfer in an unsteady hydromagnetic boundary layer flow of a nanofluid over a flat surface. The model employed for the nanofluid transport equations incorporate the effects of Brownian motion and thermophoresis in the presence of thermal and solutal stratification. The governing nonlinear partial differential equations and their associated boundary conditions are initially transformed into dimensionless form by using similarity variables, before being solved numerically by employing the Runge–Kutta–Fehlberg fourth-order method with shooting technique. The effects of different controlling parameters, viz. solutal and thermal stratification, Lewis number, thermophoresis, Brownian motion, magnetic field and unsteadiness on the fluid velocity, temperature, skin friction coefficient, the local Nusselt number, and the local Sherwood number are graphically depicted and quantitatively discussed in detail taking into account the practical applications of each profile. It is noted that thermal stratification reduces the fluid temperature, while the solutal stratification reduces the nanoparticle concentration.

Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface

In this article, the unsteady boundary layer flow of an incompressible Williamson fluid over a permeable radiative stretched surface. Both electric and magnetic fields are taken into account. The nonlinear system of ordinary differential equations are obtained through suitable transformations and then solved statistically and analytically. Influence of physical on the velocity and temperature are graphically analyzed. The expressions of skin friction coefficient and local Nusselt number are presented and examined numerically. Correlation coefficient and probable error are calculated to check the significance and insignificant relation of parameters with skin friction and Nusselt number.

Effects of Variable Thermal Conductivity with Thermal Radiation on MHD Flow and Heat Transfer of Casson Liquid Film Over an Unsteady Stretching Surface

In the present work, the hydromagnetic boundary layer flow and heat transfer of Casson fluid in a thin liquid film over an unsteady stretching sheet in the presence of variable thermal conductivity, thermal radiation, and viscous dissipation is investigated numerically. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. Similarity equations are derived and then solved numerically by using a shooting method with fourth order Runge–Kutta integration scheme. Comparisons with previous literature are accomplished and obtained an excellent agreement. The influences of parameters governing a thin liquid film of Casson fluid and heat transfer characteristics are presented graphically and analyzed. It is observed that the heat transfer rate diminishes with a rise in thermal conductivity parameter and Eckert number. Further, the opposite influence is found with an increase in radiation parameter.

New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals

In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4) and Optimal Homotopy Asymptotic Method (OHAM-1). The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.

Thermal radiation, viscous dissipation, ohmic dissipation and mass transfer effects on unsteady hydromagnetic flow over a stretching surface

Abstract The aim of present investigation was to study the effects of thermal radiation, viscous dissipation, ohmic dissipation and mass transfer effects on unsteady hydromagnetic boundary layer flow over a stretching surface. The governing equations of momentum, thermal and concentration boundary layers are reduced to a set of ordinary differential equations by means of suitable similarity transformations. Those equations are solved numerically for some arbitrary values of the governing physical parameters such as the Unsteadiness parameter ( A ), Magnetic interaction parameter ( M 2 ), Prandtl number ( Pr ), Radiation parameter ( R d ), Eckert number ( Ec ) and Schmidt number ( Sc ) using Runge Kutta method of fourth order along with an efficient shooting method called Nachtsheim Swigert integration technique for the satisfaction of asymptotic boundary conditions. The results obtained are discussed with the help of graphical illustrations. Important physical concepts such as skin friction coefficient, Nusselt number and Sherwood number are also obtained and are discussed in detail.

Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation

This paper is concerned with the unsteady two-dimensional boundary layer flow of an incompressible Williamson fluid over an unsteady permeable stretching surface with thermal radiation. Effects of electric and magnetic fields are considered. The nonlinear boundary layer partial differential equations are first converted into the system of ordinary differential equations and then solved analytically. Effects of physical parameters such as Weissenberg number, unsteadiness parameter, suction parameter, magnetic parameter, electric parameter, radiation parameter, Prandtl number and Eckert number on the velocity and temperature are graphically analyzed. The expressions of skin friction coefficient and local Nusselt number are presented and examined numerically.

Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid

The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs.

Heat and Mass Transfer in Visco-Elastic Fluid through Rotating Porous Channel with Hall Effect

This paper examined the hydromagnetic boundary layer flow of viscoelastic fluid with heat and mass transfer in a vertical channel with rotation and Hall current. A constant suction and injection is applied to the plates. A strong magnetic field is applied in the direction normal to the plates. The entire system rotates with uniform angular velocity (Ω), about the axis perpendicular to the plates. The governing equations are solved by perturbation technique to obtain an analytical result for velocity, temperature, concentration distributions and results are presented graphically for various values of viscoelastic parameter (K2), Prandtl number (Pr), Schmidt number (Sc), radiation parameter (R), heat generation parameter (Qh) and Hall parameter (m).

Entropy analysis in MHD nanofluid flow near a convectively heated stretching surface

A comprehensive study of entropy generation in hydromagnetic boundary layer flow of nanofluid over a convectively heated stretching surface is conducted in the presence of viscous and joule dissipation. The Buongiorno model is employed to represent the nanofluid where the thermophoresis and Brownian motion effects are of prime focus. The partial differential equations governing the transport phenomena are converted to non-linear ordinary differential equations using suitable similarity transformations. These transformed equations are then solved analytically with the help of optimal homotopy analysis method (OHAM). Comparison of the obtained results is made with the previous studies under certain limiting cases. The main emphasis is kept on examining the effects of pertinent parameters involved in the problem on entropy production. Detail parametric study is carried out and the results are represented through graphs and tables.

Mathematical model for velocity and temperature of gravity-driven convective optically thick nanofluid flow past an oscillating vertical plate in presence of magnetic field and radiation

Analytic expression for unsteady hydromagnetic boundary layer flow past an oscillating vertical plate in optically thick nanofluid in presence of thermal radiation and uniform transverse magnetic field is obtained. The Rosseland diffusion flux model is adopted to simulate thermal radiation effects. The momentum and energy conservation equations are made dimensionless and analytic solution is obtained using the Laplace transform. The results for velocity and temperature are obtained and plotted graphically. It is found that the velocity of the nanofluid increases with radiation parameter Nr, Grashof number Gr and time while decreases with increase in magnetic field and Prandtl number Pr. Temperature of nano-fluids increases with time while decrease with increase in Nr and Pr.

Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension

This paper investigates the problem of MHD boundary layer flow and heat transfer of an electrically conducting dusty fluid over an unsteady stretching surface through a non-Darcy porous medium. The flow in porous medium is described by employing the Darcy–Forchheimer based model. The unsteadiness in the flow and temperature fields are because of time-dependent stretching velocity and surface temperature. The effect of thermal radiation, viscous dissipation and non-uniform heat source/sink are also taken into account. The pertinent time-dependent equations, governing the flow and heat transfer are reduced into a set of non-linear ordinary differential equations with the aid of suitable similarity transformations. The transformed equations are numerically integrated using fourth–fifth order Runge–Kutta–Fehlberg method. The effects of various physical parameters on the velocity and temperature profiles of both phases are analyzed through several plots. Obtained numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. It is found that, by suspending fine dust particles in the clean fluid reduces the thermal boundary layer thickness. Therefore, the dusty fluids are preferable in engineering and scientific applications, involving cooling processes.

Nonlinear Radiation Effects on Hydromagnetic Boundary Layer Flow and Heat Transfer over a Shrinking Surface

The effects of nonlinear radiation on hydromagnetic boundary layer flow and heat transfer over a shrinking surface is investigated in the present work. Using suitable similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. The resultant equations which are highly nonlinear are solved numerically using Nachtsheim Swigert shooting iteration scheme together with Fourth Order Runge Kutta method. Numerical solutions for velocity, skin friction coefficient and temperature are obtained for various values of physical parameters involved in the study namely Suction parameter, Magnetic parameter, Prandtl number, Radiation parameter and Temperature ratio parameter. Numerical values for dimensionless rate of heat transfer are also obtained for various physical parameters and are shown through tables. The analytical solution of the energy equation when the radiation term is taken in linear form is obtained using Confluent hypergeometric function.

Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate

An investigation of the hydromagnetic boundary layer flow past a moving vertical plate in nanofluids in the presence of a uniform transverse magnetic field and thermal radiation has been carried out. Three different types of water-based nanofluids containing copper, aluminum oxide and titanium dioxide are taken into consideration. The governing equations are solved using Laplace transform technique and the solutions are presented in closed form. The numerical values of nanofluid temperature, velocity, the rate of heat transfer and the shear stress at the plate are presented graphically for several values of the pertinent parameters. The present study finds applications in engineering devices.

Hydromagnetic Boundary Layer Flow and Heat Transfer Characteristics of a Nanofluid over an Inclined Stretching Surface in the Presence of a Convective Surface: A Comprehensive Study

In this paper we investigate numerically the hydromagnetic boundary layer flow and heat transfer characteristics of a nanofluid using three types of nanoparticles (copper, aluminium oxide and titanium dioxide) having various shapes (spherical, cylindrical, arbitrary, etc) by considering three kinds of base fluids (water, ethylene glycol and engine oil) over a nonlinear inclined stretching surface, taking into account the effect of convective surface condition. Using similarity transformations, the governing nonlinear partial differential equations of the physical model are transformed into non-dimensional ordinary differential equations which are solved for local similar solutions using the very robust computer algebra software, Maple 13. The numerical simulation is carried out to investigate the role of the pertinent parameters on the flow and temperature fields as well as on the rate of heat transfer and on the rate of shear stress. The results show that the addition of nanoparticles to the base fluid may not always increase the rate of heat transfer. It depends significantly on the surface convection, type of base fluid and nanoparticles. The finding of this study will open a gate for better understanding of nanofluid characteristics.

Effect of partial slip on hydromagnetic flow over a porous stretching sheet with non-uniform heat source/sink, thermal radiation and wall mass transfer

In this work, we have investigated the effect of partial slip on hydromagnetic boundary layer flow in porous medium over a stretching surface with space and temperature dependent internal heat generation/absorption, thermal radiation and wall mass transfer (suction/blowing). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations are converted into non-linear ordinary differential equations by means of similarity transformations. The dimensionless governing equations for this investigation are solved analytically using hypergeometric functions. The results are carried out for prescribed surface temperature (PST) and prescribed power law surface heat flux (PHF). The effect of partial slip parameter with magnetic parameter, porosity parameter, wall mass transfer parameter (suction/blowing), space and temperature dependent internal heat generation/absorption parameter, Prandtl number and radiation parameter on velocity and temperature distributions are depicted graphically and are analyzed in detail.

Effect of Hall Current on Hydromagnetic Boundary Layer in Rotating Dusty Fluid with Exponential Pressure Gradient

An asymptotic analysis of an unsteady hydromagnetic boundary layer flow of an incompressible viscous conducting fluid with uniform distribution of dust particle bounded by semi-infinite plate in the presence of exponential decaying pressure gradient is investigated. The exact solutions of the boundary layer equations are obtained by asymptotic behaviour of Laplace transform treatment. The structure of velocity distribution is investigated and the effect of various physical parameters likes magnetic parameter, Ekman parameter and Hall current parameter on velocities of both fluid and dust phase are depicted graphically.

Convection heat and mass transfer in a hydromagnetic flow of a micropolar fluid over a porous medium

This study presents a mathematical analysis of a hydromagnetic boundary layer flow, heat and mass transfer characteristics on steady twodimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field in the presence of thermal radiation. The governing system of partial differential equations is first transformed into a system of non- linear ordinary differential equation using the usual similarity transformation. The resulting coupled non-linear ordinary differential equations are then solved using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, temperature and concentration fields within the boundary layer are separately discussed. The effects of the pertinent parameters on the wall temperature, wall solutal concentration, skin friction coefficient and the rate of heat and mass transfer are presented numerically in tabular form. The results obtained showed that these parameters have significant influence on the flow.

Analytical Solution of MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet with Partial Slip

This paper investigates the hydromagnetic boundary layer flow and heat transfer of a non-Newtonian Casson fluid in the neighborhood of a stagnation point over a stretching surface in the presence of velocity and thermal slips at the boundary. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformations. The analytic solutions are developed by a homotopy analysis method (HAM). The results pertaining to the present study indicate that the flow and temperature fields are significantly influenced by Casson parameter (), the magnetic parameter , the velocity slip parameter , and the thermal slip parameter . An increase in the velocity slip parameter causes decrease in the flow velocity, while an increase in the value of the thermal slip parameter causes increase in the temperature of the fluid. It is also observed that the velocity at a point decreases with increase in .