Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

This article studies the three-dimensional boundary layer flow of an elasticoviscous luid over a stretching surface. Velocity of the stretching sheet is assumed to be ime-dependent. Effect of mass transfer with higher order chemical reaction is further onsidered. Computations are made by the homptopy analysis method (HAM). Convergence f the obtained series solutions is explicitly analyzed. Variations of embedding arameters on the velocity and concentration are graphically discussed. Numerical computations f surface mass transfer are reported. Comparison of the present results with he numerical solutions is also given.     

Similar solutions of stretching flow with mass transfer

This study describes the influence of mass transfer on the steady two‐dimensional magnetohydrodynamic boundary layer flow of a Jeffery fluid bounded by a stretching sheet. A uniform magnetic field in the presence of chemical reaction is applied. The arising nonlinear partial differential equations are reduced to nonlinear ordinary differential equations by similarity variables. Similar solutions of velocity and concentration fields are derived by a homotopy analysis method. The values of surface mass transfer and gradient of mass transfer are also tabulated. Copyright © 2009 John Wiley & Sons, Ltd.     

Note on the Heat Transfer of Flows over a Stretching Wall in Porous Media: Exact Solutions

In this note, heat transfer over a stretching sheet with mass transfer in a porous medium is revisited. Analytical solutions are presented for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions are expressed by the Kummer’s function. Closed-form solutions are found and presented for some special parameters. The solutions might offer more insights of the heat transfer characteristics compared with the numerical solutions.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.     

Analytic solutions for a liquid film on an unsteady stretching surface

The momentum and heat transfer in a laminar liquid film on a horizontal stretching sheet is analyzed by the Homotopy analysis method (HAM). Analytic series solutions are given and compared with numerical results given by other authors. The good agreement between them shows the effectiveness of HAM to the problem of liquid film on an unsteady stretching surface.     

Darcy-Forchheimer flow with nonlinear mixed convection

An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed. Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy, respectively. The nonlinear Darcy-Forchheimer relation is deliberated. The dimensionless problem is obtained through appropriate transformations. Convergent series solutions are obtained by utilizing an optimal homotopic analysis method (OHAM). Graphs depicting the consequence of influential variables on physical quantities are presented. Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.     

Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet

This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet.     

Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature

The steady nonlinear hydromagnetic flow of an incompressible, viscous and electrically conducting fluid with heat transfer over a surface of variable temperature stretching with a power-law velocity in the presence of variable transverse magnetic field is analysed. Utilizing similarity transformation, governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations and they are numerically solved using fourth-order Runge–Kutta shooting method. Numerical solutions are illustrated graphically by means of graphs. The effects of magnetic field, stretching parameter and Prandtl number on velocity, skin friction, temperature distribution and rate of heat transfer are discussed.     

Three‐dimensional flow of an elastico‐viscous fluid with mass transfer

This paper looks at the unsteady three‐dimensional MHD flow of an elastico‐viscous fluid over a stretching surface. The analysis of mass transfer is also analyzed. The governing boundary layer equations are reduced into partial differential equations with three dependent variables through similarity transformations. The transformed system of equations is solved analytically by employing homotopy analysis method (HAM). Plots for various interesting parameters are presented and discussed. Numerical data for surface shear stresses and surface mass transfer in steady case are also tabulated. Copyright © 2010 John Wiley & Sons, Ltd.     

Boundary layer flow and heat transfer over an unsteady stretching vertical surface

The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with three independent variables are first transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter is small. Comparison with known results for steady-state flow is excellent.     

Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity

The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form u_w=Bx^0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water.     

Effects of partial slip on chemically reactive solute transfer in the boundary layer flow over an exponentially stretching sheet with suction/blowing

The boundary layer flow and mass transfer toward an exponentially stretching porous sheet are analyzed in this paper. Velocity slip is considered instead of the no-slip condition on the boundary. Self-similar equations are obtained by using similarity transformations. Numerical solutions of these equations are obtained by the shooting method. It is found that the fluid velocity and concentration decrease with increasing slip parameter. The fluid velocity decreases with increasing suction parameter.     

Flow and heat transfer in a second grade fluid over a stretching sheet

An analysis is carried out to study the flow and heat transfer characteristics in a second grade fluid over a stretching sheet with prescribed surface temperature including the effects of frictional heating, internal heat generation or absorption, and work due to deformation. In order to solve the fourth-order non-linear differential equation, associated with the flow problem, a fourth boundary condition is augmented and a proper sign for the normal stress modulus is used. It is observed that for a physical flow problem the solution is unique. The solutions for the temperature and the heat transfer characteristics are obtained numerically and presented by a table and graphs. Furthermore, it is shown that the heat flow is always from the stretching sheet to the fluid.     

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.     

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.     

Heat transfer in a hydromagnetic flow over a stretching sheet

Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.     

Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature,and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.     

An exact analytical solution of the Falkner-Skan equation with mass transfer and wall stretching

In this paper, an exact analytical solution of the famous Falkner-Skan equation is obtained. The solution involves the boundary layer flow over a moving wall with mass transfer in presence of a free stream with a power-law velocity distribution. Multiple solution branches are observed. The effects of mass transfer and wall stretching are analyzed. Interesting velocity profiles including velocity overshoot and reversal flows are observed in the presence of both mass transfer and wall stretching. These solutions greatly enrich the analytical solution for the celebrated Falkner-Skan equation and the understanding of this important and interesting equation.     

Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet

The mixed convection two-dimensional boundary layer flow of a micropolar fluid near the stagnation point on a stretching vertical sheet is investigated. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a finite-difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed. Both assisting and opposing flows are considered. Results are presented in terms of the skin friction coefficient and the local Nusselt number with selections of velocity, microrotation and temperature profiles. Dual solutions are found to exist for the opposing flow.