Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface

A mixed convection flow of an Oldroyd-B fluid in the presence of thermal radiation is investigated. The flow is induced by an inclined stretching surface. The boundary layer equations of the Oldroyd-B fluid in the presence of heat transfer are used. Appropriate transformations reduce partial differential equations to ordinary differential equations. A computational analysis is performed for convergent series solutions. The values of the local Nusselt number are numerically analyzed. The effects of various parameters on velocity and temperature are discussed.     

Radiation effect on free convection of a non-Newtonian fluid over a vertical cone embedded in a porous medium with heat generation

The effects of thermal radiation on free convection in a non-Newtonian fluid over a vertical cone embedded in a porous medium in the presence of heat generation are studied. By using similarity transformations, the governing equations describing the problem are transformed to a system of nonlinear ordinary differential equations, which are solved numerically. The results are presented in the graphical form. The effects of various physical parameters and of the local Nusselt number on the velocity and the temperature profiles are discussed.     

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.     

Effect of Viscous Dissipation on the Boundary Layer Flow and Heat Transfer Past a Permeable Stretching Surface Embedded in a Porous Medium with a Second-Order Slip Using Chebyshev Finite Difference Method

This article investigates a theoretical and numerical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid toward a permeable stretching surface embedded in a porous medium with a second-order slip and thermal slip. The governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs) using similarity variables. The resulting ODEs are successfully solved numerically with the help of Chebyshev finite difference method. Graphically results are shown for non-dimensional velocities and temperature. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first- and second-order velocity slip parameter, the thermal slip parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. A comparison of numerical results is made with the earlier published results under limiting cases.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.     

Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity.The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature.The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters.In comparison with the previously published work,the excellent agreement is shown.The effects of various parameters on the velocity,the microrotation velocity,and the temperature profiles,as well as the skin-friction coefficient and the Nusselt number,are plotted and discussed.     

Mixed convection boundary layer flow past a wedge with permeable walls

The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f ₀, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow.     

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip

In this paper, the effects of viscous and Ohmic heating and heat generation/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similarity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4 th order Runge-Kutta method is used to solve the transformed equations. Computations are carried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration(VLSI) of electronic chips and film coating.     

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.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.     

Three-dimensional mixed convection squeezing flow

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations (ODEs) by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.     

Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point

The unsteady mixed convection of the Al2O3-Cu/H2O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed. The bvp4c technique is used to solve the resulting ordinary differential equations. The combined effects of the velocity and thermal slip are addressed. The effects of different relevant physical parameters are studied numerically. The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases, while the unsteadiness...     

Effects of the chemical reaction and heat generation or absorption on a mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer

An analysis is performed to study the effects of the chemical reaction and heat generation or absorption on a steady mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer. The governing boundary layer equations with boundary conditions are transformed into the dimensionless form by a group of nonsimilar transformations. Nonsimilar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasi-linearization technique combined with an implicit finite difference scheme. The numerical computations are carried out for different values of dimensionless parameters to display the distributions of the velocity, temperature, concentration, local skin friction coefficient, local Nusselt number, and local Sherwood number. The results obtained indicate that the local Nusselt and Sherwood numbers increase with nonuniform slot suction, but nonuniform slot injection produces the opposite effect. The local Nusselt number decreases with heat generation and increases with heat absorption.     

Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.     

Steady laminar mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface in the presence of a magnetic field

A similarity solution for a steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation point on a vertical permeable plate with a magnetic field and a buoyancy force is obtained by solving a system of nonlinear ordinary differential equations. These equations are solved analytically by using a new kind of a powerful analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). Three different types of nanoparticles, namely, copper (Cu), alumina (Al₂O₃), and titanium oxide (TiO₂), with water as the base fluid are considered. The influence of the volume fraction of nanoparticles, permeability parameter, magnetic parameter, and mixed convection parameter on the surface shear stress and surface heat transfer, as well as on the velocity and temperature profiles, is considered. It is observed that the skin friction coefficient and the local Nusselt number increase with the nanoparticle volume fraction for all types of nanoparticles considered in this study. The greatest values of the skin friction coefficient and the local Nusselt number are obtained for Cu nanoparticles.     

Transport Phenomenon in a Third-Grade Fluid Over an Oscillating Surface

The heat and mass transfer effects on the flow of a conducting third-grade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the third-grade fluid are solved analytically by using a multi-parameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter.     

Viscous Dissipation and Thermal Radiation Effects on Mixed Convection from a Vertical Plate in a Non-Darcy Porous Medium

The paper presents an investigation of the influence of thermal radiation and viscous dissipation on the mixed convective flow due to a vertical plate immersed in a non-Darcy porous medium saturated with a Newtonian fluid. The physical properties of the fluid are assumed to be constant. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically using a shooting method. The results are analyzed for the effects of various physical parameters such as viscous dissipation, thermal radiation, mixed convection parameters, and the modified Reynolds number on dynamics. The heat transfer coefficient is also tabulated for different values of the physical parameters.     

Soret and Dufour effects on heat and mass transfer by mixed convection over a vertical surface saturated porous medium with temperature dependent viscosity

The diffusion‐thermo and thermal‐diffusion effects on heat and mass transfer by mixed convection boundary layer flow over a vertical isothermal permeable surface embedded in a porous medium were studied numerically in the presence of chemical reaction with temperature‐dependent viscosity. The governing nonlinear partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved numerically by using Runge–Kutta method with shooting technique. Numerical results are obtained for the velocity, temperature and concentration distributions, and the local skin friction coefficient, local Nusselt number and local Sherwood number for several values of the parameters, namely, the variable viscosity parameter, suction/injection parameter, Darcy number, chemical reaction parameter, and Dufour and Soret numbers. The obtained results are presented graphically and in tabulated form, and the physical aspects of the problem are discussed. Copyright © 2011 John Wiley & Sons, Ltd.