Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite fiat 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 w...     

Slip effects on heat and mass transfer in MHD micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction

The influence of partial slip, thermal radiation, chemical reaction and temperature‐dependent fluid properties on heat and mass transfer in hydro‐magnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non‐uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. With the use of the similarity transformation, the governing system of non‐linear partial differential equations are transformed into non‐linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0 (Wolfram Research, Champaign, IL). The numerical values obtained for the velocity, microrotation, temperature, species concentration, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed.Copyright © 2011 John Wiley & Sons, Ltd.     

Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis

The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.     

Finite element system of elastic structure

The article deals with the problems of controllability, observability and stabilizability of an elastic-structural system treated by the finite element method. The results obtained here agree with that obtained in distributed parameter-system model, nevertheless, they are more convenient than those in carrying out the computation with a computer, at the same time the method appears much easier that the conventional one. In section one, the system's controllability and observability are studied and some conditions which are easier to be justified by computer are given. In section two, the problem of stabilizing an elastic object by the use of linear feedback is fully discussed. As the attained results there show that, so far as an elastic-structural system is concerned, it is possible to assign arbitrary frequencies of vibration only by the use of displacement feedback, however, it is impossible to stabilize the system while the system is completely controllable. While the velocity feedback can stabilize the system, but its ability is limited. The case of rigid body motion involved in the system equation has also been discussed. In section three, the control of a straight beam is treated by the finite element method. The whole system of a beam can be decomposed into four irrelevant subsystems of tension-compression, torsion, bending in two directions, their controllability and observability are also analyzed respectively. The controllability and observability of segment-shaped beam are discussed in the end.     

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.     

MHD flow and heat transfer over permeable stretching sheet with slip conditions

The magnetohydrodynamic (MHD) flow and heat transfer characteristics for the boundary layer flow over a permeable stretching sheet are considered. Velocity and thermal slip conditions are taken into account. Problem formulation is developed in the presence of thermal radiation. Governing non‐linear problem is solved by a homotopy analysis method. Convergence of the derived solutions is studied. Numerical values of skin‐friction coefficient and local Nusselt number are tabulated. Effects of pertinent parameters on the velocity and temperature profiles are discussed. Comparison between the present and previous limiting results is shown. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohy-drodynamic (MHD) flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transformarion is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.     

Blasius flow and heat transfer of fourth-grade fluid with slip

This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.     

Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation

The aim of the present paper is to study flow and heat transfer characteristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The resulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are made, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.     

Thermal radiation effects on the flow and heat transfer in a liquid film on an unsteady stretching sheet

The influence of thermal radiation on the flow and heat transfer within Newtonian liquid film over an unsteady stretching sheet with and without thermocapillarity is examined. The governing non‐linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformation, which is solved numerically for different values of the thermal radiation parameter and the thermocapillarity parameter. The results show that the dimensionless velocity, the film thickness and the local Nusselt number increase as the thermocapillarity parameter increases, while the free surface temperature decreases with increasing the thermocapillarity parameter. Also, both the dimensionless temperature and the free surface temperature increase and the local Nusselt number decreases as the thermal radiation parameter increases. Copyright © 2010 John Wiley & Sons, Ltd.     

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 Al₂O₃, 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 are 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.     

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness,variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.     

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation （absorption）

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.     

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.     

Effects of slip,viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially 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 equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra 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 temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the 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. The presence of a magnetic field has also substantial effects on velocity and temperature fields.     

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.     

Effects of heat and mass transfer on peristaltic flow of Williamson fluid in a non‐uniform channel with slip conditions

The combined influence of heat and mass transfer has been explored in a study of peristaltic transport of magnetohydrodynamic Williamson fluid in a non‐uniform channel with flexible walls. The slip conditions are paid due attention and long wavelength and small Reynolds number assumptions are adopted in the problem formulation. The obtained results are valid for small Weissenberg number. A detailed study of involved key parameters in the obtained solutions is made by the sketched graphs. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite difference analysis of mass transfer effects on flow past an impulsively started infinite vertical plate in dissipative fluid and constant heat flux

A finite-difference solution to the flow past an impulsively started infinite vertical plate is derived by assuming 1) presence of species concentration like water vapour, CO₂ etc. and 2) constant heat flux at the plate. The velocity and the temperature profiles, the skin-friction and the rate of heat transfer are shown graphically. The effects of the modified Grashof number,Gm, the Eckert numberE, the Schmidt numberSc on the flow of air are discussed.     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.     

Heat and mass transfer on a MHD third grade fluid with partial slip flow past an infinite vertical insulated porous plate in a porous medium

The influence of third grade, partial slip and other thermophysical parameters on the steady flow, heat and mass transfer of viscoelastic third grade fluid past an infinite vertical insulated plate subject to suction across the boundary layer has been investigated. The space occupying the fluid is porous. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. An efficient numerical scheme of midpoint technique with Richardson’s extrapolation is employed to solve the governing system of coupled nonlinear equations of momentum, energy and concentration. Numerical calculations were carried out for different values of various interesting non-dimensional quantities in the slip flow regime with heat and mass transfer and were shown with the aid of figures. The values of the wall shear stress, the local rate of heat and mass transfers were obtained and tabulated. The analysis shows that as the fluid becomes more shear thickening, the momentum boundary layer decreases but the thermal boundary layer increases; the magnetic field strength is found to decrease with an increasing temperature distribution when the porous plate is insulated. The consequences of increasing the permeability parameter and Schmidt number decrease both the momentum and concentration boundary layer thicknesses respectively whereas an increase in the thermal Grashof number gives rise to the thermal boundary layer thickness.