The effects of temperature-dependent fluid properties on free convective flow along a semi-infinite vertical plate by the presence of radiation

The effects of temperature-dependent density, viscosity and thermal conductivity on the free convective steady laminar boundary layer flow by the presence of radiation for large temperature differences, are studied. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. The fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The usual Boussinesq approximation is neglected due to the large temperature difference between the plate and the fluid. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the shooting method. The effects of the density/temperature parameter n, the thermal conductivity parameter , the viscosity/temperature parameter _r and the radiation parameter F are examined on the velocity and temperature fields as well as the coefficient of heat flux and the shearing stress at the plate.     

Thermal dispersion effects on non-Darcy natural convection with lateral mass flux

The method of similarity solution is used to study the influence of lateral mass flux and thermal dispersion on non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations and the coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The suction/injection velocity distribution has been assumed to have power function form Ax ^l , where x is the distance from the leading edge and the wall temperature distribution is assumed to be uniform. When l=−1/2, similarity solution is possible, and the results indicate that the boundary layer thickness decreases where as the heat transfer rate increases as the mass flux parameter passes from injection domain to the suction domain. The increase in the thermal dispersion parameter is observed to enhance the heat transfer. The combined effect of thermal dispersion and fluid suction/injection on the heat transfer rate is discussed. Received on 9 September 1996     

Thermal radiation effect on non-Darcy natural convection with lateral mass transfer

 A boundary layer analysis has been presented to study the influence of thermal radiation and lateral mass flux on non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained and the combined effect of thermal radiation and fluid suction/injection on the heat transfer rate is discussed. Numerical results for the details of the velocity and temperature profiles as well as Nusselt number have been presented. Received on 7 July 1999     

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.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet

In the present work, the effect of MHD flow and heat transfer within a boundary layer flow on an upper-convected Maxwell (UCM) fluid over a stretching sheet is examined. The governing boundary layer equations of motion and heat transfer are non-dimensionalized using suitable similarity variables and the resulting transformed, ordinary differential equations are then solved numerically by shooting technique with fourth order Runge–Kutta method. For a UCM fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for higher the elastic number. The objective of the present work is to investigate the effect of Maxwell parameter β, magnetic parameter Mn and Prandtl number Pr on the temperature field above the sheet.     

Thermal dispersion effects on non-Darcy natural convection over horizontal plate with surface mass flux

Summary The effect of surface mass flux on the non-Darcy natural convection over a horizontal flat plate in a saturated porous medium is studied using similarity solution technique. Forchheimer extension is considered in the flow equations. The suction/injection velocity distribution has been assumed to have power function form Bx ^l , similar to that of the wall temperature distribution Ax ⁿ , where x is the distance from the leading edge. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The dynamic diffusivity is assumed to vary linearly with the velocity component in the x direction, i.e. along the hot wall. For the problem of constant heat flux from the surface (n=1/2), similarity solution is possible when the exponent l takes the value −1/2. Results indicate that the boundary layer thickness decreases whereas the heat transfer rate increases as the mass flux parameter passes from the injection domain to the suction domain. The increase in the thermal dispersion parameter is observed to favor the heat transfer by reducing the boundary layer thickness. The combined effect of thermal dispersion and fluid suction/injection on the heat transfer rate is discussed. Received 7 December 1995; accepted for publication 7 January 1997     

Hydrodymagnetic three-dimensional flow over a stretching surface with heat and mass transfer

A general analysis has been developed to study the combined effect of the free convective heat and mass transfer on the steady three-dimensional laminar boundary layer flow over a stretching surface. The flow is subject to a transverse magnetic field normal to the plate. The governing three-dimensional partial differential equations for the present case are transformed into ordinary differential equation using three-dimensional similarity variables. The resulting equations, are solved numerically by applying a fifth order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl number Pr and Schmidt number Sc are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions. The results are compared with known from the literature.     

COUPLING BETWEEN LAMINAR FILM CONDENSATION AND NATURAL CONVECTION ON OPPOSITE SIDES OF A VERTICAL PLATE

Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the plate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Pr_c is not negligible for larger values of A* (thermal resistance ratio between natural convecti on side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of R_t (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of R_t. © by 1997 John Wiley & Sons, Ltd.     

MHD mixed convective heat transfer flow about an inclined plate

Mixed convection heat transfer about a semi-infinite inclined plate in the presence of magneto and thermal radiation effects is studied. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the mixed convection parameter R _i, the angle of inclination α, the magnetic parameter M and the radiation–conduction parameter R _d on the velocity and temperature profiles as well as on the local skin friction and local heat transfer parameters. For some specific values of the governing parameters, the results are compared with those available in the literature and a fairly good agreement is obtained.     

A similarity solution for the flow and heat transfer over a moving permeable flat plate in a parallel free stream

This paper presents both a numerical and analytical study in connection with the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream. Both the velocities of the flat plate and the free stream are proportional to x ^1/3. The surface temperature is assumed to be constant. The governing partial differential equations are converted into ordinary differential equations by a new similarity transformation. Numerical results for the flow and heat transfer characteristics are obtained for various values of the moving parameter, transpiration parameter and the Prandtl number. Approximate analytical solutions are also obtained when the suction or injection parameter is very large. It is found that dual solutions exist for the case when the fluid and the plate move in the opposite directions.     

Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Numerical solutions of free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

In this paper, the problem of free convection boundary layer flow on a solid sphere in a micropolar fluid with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of partial differential equations are solved numerically using an implicit finite-difference scheme. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the material or micropolar parameter K, the Prandtl number Pr and the conjugate parameter γ are analyzed and discussed.     

Laminar forced convection conjugate heat transfer over a flat plate

Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied. The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br _x , which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results indicate that for Br _x ≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest. Received on 19 August 1998     

Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.     

Hall effect on MHD free convection boundary layer flow past a vertical flat plate

Effects of Hall current on MHD free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a heated vertical flat plate of finite dimension in the presence of a uniform transverse magnetic field have been studied. An exact solution of the governing equations describing the flow has been obtained. The velocity field, induced magnetic field and bulk temperature distributions in the boundary layer flow have been discussed. It is found that the velocity components increase with an increase in Hall parameter. It is noticed that the induced magnetic field components are radically influenced by the Hall parameter. It is also found that the magnitude of bulk temperature in the x-direction decreases with an increase in either Hall parameter or magnetic parameter. On the other hand, the magnitude of the bulk temperature in the z-direction increases with an increase in Hall parameter whereas it decreases with an increase in magnetic parameter.     

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

 The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le. Received on 26 April 2000     

Radiation-conduction interaction in mixed convection along rotating bodies

This paper investigates the interaction of the steady mixed convection boundary layer flow past a rotating impermeable body placed in a uniform stream moving opposite to the gravitational force and parallel to the axes of the body of revolution with uniform surface temperature and thermal radiation. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The difficulty of having a unified mathematical treatment of this problem is due to the nonsimilarity nature of the governing equations arising from the buoyant force-field and the transverse curvature of the bodies. The important parameters of this problem are the radiation-conduction parameter R _d and the wall to free stream temperature ratio θ _w , for the case of a heated surface. Numerical simulations of the boundary layer equations are performed using the local nonsimilarity method as well as an implicit finite-difference method. The theory is applied to a rotating sphere for the gases with Prandtl number of 0.7. The results are shown graphically in terms of the local skin-friction coefficients and the local rate of heat transfer. Effects of the pertinent parameters R _d and θ _w are also shown on the components of the velocity distribution as well as on the temperature distribution in the boundary layer. Received on 14 January 1997