Laminar mixed convection from a continuously moving vertical surface with suction or injection

The boundary layer flow over a uniformly moving vertical surface with suction or injection is studied when the buoyancy forces assist or oppose the flow. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity boundary conditions. The effect is of various governing parameters, such as Prandtl number Pr, temperature exponent n, injection parameter d, and the mixed convection parameter λ=Gr/Re², which determine the velocity and temperature distributions and the heat transfer coefficient, are studied. The heat transfer coefficient increases as λ assisting the flow for all d at Pr=0.72 however, for n=−1 it decreases sharply with λ. On the other hand, increasing λ has no effect on heat transfer coefficient for Pr=10 at n=0, and 1 for almost all values of d studied. However, for n=−1 it has similar effect as for Pr=0.72. It is also found that Nusselt number increases as n increases for fixed λ and d. Received on 26 March 1997     

The effect of radiation on mixed convection flow past a stretching surface

A boundary layer analysis is presented for a study of the influence of radiation and buoyancy on heat and mass transfer characteristics of continuous surfaces having a prescribed variable surface temperature and stretched with rapidly decreasing power law velocities. The effects of suction in the presence of a quiescent fluid medium of constant temperature are considered. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The transformed governing equations are solved numerically and the velocity and temperature profiles as well as the local Nusselt number and skin friction coefficient are presented. Results show that the effect of radiation is to keep the molten mass away from the slot warmer, reduces the friction factor and increases the heat transfer rate compared to the case with no radiation.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.     

The effect of suction or injection on the boundary layer flows induced by continuous surfaces stretched with prescribed skin friction

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. Three major cases are studied for isothermal surface (n=0) stretched corresponding to different dimensional skin friction boundary conditions namely; skin friction at the surface scales as (x ^?1/2) at m=0, constant skin friction at m=1/3 and skin friction scales as (x) at m=1. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, suction/injection parameter f _w , m and n are studied. The results show that for isothermal surface increasing m enhances the dimensionless heat transfer coefficient for fixed f _w at the suction case and the reverse is true at the injection case. Furthermore, for fixed m, as f _w increases the dimensionless heat transfer coefficient increases. Large enhancements are observed in the heat transfer coefficient as the temperature boundary condition along the surface changes from uniform to linear where the dimensional skin friction is of order (x) at m=1. This enhancement decreases as the suction increases.     

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     

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     

Unsteady shrinking sheet with mass transfer in a rotating fluid

In this paper, the problem of unsteady flow induced by a shrinking sheet with mass transfer in a rotating fluid is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of rotation, unsteadiness and mass suction parameters on the reduced skin friction coefficients f″(0) and g′(0), as well as the lateral velocity and velocity profiles are presented and discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.     

Radiation effects on Marangoni convection boundary layer over a permeable surface

The problem of Marangoni convection boundary layer flow that can be formed along the interface of two immiscible fluids when the wall is permeable, where there is suction or injection effect, is considered. Similarity equations are obtained through the application of similarity transformation techniques. The effects of suction/injection and radiation parameters on the heat transfer characteristics are numerically studied using the shooting method for a fixed value of the Prandtl number (Pr=0.7). Numerical results are obtained for the surface temperature gradient or the heat transfer rate as well as the temperature profiles for some values of the governing parameters. Comparisons with known results from the open literature show very good agreements. The results indicate that the heat transfer rate at the surface decreases as the radiation parameter increases. Further, results show that multiple (dual) solutions exist for a certain range of the governing parameters.     

Forced convective flow and heat transfer over a?porous plate in a?Darcy-Forchheimer porous medium in presence of?radiation

A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a plate embedded in a Darcy-Forchheimer porous medium. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is noticed that the boundary layer decreases with an increase in the value of inertial parameter and in this case the temperature profile is found to decrease smoothly within the boundary layer. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter. The rate of heat transfer increases with the increasing values of Prandtl number. The effect of thermal radiation on temperature field is also analyzed.     

Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium

In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered. Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation for negative values of Ec (T _w < T _∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T _w > T _∞). The results are compared with those available in the existing literature and an excellent agreement is obtained.     

On thermal boundary layer of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection

 Heat transfer characteristics of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer and fluid flow in a quiescent fluid were obtained and solved numerically. Velocity and temperature profiles as well as the Nusselt number, Nu, were studied for two thermal boundary conditions; uniform surface temperature and variable surface temperature, for different parameters; Prandtl number Pr, temperature exponent b, velocity exponent m, injection parameter d and power-law index n. It was found that decreasing injection parameter d, and power-law index n and increasing Prandtl number Pr and surface temperature exponent b enhance the heat transfer coefficient. Received on 27 April 2000     

Effects of prescribed heat flux and transpiration on MHD axisymmetric flow impinging on stretching cylinder

A numerical treatment for axisymmetric flow and heat transfer due to a stretching cylinder under the influence of a uniform magnetic field and prescribed surface heat flux is presented. Numerical results are obtained for dimensionless velocity, temperature, skin friction coefficient and Nusselt number for several values of the suction/injection, magnetic and curvature parameters as well as the Prandtl number. The present study reveals that the controlling parameters have strong effects on the physical quantities of interest. It is seen that the magnetic field enhances the dimensionless temperature inside the thermal boundary layer, whereas it reduces the dimensionless velocity inside the hydrodynamic boundary layer. Heat transfer rate reduces, while the skin friction coefficient increases with magnetic field.     

Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation

An unsteady boundary layer flow of a non-Newtonian fluid over a continuously stretching permeable surface in the presence of thermal radiation is investigated. The Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are then solved numerically by the shooting method. The flow features and heat transfer characteristics for different values of the governing parameters (unsteadiness parameter, Maxwell parameter, permeability parameter, suction/blowing parameter, thermal radiation parameter, and Prandtl number) are analyzed and discussed in detail.     

Squeezed flow and heat transfer over a porous surface for viscous fluid

Flow and heat transfer over a permeable sensor surface placed in a squeezing channel is analyzed. A constant transpiration through the sensor surface is assumed. Locally non-similar momentum and energy equations are solved by three different methods, against the transpiration parameter τ, for different values of the squeezing parameter b, and Prandtl number Pr. From the investigation, it is found that when the channel being squeezed, the skin-friction reduces but the heat transfer coefficient increases. Increase in the value of the squeezing parameter onsets reverse flow at the sensor surface when fluid is being injected and the affect is enhanced with the increase of injection through the surface. It is further observed that increase of suction of fluid through the sensor thins the thermal and the momentum boundary layer regions, whereas injection of fluid leads to thickening of both the thermal and the momentum boundary layer regions. Heat transfer from the surface of the sensor increases with the increase of the value of Pr for the entire range of surface mass-flux parameter τ. M. A. Hossain is on leave of absence from University of Dhaka.     

Unsteady laminar boundary layers on an infinite plate in an optically thick radiating gas

Unsteady laminar boundary layers on an infinite plate including the effects of radiative heat transfer and injection or suction on the surface of the plate have been studied. Similar solutions for the velocity and for the temperature are analyzed. Numerical examples for velocity and temperature profiles are given. The effectiveness of transpiration cooling decreases with increasing radiation parameter R _F. The peak temperature in the boundary layer is suppressed if R _F is high enough. This work was initiated when the authors were Summer Consultants at North American Aviation, Inc., Space and Information System Division in 1965 and completed at the University of Maryland and Wayne State University and was supported in part by U.S. Air Force through AFOSR Grant No. AFOSR-1015A-67.     

Heat transfer experiments in rotating boundary layer flow

The influence of Coriolis force on heat transfer in a rotating transitional boundary layer has been experimentally investigated. The experiments have been conducted for local Görtler numbers up to 150. Heat transfer measurements have been performed for a flat plate with nearly uniform heat flux applied to the surface, where the temperature was measured by the thermochromic liquid crystal method. The results indicate that heat transfer is enhanced when Coriolis force acts towards the wall, i.e., on the pressure surface. The velocity measurements under equivalent conditions show that Coriolis instability induces counter-rotating longitudinal vortices which augment the lateral transport of the fluid on the pressure surface. On the other hand, the heat transfer on the suction surface remains at the same level as compared to the case without system rotation. As a consequence, the heat transfer coefficient on the pressure surface is 1.8 times higher than that measured on the suction surface when averaged over the measured surface.     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.     

Scaling Transformations for Boundary Layer Flow near the Stagnation-Point on a Heated Permeable Stretching Surface in a Porous Medium Saturated with a Nanofluid and Heat Generation/Absorption Effects

In this article, a similarity solution of the steady boundary layer flow near the stagnation-point flow on a permeable stretching sheet in a porous medium saturated with a nanofluid and in the presence of internal heat generation/absorption is theoretically studied. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions via Lie-group analysis. Copper (Cu) with water as its base fluid has been considered and representative results have been obtained for the nanoparticle volume fraction parameter f{\phi} in the range 0 ￡ f ￡ 0.2{0\leq \phi \leq 0.2} with the Prandtl number of Pr = 6.8 for the water working fluid. Velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are determined numerically. The influence of pertinent parameters such as nanofluid volume fraction parameter, the ratio of free stream velocity and stretching velocity parameter, the permeability parameter, suction/blowing parameter, and heat source/sink parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results are also presented. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.