Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

Summary The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.     

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.     

Mixed convection of micropolar fluid about a sphere with blowing and suction

An analysis is performed to study the skin friction characteristics of laminar mixed forced and free convection flow of micropolar fluid about a permeable sphere with various prescribed thermal conditions on the surface. The problem was formulated by applying a suitable variables transformation and solutions were obtained by an efficient difference method. Numerical results were carried out for a wide range of mass transfer parameter as the Prandtl number at 0.7 or 7 with several values of material parameters and buoyancy force parameter of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed. A comparison between the present solution and finite-difference solution from T.S. Chen, etc. is also shown.     

Natural convection on a thin vertical cylinder moving in a high-porosity ambient medium

An analysis has been performed to study the natural convection flow over a thin vertical cylinder which is moving with a constant velocity in a non-Darcy high-porosity ambient medium. Both constant wall temperature and constant heat flux conditions have been considered. The coupled non-linear parabolic partial differential equations have been solved numerically by using an implicit finite-difference scheme. The heat transfer is found to be significantly affected by the inertia and porosity parameters, and the Prandtl number, whereas the skin friction is weakly affected. The heat transfer for the constant heat flux case is more than that of the constant wall temperature case and this difference increases with the Prandtl number. The heat transfer increases with the buoyancy force, but the skin friction is slightly reduced.     

Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate

Summary A laminar forced and free mixed convection flow on a flat plate with uniform suction or injection was theoretically investigated. Nonsimilar partial differential equations are transformed into nonsimilar ordinary ones by means of difference-differential method. The solutions of the resulting equations are obtained with integral forms, and are calculated by the method of successive iteration. The velocity profiles, temperature profiles, friction coefficient and heat transfer coefficient are obtained for various values of suction/injection parameter and buoyancy parameter.     

Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer

Combined free and forced convection in the boundary layer flow of a micropolar fluid over a horizontal surface is studied. Buoyancy effects on the flow and temperature fields are discussed. The influence of uniform mass transfer from the surface is also considered. Wall friction and heat transfer results are presented for various cases representing the relative effects of blowing or suction as compared to the combined effects of buoyancy and mass transfer.     

Analysis of forced convection micropolar boundary layer about a permeable sphere

The heat transfer characteristics and local skin friction for forced convection flow of micropolar fluid over an isothermal or a constant-heat-flux surface of sphere with surface mass transfer have been studied. The problem was formulated by applying a suitable variables transformation and the solutions were obtained by an implicit finite difference method. Numerical results were carried out for a wide range of mass transfer parameters as the Prandtl number at 0.7 or 7 with several values of material parameters of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed.     

Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers

The mixed convection boundary-layer flow over a vertical surface with a prescribed surface heat flux is considered for both large and small values of the Prandtl number. The similarity equations are treated first. It is shown that, for large values of the Prandtl number, the solution approaches the forced convection limit with the free convection effects having only a small perturbation on this. The opposite is seen to be the case for small values of the Prandtl number, now free convection becomes the dominant heat transfer mechanism. A consequence of this is seen to be that the range of negative buoyancy parameter (opposed flow) over which a solution can exist decreases to zero as the Prandtl number is decreased.The scalings worked out for the similarity equations are then applied to the general boundary-layer flow, with the particular example of a uniform stream over a flat plate with uniform surface heat flux being treated in detail. Again it is seen that, for large Prandtl numbers, the solution approaches the forced convection limit whereas, for small Prandtl numbers, free convection dominates the flow. The effect of this is seen, for opposed flow, to delay the onset of separation for large Prandtl numbers, and to bring the separation point closer to the leading edge as the Prandtl number is decreased. An estimate for this effect is obtained.     

Investigation of the effect of transverse thermal dispersion on forced convection in porous media

Summary In this paper an analytical study of the effect of the transverse thermal dispersion on fully developed forced convection in a parallel-plate channel filled with an isotropic fluid saturated porous medium is carried out. It is assumed that the momentum flow in the channel is governed by the Brinkman-Forchheimer-extended Darcy equation. The objective of the present research is to determine in which situations thermal dispersion can significantly influence heat transfer in the channel.     

Nonlinear instability of mixed convection flow over a horizontal cylinder

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy—with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation—that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer.     

Influence of radiation on mixed convection over a wedge in non-Darcy porous medium

The influences of radiation on mixed convection flow of an optically dense viscous fluid along an isothermal wedge embedded in non-Darcy porous medium, in the presence of heat source/sink are numerically investigated. The entire mixed convection regime is covered by a single parameter χ from the pure free convection limit (χ=0) to the pure forced convection limit (χ=1). Forchheimer’s extension is employed to describe the fluid flow in the porous medium and the Rosseland diffusion approximation is considered to describe the radiative heat flux in the energy equation. The governing equations, including internal heat source/sink, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by the Keller box method. The effect of the radiation parameter, mixed convection parameter, Forchheimer number and heat source/sink parameter on the velocity and temperature profiles as well as on the local Nusselt number is presented and analyzed. The results are compared with those known from the literature and excellent agreement between the results is obtained.     

Thermal convection of micropolar fluids past two-dimensional or axisymmetric bodies with suction/injection

Steady laminar forced convection of micropolar fluids past two-dimensional or axisymmetric bodies with porous walls and different thermal boundary conditions has been analyzed. New coordinate transformations are employed to reduce the streamwise-dependence in the coupled nonlinear boundary-layer equations. The analysis is applied to cylinders and spheres with fluid injection/suction at the surface. Of interest are the effects of material parameters, wall mass transfer, the Prandtl number and the distinct thermal boundary conditions on the local skin friction coefficient and heat transfer coefficient.     

Effect of magnetic field on the heat and mass transfer in a vertical annulus

This paper reports the effect of axial or radial magnetic field on the double-diffusive natural convection in a vertical cylindrical annular cavity. The boundary conditions at the side walls are imposed in such a way that the thermal and solutal buoyancy effects are either cooperating or opposing, resulting in a cooperating gradients or opposing gradients flow configuration. The top and bottom walls are insulated and impermeable. The governing equations of this fluid system are solved by the Alternating Direction Implicit and the Successive Line Over Relaxation methods. Total heat and mass transfer rates across the cavity are calculated by evaluating the average Nusselt and Sherwood numbers. The main objective of the present numerical study is to understand the effect of magnetic field on the double-diffusive convection in the annular cavity. From the numerical results, it is found that the magnetic field suppresses the double-diffusive convection only for small buoyancy ratios. But, for larger buoyancy ratio, the magnetic field is effective in suppressing the thermal convective flow. Further, the magnetic field is effective when it is applied perpendicular to the main flow.     

Theoretical analysis on mixed convection boundary layer flow over a wedge with uniform suction or injection

Summary Forced and free mixed convection boundary layer flow over a wedge with uniform suction or injection is theoretically investigated. Nonsimilar partial differential equations are transformed into ordinary differential equations by means of difference-differential method. The solutions of the resulting equations are obtained in integral forms and are calculated by iterative numerical procedures. The results were given for velocity profiles, temperature profiles, friction and heat transfer parameters for various values of suction/injection parameter, pressure gradient parameter and buoyancy parameter.     

Flow Pattern and Heat Transfer in a Cylindrical Annulus Under 1 g and Low-g Conditions: Experiments

We investigate the thermal convection in an annular cavity, with differentially heated inner and outer cylinders, under the influence of a dielectrophoretic (DEP) force. Applying a temperature gradient to a liquid creates buoyancy driven thermal convection. When additionally a radially acting DEP-force is applied by means of an alternating electric field, the pattern of this convective flow changes which also leads to a change in the heat transfer. Depending on the parameters, e.g. an axisymmetric structure with toroidal vortices appears. Another possible structure are columnar vortices, which extend through the annulus. To isolate the effect of the DEP-force, this experiment is not only conducted in the laboratory, but also in microgravity conditions during parabolic flights. By using DEP-induced convective flows in microgravity a comparable heat transfer as with buoyancy convection under Earth’s condition can be obtained. A better understanding of the heat transport mechanisms inside a dielectric liquid confined between two concentric cylinders can deliver solutions for the improvement of the heat transport in many technical applications.     

A steady viscous-thermogravitational flow of capillary liquid and heat transfer in a vertical cavity under asymmetric heat conditions

The problem of joint forced and free laminar convection and heat transfer for liquid with a variable viscosity under a linear temperature distribution between surfaces of a vertical two-dimensional channel is solved analytically. The dependences obtained manifest a strong difference (upon a relatively small variation in viscosity) of the distributions of velocity, friction drag coefficient, and heat transfer from the case of the full Boussinesq approximation while solving problems of mixed convection.     

Mixed convection in a laminar axisymmetric water plume in a vertical coflowing stream at temperatures around the density extremum

Summary.  In all studies concerning mixed convection in round laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the density-temperature relationship for water is nonlinear at low temperatures. In this study the problem of a round laminar water plume in a coflowing vertical free stream has been investigated in the temperature range between 20 °C and 0 °C taking into account the nonlinearity between density and temperature. The results are obtained with the numerical solution of the boundary-layer equations. The paper deals mainly with assisting mixed convection and with some special cases of opposing and assisting mixed convection at the same plume flow. For the assisting mixed convection it was found that the plume behavior depends on the temperature difference between the plume orifice and the ambient water due to the nonlinear relationship between water density and temperature. This dependence weakens and finally diminishes as the buoyancy parameter ξ increases and the mixed convection becomes pure forced convection. Received April 29, 2002; revised November 6, 2002 Published online: June 12, 2003     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.     

Mixed convection in wall plume of power-law fluids

Summary The non-similar boundary layer solutions are presented to study the mixed convective flow of a power-law fluid above a vertical adiabatic surface with a steady thermal source at the leading edge. The boundary layer equations contain an important mixed convection parameter. The governing non-similar equations are solved by means of a novel finite difference scheme for several values of the power-law viscosity index, the buoyancy parameter and the non-Newtonian Prandtl number of the fluid. The solutions obtained are uniformly valid over the entire regime of the buoyancy parameter ranging from forced convection to free convection limits. Consideration is given to the case of buoyancy-assisted and buoyancy-opposed plumes.     

Mixed Convection of Water at 4 °C Along a Wedge with Variable Surface Temperature in a Porous Medium

In this study, the mixed convection of water at 4 °C along a wedge in a porous medium is investigated numerically using a finite difference method. To explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable walltemperature boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and the Nusselt number are obtained and compared with available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ ranged from 0 to 1 in both regimes, whereas different values of λ are considered for the purpose of comparison of heat transfer results.