Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed.With the appropriate transformations,the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter.The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter.The results are discussed in terms of the skin friction,the heat transfer coefficient,the mass transfer coefficient,and the velocity,temperature,and concentration profiles for different values of the Prandtl number,the Schmidt number,the squeezing index,and the mixed convection parameter.     

Constant heat flux solution for mixed convection boundary layer viscoelastic fluid

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.     

Numerical analysis of mixed convection in three‐dimensional rectangular channel with flush‐mounted heat sources based on field synergy principle

In this paper the fluid flow and heat transfer characteristics of mixed convection in three‐dimensional rectangular channel with four heat sources are investigated numerically. The SIMPLEC algorithm is applied to deal with the coupling between pressure and velocity, and a new high‐order stability‐guaranteed second‐order difference (SGSD) scheme is adopted to discretize the convection term. The influence of four parameters is studied: Richardson number, heat source distribution, channel height and inclination angle. The numerical results are analysed from the viewpoint of the field synergy principle, which says that the enhanced convective heat transfer is related not only to the velocity field and temperature field, but also to the synergy between them. It is found that the effects of the four parameters on the thermal performance can all be explained with the field synergy principle. To obtain better electronic cooling, the synergy between the velocity and temperature gradient should be increased when other conditions are unchanged. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermophoretic deposition of particles in fully developed mixed convection flow in a parallel-plate vertical channel

A theoretical analysis is made for thermophoretic transport of small particles through a fully developed laminar, mixed convection flow in a parallel vertical channel. The governing gas-particle ordinary differential equations are expressed in non-dimensional form and are solved numerically for some values of the governing parameters so as to investigate extensively their distinct influence on the flow pattern. These equations are solved also analytically in the special case when the thermophoretic effect is absent and the obtained analytical solution can be regarded as a verification of the numerical results, simultaneously. The parameter zone for the occurrence of reversed flow is presented. It is found that the effect of thermophoretic can be quite significant in appropriate situations.     

An experimental study of ice-layer transition phenomena in a rectangular duct containing water flow

Measurements of both the velocity and turbulence-intensity distributions above an ice-layer surface along flow direction have been performed to clarify the ice-layer transition phenomena observed in a rectangular duct. The test duct which has a lower cooled wall kept less than the freezing temperature of water with cross-sectional dimension of 50 mm by 19 mm was used in the present measurements. The velocity and turbulence-intensity distributions in the test duct were measured using Laser Doppler Velocimeter set up on the two-dimensional traversing table. The freezing experiments were carried out under the condition of uniform water-flow rate even after the ice layer has developed in the test duct. It was found that inlet water flow tended to be laminarized under an influence of developing ice layer, and that onset of the ice-layer transition phenomena might be closely related to an increase in turbulence intensity in the water flow above the developing ice-layer surface.     

Marangoni Mixed Convection Boundary Layer Flow

The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated when besides the Marangoni effects there are also buoyancy effects due to gravity and external pressure gradient effects. We shall use a model proposed by Golia and Viviani (L’ Aerotecnica missili e Spazio 64 (1985) 29–35, Meccanica 21 (1986) 200–204) wherein the Marangoni coupling condition has been included into the boundary conditions at the interface. The similarity equations are first determined, and the pertinent equations are solved numerically for some values of the governing parameters and the features of the flow and temperature fields as well as the interface velocity and heat transfer at the interface are analysed and discussed.     

Convective self-oscillations near an air-bubble surface in a horizontal rectangular channel

The concentration convection in an isothermal fluid near an air bubble clamped between the vertical walls of a horizontal channel with a rectangular cross-section is studied experimentally and numerically. The channel is filled with an aqueous solution of a surfactant with a nonuniform concentration. As a result of the competition between the gravitational convection in the cavity volume and the Marangoni convection near the bubble surface, an oscillation flow regime is established. This regime is observed experimentally over several hours. In the numerical experiment, the oscillations are obtained in the presence of an initial horizontal surfactant concentration gradient. Against the background of gravitational convection, short bursts of Marangoni convection with ten times greater intensity are observed. The convective flow patterns and the oscillation periods obtained experimentally and numerically are in fairly good agreement.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

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.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

Influence of buoyancy in a mixed convection liquid metal flow for a horizontal channel configuration

This article presents the direct numerical simulation (DNS) of mixed convection turbulent heat transfer in a horizontal channel case for liquid lead. Cartesian mesh is used and the incompressible Navier-Stokes equations are discretized with highly accurate finite difference sixth-order compact schemes to perform the DNS. The influence of mixed convection in liquid metal with Prandtl number equal to 0.025 and Reynolds number equal to 4667 has been studied by varying the Richardson number (Ri = 0, 0.25, 0.50, 1.00). The obtained results are extensively analyzed and discussed in this article. In particular, large-scale circulation is observed under the influence of buoyancy. Compared to the forced convection case (Ri = 0), stronger velocity fluctuations are noticed that highlight the fact that turbulence is strongly enhanced with the increasing buoyancy. It also proves that the thermal plumes rising up from the hot wall of the channel activate the cross-stream eddies. Moreover, temperature fluctuations are found to be more homogeneously distributed with increasing buoyancy effects and mixing is more effective in the center of the channel. In addition, compared with forced convection, mixed convection has shown enlargement of the large-scale structures that only appear in the temperature field for low Prandtl number fluids. Extensive results of flow and temperature fields are analyzed and presented.     

Effects of Brownian Motion and Thermophoresis on the Mixed Convection of Nanofluid in a Porous Channel Including Flow Reversal

This article is devoted to combined convection heat transfer of nanofluids through a vertical channel filled with a homogeneous and isotropic porous medium. The flow is assumed to be fully developed and the “Brinkman extended Darcy” model is used for the flow in the porous media and “clear compatible” viscous dissipation model is considered. Also the model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing momentum, energy, and nanopartices volume fraction equations are solved both analytically and numerically. The effects of the influential dimensionless parameters such as Brownian and thermophoresis parameters, mixed convection parameter (Gr/Re), Brinkman, Darcy and Lewis numbers on dimensionless velocity and temperature distributions and pressure drop are studied. Also, the results of the Nusselt number for the both left and right walls are presented and 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.     

On diffusion velocity and the mass conservation equation for components

The mass migration velocity(absolute velocity)of component i in a multicomponent flow is equal to the convection velocity(frame velocity)plus the diffusion velocity(relativevelocity).The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow,the mass migration velocity of component i is(?)(mass-weighted time average velocity).The diffusion velocity(-a)consists of turbulent diffusionvelocity(?)and molecular diffusion velocity(?)(?is the simple time average velocity of component i and a is a certain convection velocity).So,the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mass conservation equation for component i,the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes.In turbulent flow,there could be no diffusion terms,or a turbulent diffusion term only,or both the turbulent and molecular diffusion     

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

The magnetohydrodynamic(MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al₂O₃ nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the...     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Freezing in turbulent flow inside tubes and channels

A simple and quite flexible numerical model is presented to predict the steady state ice-layer formation inside a cooled two dimensional channel or a tube containing a turbulent flow. The effects of arbitrary entrance velocity distributions upon the shape of the ice-layers are examined. The presented numerical scheme is verified by comparing the predicted ice-layers with measurements and generally good agreement was found.     

Developing laminar convection in a vertical double-passage channel

 The effect of the presence of a thin, perfectly conductive baffle on the development of laminar convection in a vertical channel has been investigated numerically. The channel has different constant wall temperatures which are higher than those at the entrance. Velocity and temperature profiles have been presented. The effect of the different parameters on heat transfer in the channel has been discussed. The occurrence of flow reversal has been observed in some cases but examination of this phenomenon has been considered to be beyond the scope of the present work. For long channels, the numerical solutions approach the fully developed flow analytical solution. Finally, the results showed that higher values of Nu_h can be obtained when the baffle is near the hot wall. Received on 23 May 2000     

Flow analysis for wormlike micellar solutions in an axisymmetric capillary channel

Flows of wormlike micellar solutions in an axisymmetric capillary channel were studied both numerically and experimentally. In the experiments, an aqueous solution of cetyltrimethylammonium bromide (CTAB) with sodium salicylate (NaSal) was used as a test fluid. The mole concentration of CTAB is 0.03 mol/l, and that of NaSal is 0.06 mol/l. The velocity distribution was measured with a particle tracking velocimetry and flow visualization experiments were performed. The velocity profile showed a plug-like shape and had inflection points where the velocity gradient rapidly changed. High-shear-rate regions near the channel wall spread with increasing the average velocity. Moreover, the flow turned out to be unstable at high average velocities, and when the flow was unstable, white turbidity was observed near the capillary wall. Shear rates showing a white turbidity were included in the range of shear rate where a shear-rate jump in a flow curve occurred. These results suggest that both the characteristic velocity profile and the emergence of white turbidity relate the shear-rate-jump property of wormlike micellar solution. In the numerical analysis, startup flows were considered. A modified Bautista–Manero model was employed as a constitutive equation, and startup flows at a constant average velocity were numerically simulated. The velocity profile at steady state predicted by the numerical simulation adequately agreed with corresponding experimental data. The velocity profile changes from Newton-like to plug-like with time. Inflection points in velocity profile appeared and moved towards the center-side with time. Temporal changes in both velocity gradient and fluidity indicated that the behavior in velocity depended on the shear-rate-jump property of wormlike micellar solution. The velocity gradient rapidly changed around the inflection point and the range of velocity gradient corresponds to that where a white turbidity was observed in the experiments. An erratum to this article can be found at