Showing papers on "Combined forced and natural convection published in 2005"

Convection Heat Transfer

Abstract: Geometry: shape, size, aspect ratio and orientation Flow Type: forced, natural, laminar, turbulent, internal, external Boundary: isothermal (Tw = constant) or isoflux (q̇w = constant) Fluid Type: viscous oil, water, gases or liquid metals Properties: all properties determined at film temperature Tf = (Tw + T∞)/2 Note: ρ and ν ∝ 1/Patm ⇒ see Q12-40 density: ρ ((kg/m) specific heat: Cp (J/kg ·K) dynamic viscosity: μ, (N · s/m) kinematic viscosity: ν ≡ μ/ρ (m/s) thermal conductivity: k, (W/m ·K) thermal diffusivity: α, ≡ k/(ρ · Cp) (m/s) Prandtl number: Pr, ≡ ν/α (−−) volumetric compressibility: β, (1/K)

Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions

Abstract: Previous studies of fluid convection in porous media have considered the onset of convection in isotropic systems and the steady convection in anisotropic systems. This paper bridges between these and develops new results for the onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. These results are relevant to sedimentary formations where the average vertical permeability is some fraction γ of the average horizontal permeability. Linear and global stability analyses are used to define the critical time tc at which the instability occurs as a function of γ and the dimensionless Rayleigh-Darcy number Ra* for both thermal and solute-driven convection in an infinite horizontal slab. Numerical results and approximate analytical solutions are obtained for both a slab of finite thickness and the limit of large slab thickness. For a thick slab, the increase in tc as γ decreases is approximately given by (1+γ)4∕(16γ2). One important application is to the geological storage of carbon dioxide where it is shown that the use of an effective vertical permeability in estimating the critical time is only valid for low permeabilities. The time scale for the onset of convection in geological storage can range from less than a year (for high-permeability formations) to decades or centuries (for low-permeability ones).

Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface

Abstract: The mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent fluid is analyzed using similarity solution technique. Wall temperature and stretching velocity are assumed to have specific exponential function forms. The influence of buoyancy along with viscous dissipation on the convective transport in the boundary layer region is analyzed in both aiding and opposing flow situations. The flow is governed by the mixed convection parameter Gr/Re2. The velocity and temperature inside the boundary layer are observed to be influenced by the parameters like Prandtl number Pr, Gebhart number Gb. Significant changes are observed in non-dimensional skin friction and heat transfer coefficients due to viscous dissipation in the medium. The flow and temperature distributions inside the boundary layer are analyzed and the results for non-dimensional skin friction and heat transfer coefficients are discussed through computer generated plots.

Natural Convection in a Vertical Microchannel

Abstract: It is highly desirable to understand the fluid flow and the heat transfer characteristics of buoyancy-induced micropump and microheat exchanger in microfluidic and thermal systems. In this study, we analytically investigate the fully developed natural convection in an open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions. Both of the velocity slip and the temperature jump conditions are considered because they have countereffects both on the volume flow rate and the heat transfer rate. Results reveal that in most of the natural convection situations, the volume flow rate at microscale is higher than that at macroscale, while the heat transfer rate is lower. It is, therefore, concluded that the temperature jump condition induced by the effects of rarefaction and fluid-wall interaction plays an important role in slip-flow natural convection.

Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface

Abstract: Purpose – To study the steady mixed convection boundary‐layer flow of a micropolar fluid near the region of the stagnation point on a double‐infinite vertical flat plate is studied. The results of this paper are important for the researchers in the area of micropolar fluids.Design/methodology/approach – For the case considered the problem reduces to a system of ordinary differential equations, which is solved numerically using the Keller‐box method. This method is very efficient for solving boundary‐layer problems and it can easily be applied to other general situations than that presented in this paper. Any PhD student can learn and apply it very easily.Findings – Representative results for the velocity, microrotation and temperature profiles, as well as for the reduced skin friction coefficient and the local Nusselt number have been obtained for the case of strong concentration, Prandtl number of 0.7, some values of the material parameter K and the mixed convection parameter λ(≥0). Both assisting and op...

Local thermal non-equilibrium in porous medium convection

Abstract: Many papers exist which either derive or use equations which govern local thermal nonequilibrium phenomena in porous medium convection, where the intrinsic average of the temperatures of the solid and fluid phases may be regarded as being different. We compile and present the most commonly used of these model equations. Attention is then focused on describing some of the most recent research using these equations. Attention is focussed primarily on free and forced convection boundary layers, and on free convection within cavities.

Free-Convective Heat Transfer: With Many Photographs of Flows and Heat Exchange

Abstract: Basic Statements and Equations of Free Convection.- Free Convection on a Plane.- Free Convection on Curved Surfaces.- Natural Convection in Enclosures.- Free Convection in Tubes and Channels, on Ribbed Surfaces and in Tube Bundles.- Nonstationary Processes of Free Convection.- Heat Transfer by Mixed Convection.- Heat Transfer in Media with Special Properties.

Contribution to elliptic relaxation modelling of turbulent natural and mixed convection

Abstract: We report on recent developments in modelling and numerical computations of natural and mixed convection based on newly developed quasi-linear algebraic heat flux and buoyancy extended stress models in the framework of the eddy-viscosity elliptic-relaxation approach. The DNS based 'a priori' testing of generic cases of turbulent natural convection (the side- and heated-from-below configurations) demonstrated that significant improvements are obtained in predictions of turbulent heat flux components when compared with more conventional proposals from the literature [including simple- and generalized gradient diffusion hypotheses (SGDH, GGDH), as well as algebraic flux models (AFM)]. The five equations (k-e-v 2 -f-θ 2 ) model is then applied to the computation of several 2D and 3D natural and mixed convection flows in turbulent regime

Mixed Convection in a Vertical Porous Channel

Abstract: A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman- Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal- isothermal, isoflux-isothermal and isothermal-isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell-Over-Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Gras- hof number and Reynolds number for equal and different wall temperatures. Nusselt num- ber at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it coun- ters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model.

Plume structure in high-Rayleigh-number convection

Abstract: Near-wall structures in turbulent natural convection at Rayleigh numbers of $10^{10}$ to $10^{11}$ at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log–normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Transition to turbulent convection in a fluid layer heated from below at moderate aspect ratio

Abstract: Numerical simulations of Rayleigh-Benard convection in a fluid layer heated from below between two rigid horizontal boundaries have been performed for Rayleigh numbers Ra up to 10 7 , Prandtl numbers in the range between 0.7 and 60 and for aspect ratios Γ up to 20. Periodic boundary conditions in the horizontal plane have been used. To a considerable extent, the evolution towards turbulent convection at high values of Ra is governed by processes exhibited by instabilities of steady or time periodic forms of convection at lower Rayleigh numbers. With increasing Ra, the properties of convection are increasingly determined by the thermal boundary layers. The role of mean flows which may be symmetric or antisymmetric with respect to the mid-plane of the layer is emphasized.

Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity

Abstract: The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form uw=Bx0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water.

Lattice Boltzmann simulation of natural convection with temperature-dependent viscosity in a porous cavity

Abstract: Laminar convection of a fluid with a temperature-dependent viscosity in an enclosure filled with a porous medium is studied numerically based on a Lattice Boltzmann method. It is shown that the variation in viscosity has significant influences on both flow and heat transfer behaviours. In comparison with the results for constant viscosity, the fluid with variable viscosity exhibits a higher heat transfer rate. The non-Darcy effects on fluid flow and heat transfer are also studied for both constant and variable viscosity.

Magnetohydrodynamic mixed convection in a vertical channel

Abstract: The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of e .

Natural convection flow from an isothermal horizontal circular cylinder with temperature dependent viscosity

Abstract: Free convection flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to an inverse linear function of temperature is studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations which are solved numerically by a very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and viscosity profiles of the fluid as well as heat transfer characteristics, namely the local heat transfer rate and the local skin-friction coefficients for a wide range of viscosity parameter e (= 0.0, 0.5, 1.0, 2.0, 3.0,4.0) and the Prandtl number Pr (= 1.0, 7.0, 10.0, 15.0, 20.0, 30.0).

Viscous and Joule heating effects on forced convection flow from radiate isothermal porous surfaces

Abstract: Purpose – To highlight the effect of viscous and Joule heating on different ionized gases in the presence of magneto and thermal radiation effects.Design/methodology/approach – The conservation equations are written for the MHD forced convection in the presence of thermal radiation. The governing equations are transformed into non‐similar form using a set of dimensionless variables and then solved numerically using Keller box method.Findings – The increasing of fluid suction parameter enhances local Nusselt numbers, while the increasing of injection parameter decreases local Nusselt numbers. The inclusion of thermal radiation increases the heat transfer rate for both ionized gases suction or injection. The presence of magnetic field decreases the heat transfer rate for the suction case and increases it for the injection case. Finally, the heat transfer rate is decreased due to viscous dissipation.Research limitations/implications – The combined effects of both viscous and Joule heating on the forced conve...

Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium

Abstract: In this paper, we solve the unsteady mixed convection flow near the stagnation point on a heated vertical flat plate embedded in a Darcian fluid-saturated porous medium by means of an analytic technique, namely the Homotopy Analysis Method. Different from previous perturbation results, our analytic series solutions are accurate and uniformly valid for all dimensionless times and for all possible values of mixed convection parameter, and besides agree well with numerical results. This provides us with a new analytic approach to investigate related unsteady problems.

Asymptotic analysis of the near-wall region of turbulent natural convection flows

Abstract: High-Grashof-number turbulent natural convection in the vicinity of vertical walls with heat transfer is analysed asymptotically. The near-wall boundary layer has a viscosity-influenced inner layer and a fully turbulent outer layer, similar to the structure of forced convection boundary layers. Scaling laws and wall functions are found by asymptotic matching of the temperature gradients in the overlap layer. The temperature wall function then is a simple logarithmic function of wall distance whereas the velocity profile in the overlap layer is a more complex correlation. Constants in these wall functions are deduced from high-quality data for large Grashof numbers. Experimental as well as numerical profiles as a whole are very well reproduced by the combination of wall functions and viscous sublayer profiles. Therefore these new asymptotic profiles can be used in CFD codes to avoid very fine grids close to the wall, when Grashof numbers are high.

A Two-Velocity Two-Temperature Model for a Bi-Dispersed Porous Medium: Forced Convection in a Channel

Abstract: A two-velocity two-temperature model for bi-dispersed porous media is formulated. Using the model, an analytic solution is obtained for the problem of forced convection in a channel between parallel plane walls that are held either at uniform temperature or uniform heat flux. In each case, Nusselt number values are given as functions of a conductivity ratio, a velocity ratio, a volume fraction, and an internal heat exchange parameter.