Showing papers on "Combined forced and natural convection published in 2006"

Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet

Abstract: An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.

Dufour and Soret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction

Abstract: In this paper the Dufour and Soret effects on mixed convection flow past a vertical porous flat plate embedded in a porous medi um have been studied numerically. The governing non-linear partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically by applying Nachtsheim- Swigert shooting iteration technique together with sixth order Runge-Kutta integration scheme. For fluids of medium molecular weight (H2, air), profiles of the dimensionless velocity, temperature and concentration distributions are shown graphically for various values of suction parameter fw, Dufour number Du and Soret number Sr. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusse lt number and the local Sherwood number are presented in tabular form.

The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder

Abstract: Rapidly rotating convection in spherical geometry outside the tangent cylinder is investigated using the quasi-geostrophic approximation. The validity of the approximation is discussed, and numerical simulations using these equations are performed, reaching Ekman numbers, E, down to 10 -6 . The results are compared with experiments and fully three-dimensional numerical simulations. We find that the inertial scaling developed to study rapidly rotating convection does not represent the Prandtl-number dependence of our results adequately. Instead, we find that even in strongly supercritical situations the dominant wavenumbers at the onset of convection still have a strong influence on the behaviour. We find that the local Peclet number, the product of the typical convective velocity and local convective length scale divided by the thermal diffusivity, is helpful for understanding the dynamics of rapidly rotating convection. We explore the zonal flows driven by Reynolds stresses with no-slip boundaries and explore their Prandtl-number dependence. We also study the convective heat transport at low E, and consider the boundary layer structures that can form at large Rayleigh number, slowing down the rate of growth of the Nusselt number with Rayleigh number.

Azimuthal motion of the mean wind in turbulent thermal convection.

Abstract: We present an experimental study of the azimuthal motion of the mean wind in turbulent thermal convection. The experiments were conducted with cylindrical convection cells of unity aspect ratio and over the range of the Rayleigh number from $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{10}$. The azimuthal angle of the circulation plane of the mean wind was measured using both the particle image velocimetry and flow-visualization techniques. It is found that the azimuthal motion consists of erratic fluctuations and a time-periodic oscillation. The orientation of the wind is found to be ``locked,'' i.e., it fluctuates about a preferred direction most of the time with all other orientations appearing as ``transient states,'' and large excursions of the azimuthal angle often result in a net rotation which takes the wind back to the preferred orientation. The rate of erratic rotation of the circulation plane is found to have a strong dependence on Ra. Our result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.

Mesoscale simulations of organized convection: Importance of convective equilibrium

Abstract: The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

Turbulent convection at high Rayleigh numbers and aspect ratio 4

Abstract: We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra=2×10 13 . Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the log Nu-log Ra slope saturates at a value close to 1/3, as observed previously by us in experiments with smaller aspect ratios. The increasing slope over the last half a decade of Ra is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and Ra that collapses data for different aspect ratios.

Transitional Heat Transfer in Plain Horizontal Tubes

Abstract: In this study, the heat transfer behavior in the transition region for plain horizontal tubes under a uniform wall heat flux boundary condition is discussed in detail. In particular, the influence of inlet configuration and free convection superimposed on the forced convection (or mixed convection) at the start and end of the transition region and the magnitude of heat transfer are addressed. The available correlations to predict the heat transfer coefficient in the transition region are reviewed, and their performance are evaluated based on 1290 experimental data points obtained under a wide range of experimental conditions. Appropriate correlations for the mixed and forced convection transition regions are recommended. Finally, a flow regime map for determination of the boundary between forced and mixed convection in horizontal tubes with different inlets is presented.

Global nonlinear stability in porous convection with a thermal non-equilibrium model

Abstract: We show that the global nonlinear stability threshold for convection with a thermal non-equilibrium model is exactly the same as the linear instability boundary. This result is shown to hold for the porous medium equations of Darcy, Forchheimer or Brinkman. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The equivalence of the linear instability and nonlinear stability boundaries is also demonstrated for thermal convection in a non-equilibrium model with the Darcy law, when the layer rotates with a constant angular velocity about an axis in the same direction as gravity.

Hydrodynamic simulations of he-shell flash convection

Abstract: We present the first hydrodynamic, multidimensional simulations of He shell flash convection. We investigate the properties of shell convection immediately before the He luminosity peak during the 15th thermal pulse of a stellar evolution track with initially 2 solar masses and metallicity Z = 0.01. This choice is a representative example of a low-mass asymptotic giant branch thermal pulse. We construct the initial vertical stratification with a set of polytropes to resemble the stellar evolution structure. Convection is driven by a constant volume heating in a thin layer at the bottom of the unstable layer. We calculate a grid of two-dimensional simulations with different resolutions and heating rates, plus one low-resolution three-dimensional run. The flow field is dominated by large convective cells that are centered in the lower half of the convection zone. It generates a rich spectrum of gravity waves in the stable layers both above and beneath the convective shell. The magnitude of the convective velocities from our one-dimensional mixing-length theory model and the rms-averaged vertical velocities from the hydrodynamic model are consistent within a factor of a few. However, the velocity profile in the hydrodynamic simulation is more asymmetric and decays exponentially inside the convection zone. Both g-modes and convective motions cross the formal convective boundaries, which leads to mixing across the boundaries. Our resolution study shows consistent flow structures among the higher resolution runs, and we see indications for convergence of the vertical velocity profile inside the convection zone for the highest resolution simulations. Many of the convective properties, in particular the exponential decay of the velocities, depend only weakly on the heating rate. However, the amplitudes of the gravity waves increase with both the heating rate and the resolution.

Free convection and radiation characteristics for a vertical plate embedded in a porous medium

Abstract: Steady two-dimensional free convection flow due to combined effect of radiation and convection through a porous medium bounded by a vertical infinite plate is considered. The behaviour of Darcy and non-Darcy flow is investigated. The flow of water through different porous media under different environmental conditions is discussed. Effect of four non-dimensional parameters, i.e. Prandtl number (Pr), modified Grashof number (G), permeability parameter (K) and radiation parameter (N) has been studied. Effect of these parameters on Nusselt number is analysed. Copyright © 2005 John Wiley & Sons, Ltd.

Experimental Investigation of Mixed Convection in a Channel With an Open Cavity

Abstract: Mixed convection in an open cavity with a heated wall bounded by a horizontally unheated plate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of wall temperature profiles of the heated wall and flow visualization for Re = 100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100), the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and the ratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. The present results show that the maximum dimensional temperature rise values decrease as the Reynolds and the Richardson numbers decrease. The flow visualization points out that for Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. Fo...

Natural Convection in a Square Cavity with Spatial Side-Wall Temperature Variation

Abstract: Laminar natural convection in a two-dimensional square cavity filled with a pure air (Pr = 0.71) is studied numerically in the present article with nonuniform side-wall temperature. The heated vertical wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, which is higher than the cold side-wall temperature, while the top and the bottom walls are adiabatic. A finite-volume method is used to solve numerically the nondimensional governing equations in the vorticity–stream function formulation. The effects of the amplitude and the wave number of the heated side-wall temperature variation on the natural convection in the cavity are investigated. It is found that the average Nusselt number varies based on the hot-wall temperature. It increases with an increase in the amplitude, while the maximum average Nusselt number occurs at the wave number of k = 0.7 for Rayleigh number range 103 ≤ Ra ≤ 106. It is found that the values of maximum fluid circulation occur at a...

On Dissipation inside Turbulent Convection Zones from 3D Simulations of Solar Convection

Abstract: The development of 2D and 3D simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We investigate the impact of this changed structure on the dissipation properties of the convection zone, parametrized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh 1997, applied to a numerical model of solar convection (Robinson et al. 2003) to calculate an effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of Kolmogorov turbulence (Zahn 1966, Goldreich & Keeley 1977). The results match quite closely a linear scaling with period, even though this same formalism applied to a Kolmogorov spectrum of eddies gives a scaling with power-law index of 5/3.

Marangoni mixed convection boundary layer flow

Abstract: 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.

Low‐degree mantle convection with strongly temperature‐ and depth‐dependent viscosity in a three‐dimensional spherical shell

Abstract: [1] A series of numerical simulations of thermal convection of Boussinesq fluid with infinite Prandtl number, with Rayleigh number 10 7 , and with the strongly temperature-and depth-dependent viscosity in a three-dimensional spherical shell is carried out to study the mantle convection of single-plate terrestrial planets like Venus or Mars without an Earth-like plate tectonics. The strongly temperature-dependent viscosity (the viscosity contrast across the shell is > 10 5 ) makes the convection under stagnant lid short-wavelength structures. Numerous, cylindrical upwelling plumes are developed because of the secondary downwelling plumes arising from the bottom of lid. This convection pattern is inconsistent with that inferred from the geodesic observation of the Venus or Mars. Additional effect of the stratified viscosity at the upper/lower mantle (the viscosity contrast is varied from 30 to 300) are investigated. It is found that the combination of the strongly temperature- and depth-dependent viscosity causes long-wavelength structures of convection in which the spherical harmonic degree l is dominant at 1-4. The geoid anomaly calculated by the simulated convections shows a long-wavelength structure, which is compared with observations. The degree-one (l = 1) convection like the Martian mantle is realized in the wide range of viscosity contrast from 30 to 100 when the viscosity is continuously increased with depth at the lower mantle.