Showing papers on "Combined forced and natural convection published in 1978"

Non-linear properties of thermal convection

Abstract: Thermal convection in a layer heated form below is an exemplary case for the study of non-linear fluid dynamics and the transition to turbulence. An outline is given of the present knowledge of the simplest realisation of convection in a layer of fluid satisfying the Oberbeck-Boussinesq approximation. Non-linear properties such as the dependence of the heat transport on Rayleigh and Prandtl numbers and the stability properties of convection rolls are emphasised in the discussion. Whenever possible, theoretical results are compared with experimental observations. A section on convection in rotating systems has been included, but the influence of other additional physical effects such as magnetic fields, side wall geometry, etc., has not been considered.

Instability of steady natural convection in a vertical fluid layer

Abstract: The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.

Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

Abstract: Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Benard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

Critical effects in Rayleigh-Benard convection

Abstract: 2014 The properties of the convection Rayleigh-Bénard phenomenon near its critical threshold of instability are shown to be closely related to those of a second order phase transition. A theory is developed in the framework of the Landau-Hopf hypothesis, and all its predictions are verified by experimental results. Tome 39 N° 7 JUILLET Classification Physics Abstracts 47 . 25Q

Visual observation of natural convective flow in a narrow vertical cavity

Abstract: Experimental visualization of natural convective flow was carried out by using several kinds of fluid contained in a narrow vertical rectangular cavity with one vertical wall heated, the opposing vertical wall cooled and the upper and lower walls insulated. The effects of the Prandtl number Pr of the working fluid and the width of the cavity W on the flow pattern are discussed qualitatively in the present paper. The occurrence of flow patterns consisting of unicellular flow, steady secondary flow, tertiary flow and transition (from laminar to turbulent) flow is categorically demonstrated by the photographs taken. Moreover, experimental measurements of the net heat transfer through the vertical fluid layer are given for aspect ratios of 6-30 and Prandtl numbers of 4-12 500.

Experimental study of the velocity field in Rayleigh-Benard convection

Abstract: Local velocity measurements performed in a convecting layer of fluid show that the velocity field can be described by a dominant fundamental velocity mode mixed with an increasing proportion of second and third harmonics as e, the reduced distance to the convective threshold Rc, is increased from 0 to ∼ 10. The spatial and thermal dependences of the amplitudes of these different modes are reported and compared with theoretical predictions.

Heat transfer and fluid flow phenomena in electroslag refining

Abstract: A mathematical formulation has been developed to represent the electromagnetic force field, fluid flow and heat transfer in ESR units. In the formulation, allowance has been made for both electromagnetically driven flows and natural convection; furthermore, in considering heat transfer the effect of the moving droplets has been taken into account. The computed results have shown that the electromagnetic force field appears to be the more important driving force for fluid motion, although natural convection does affect the circulation pattern. The movement of the liquid droplets through the slag plays an important role in transporting thermal energy from the slag to the molten metal pool, although the droplets are unlikely to contribute appreciably to slag-metal mass transfer The for-formulation presented here enables the prediction of thermal and fluid flow phenomena in ESR units and may be used to calculate the electrode melting rates from first principles. While a detailed comparison has not yet been made between the predictions based on the model and actual plant scale measurements, it is thought that the theoretical predictions are consistent with the plant-scale data that are available.

Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature

Abstract: The stability of two-dimensional convection rolls has been studied as a function of the Rayleigh number, wavenumber and variation in viscosity. The experiments used controlled initial conditions for the wavenumber, Rayleigh numbers up to 25 000 and variations in viscosity up to a factor of about 20. The parameter range of stable rolls is bounded by a hexagonal-cell regime at small Rayleigh numbers and large variations in viscosity. Otherwise, the rolls are subject to the same transitions as have already been studied in fluids of uniform viscosity. The bimodal instability leading to a stable three-dimensional pattern occurs at smaller values of the average Rayleigh number as the variations in viscosity increase. This appears to be a consequence of the low viscosity of the warm thermal boundary layer associated with the original rolls.

A study of thermal convection in non-Newtonian fluids

Abstract: This study considers steady-state, finite amplitude thermal convection in a non-Newtonian fluid. Pseudoplastic (power-law) fluids are considered for a power-law exponent n in the range 1 ≤ n ≤ 9. Finite-difference solutions are obtained for two-dimensional periodic convective modes in a horizontally infinite fluid layer heated from below. The results show that the patterns of convective motions differ only slightly from those in a fluid of constant viscosity for n [lsim ] 3 while for n [gsim ] 3 significant differences are observed. An average viscosity is introduced which provides a good correlation of heat transfer across the layer with the Rayleigh number for the complete range of n considered.

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell II: Effects of temperature boundary conditions

Abstract: We examine the influence on convection in a rotating spherical shell of various boundary conditions on temperature. In particular, we look at the response to constant heat flux, or fixed temperature gradient, boundaries as opposed to constant temperature boundaries assumed in Part I. We also examine the influence of an upper boundary with linear combinations of temperature and temperature gradient held fixed. To compare with earlier studies, calculations are done at Prandtl number of 1, Taylor number 105, Rayleigh numbers between 104 and 105, and convection zone depth 20% of the outer radius. We find that when a constant heat flux boundary condition is imposed at the bottom of the convective layer, equatorial acceleration is produced by Reynolds stresses in the convection for Rayleigh numbers up to 5 × 104, analogously to the constant temperature bottom case, but over the same range the heat flux differentials in latitude at the top of the layer are greatly reduced. Above this Rayleigh number, eq...

Onset of natural convection in a cylinder of water saturated porous media

Abstract: The onset of natural convection in a cylinder of water‐saturated porous media is considered. The dependence of the critical Rayleigh number and the preferred convective motion on both the aspect ratio of the cylinder and the temperature difference is established.

Free and forced convection flow in a rotating channel bounded below by a permeable bed

Abstract: The steady flow in a parallel plate channel rotating with an angular velocity Ω and bounded below by a permeable bed is analysed under the effect of buoyancy force. On the porous bed the boundary condition of Beavers and Joseph is applied and an exact solution of the governing equations is found. The solution in dimensionless form contains four parameters: The permeability parameterσ 2, the Grashof numberG, the rotation parameterK 2 and a dimensionless constantα. The effects of these parameters, specially,σ 2, G andK 2, on the slip velocities and velocity distributions are studied. For largeK 2, there arise thin boundary layers on the walls of the channel.

Experiments on centrifugally driven thermal convection in a rotating cylinder

Abstract: Heat-transfer measurements have been carried out in a right circular cylinder of fluid which is heated from above and rotated steadily about its vertical axis. Convection is produced relative to solid-body rotation through the coupling of the centrifugal acceleration and density variations in the fluid. Two silicone oils having kinematic viscosities of 350 cS and 0·65 cS were used in the experiments. In the former case viscous forces are important throughout the cylinder whereas in the latter case Ekman layers form and the Coriolis acceleration controls the interior flow. With the 350 cS oil the Nusselt number for heat transfer from the top to the bottom of the cylinder is a function of Gr ω and r 0 , where Gr ω is a Grashof number defined by employing the centrifugal acceleration evaluated at the outer edge of the cylinder in place of the gravitational acceleration, and r 0 is the cylinder aspect ratio. The behaviour is quite different for the 0·65 cS oil. Ekman layers form on the horizontal surfaces and heat is convected by Ekman suction. The Nusselt number is given by \[ Nu = 4.16\beta^{0.822}\epsilon^{-0.499}r_0^{0.173},\quad Ac\leqslant 0.025,\quad\sigma\beta\epsilon^{-\frac{1}{2}} > 0.7, \] where β is the thermal Rossby number, e is the Ekman number, σ is the Prandtl number, and Ac is the ratio of gravitational to centrifugal accelerations. This is consistent with previous theories which indicate that the system should depend on the parameters σβe −½ and r 0 in the limit as e and β approach zero.

On a High-Order Accurate Method for the Numerical Study of Natural Convection in a Vertical Square Cavity

Abstract: A high-order accurate finite-difference method for solving the two-dimensional Navier-Stokes equations has been adapted to study natural convection in cavities. This method has been applied to determine the limit of the conduction and boundary-layer regimes for a square cavity, when the vertical walls are maintained at two different constant temperatures and the horizontal walls are either perfectly insulated or perfectly conducting. Most of the calculations have been carried out for an air cavity (Pr ≡ 0.7). The values of Ra considered range from 100 to 105. Relationships Nu have been derived for the boundary-layer regime.