Showing papers on "Combined forced and natural convection published in 1983"

Convection in Liquids

Abstract: A : Introduction.- I - Fundamental Laws and Basic Concepts.- 1. Balance equations for incompressible fluids.- A. Conservation of mass.- B. Conservation of momentum.- C. Conservation of energy.- 2. Fundamental thermodynamic relations entropy balance equation and second law.- A. Alternative forms of the energy balance equation.- B. The entropy balance equation and the second law of thermodynamics.- 3. Kinetic and constitutive equations.- 4. Systems of coordinates.- A. Rectangular coordinates.- B. Cylindrical coordinates.- C. Special two-dimentional case : the stream function.- 5. Equations for the fluctuations around a steady state.- 6. Definition of stability.- 7. Normal modes.- 8. Dimensionless numbers in fluid dynamics and heat transfer problems.- Exercices.- Bibliographical notes.- II - Mathematical Background and Computational Techniques.- 1. Use of variational principles and/or stationary properties of integrals.- A. Elements of variational calculus. The Euler-Lagrange equations.- B. Variational approach to the conservations laws based on nonequilibrium thermodynamics : the theory of the local potential.- C. The numerical methods associated with the local potential theory.- D. Relation between the local potential and the Galerkin techniques.- 2. Applications to stability problems.- A. The excess local potential.- B. Variational methods for linear eigenvalue problems.- C. Stability criterion based on Lyapounov function.- 3. Purely numerical techniques.- A. Finite differences methods.- B. Conversion of a boundary value problem into an initial value problem.- Exercices.- Bibliographical notes.- B : Fluids at Constant Density, Isothermal Forced Convection.- III - Planar Flows of Newtonian Fluids.- 1. Poiseuille and Couette flow.- A. Plane Poiseuille flow and Poiseuille flow in rectangular channels.- B. Plane Couette flow.- 2. General statements of linear hydrodynamic stability of forced convection.- A. The Orr-Sommerfeld equation.- B. Variational or stationary presentations of the Orr-Sommerfeld equation. Its relation with the Galerkin technique.- C. The Chock-Schechter integration scheme.- D. The Orr and the Prigogine-Glansdorff criterion.- 3. Numerical solutions of the Orr-Sommerfeld equation.- A. Selection of trial functions.- B. Solution for U = constant.- C. Solution for plane Poiseuille flow.- a. Effect of trial functions.- b. High Reynolds numbers.- c. Two and three dimensional perturbations without elimination of variables. Relation to Squire's theorem.- d. Finite difference methods.- e. Solution using the Chock-Schechter method.- f. General discussion, comparison with experiments.- D. Solution for Couette flow.- 4. Nonlinear stability of Poiseuille flow.- A. Introduction.- B. A restricted variational approach to the nonlinear equations.- C. Influence of the initial amplitude of the disturbance.- 5. An oscillatory solution in planar-Poiseuille flow.- A. Introduction.- B. Existence of statistically steady states.- C. Existence of periodic flows.- D. Stability and/or instability of the new periodic flow.- 6. Remarks on the transition to turbulence.- Bibliographical notes.- IV - Cylindrical Flows of Newtonian Fluids.- 1. A. Poiseuille flow in a pipe.- B. Poiseuille flow down an annular pipe.- 2. General statements on linear stability of forced convection in cylindrical coordinates.- A. An equivalent of the Orr-Sommerfeld equation.- B. Non axisymmetric disturbances.- 3. Linear stability of pipe Poiseuille flow.- A. Stability with respect to two-dimensional axisymmetric disturbances.- B. Stability with respect to three-dimensional non axisymmetric disturbances.- Bibliographical notes.- V - Flow Stability of Non-Newtonian Fluids.- 1. Stress-Strain relations for some particular non-newtonian fluids.- A. Introduction.- B. The Coleman-Noll model.- 2. Stability of plane Poiseuille flow for a second order viscoelastic fluid.- A. The generalized Orr-Sommerfeld equation.- B. The solution of the generalized Orr-Sommerfeld equation for plane flow.- C. Plane Poiseuille flow : sufficient condition for stability.- D. Instability of plane Poiseuille flow of a second order fluid : a numerical result.- 3. Stability of pipe Poiseuille flow for a second order fluid..- Bibliographical notes.- C : Non Isothermal One Component Systems.- VI - Free Convection in One Component Fluid.- 1. Introduction.- 2. The linear theory of the Benard problem.- A. The eigenvalue problem. Its solution for simple boundary conditions.- B. Solutions based on approximate numerical calculations.- a. The local potential method.- b. The Chock-Schechter numerical integration.- C. Solution based on the thermodynamic stability criterion.- D. Experimental aspect.- E. Effect of lateral boundaries.- F. Extension of the Benard problem.- a. Surface tension effect.- b. Effect of a magnetic field.- 3. The non-linear theory of the Benard problem.- A. Approximate computational techniques.- B. Global properties of the flow.- a. Variation of the Nusselt number with the Rayleigh number (free boundary conditions).- b. Variation of the Nusselt number with the Rayleigh number (rigid boundary conditions).- c. Variation of the number of convective cells with the Rayleigh number.- C. Fine structure of the flow.- D. Behavior near threshold.- E. Behavior far from the critical point.- a. The Lorenz model.- b. The routes to turbulence.- 4. The thermogravitational process.- A. The steady state profile.- B. The stability of the steady state profile.- Bibliographical notes.- VII - Non Isothermal Forced Convection in a One-Component Fluid.- 1. General aspects of the effect of temperature gradients.- 2. Temperature gradients imposed by the boundary conditions.- 3. Temperature gradients due to viscous heating.- A. Experimental interest.- B. Cylindrical Poiseuille flow with viscous heating.- a. the steady state.- b. stability of cylindrical Poiseuille flow including viscous heating.- 4. Further discussion on the multiplicity of steady states when taking into account viscous heating.- Bibliographical notes.- VIII - Mixed Convection in a One-Component Fluid.- 1. Introduction in the Benard problem with flow.- 2. Relation between two and three dimensional disturbances extension of Squire's theorem.- 3. Experiments on the onset of free convection with a superposed small laminar flow.- 4. Effect of lateral boundaries.- Bibliographical notes.- D : Multicomponent Systems.- IX - Free Convection in a Multicomponent Fluid.- 1. Introduction to the influence of concentration gradients on hydrodynamic stability.- 2. Formulation of the linearized problem.- A. The conservation equations.- B. The thermohaline problem.- C. The effect of thermal diffusion (or Soret effect).- 3. The thermohaline convection : linear stability analysis.- A. The role of boundary conditions.- B. Free boundaries with specified solute concentrations and temperatures.- C. Experimental observations.- 4. Free convection with thermal diffusion : linear analysis.- A. Coupled equations for temperature and mass.- B. Exact solution of the simplified problem for free and pervious boundaries.- C. Variational solution for rigid boundaries.- D. 0.- B. Results for s < 0.- 3. Postface.- Bibliographical notes.- Appendix A.- Appendix B.

Heat transfer and horizontally averaged temperature of convection with large viscosity variations

Abstract: It is pointed out that the understanding of convection in large-Prandtl-number Boussinesq fluids with uniform properties and contained in simple geometries is virtually complete. Present efforts are typically directed towards relaxing some of the original assumptions by going to lower Prandtl number, more complicated geometries, variable material properties, or introducing new dynamical processes such as the Lorentz forces. A description is given of experiments which are concerned with the effect on convection of relaxing the assumption of a uniform viscosity. The reported experiments were designed to measure both the horizontally averaged temperature as a function of depth and the heat transfer of convection over a range of viscosity variations up to 100,000.

Radiation-Natural Convection Interactions in Two-Dimensional Complex Enclosures

Abstract: A numerical finite-difference study has been carried out for the two-dimensional radiation-natural convection interaction phenomena in square enclosures with equal vertical finite-thickness partitions located at the centers of the ceiling and floor. Both participating gases (CO2 and NH3 ) and nonparticipating gas (air) are considered. In the radiation calculations, the nongray exponential wide-band models for CO2 and NH3 are used, together with a radial flux method utilizing a more realistic polar description for the radiation exchange in the enclosure. Results on the effects of both surface and gas radiation on the velocity and temperature fields and the overall heat transfer rates as functions of the partition heights at two levels of the Grashof number are presented and discussed in terms of the physical phenomena.

Laminar natural convection from a horizontal plate and the influence of plate-edge extensions

Abstract: Laminar natural convection from a horizontal plate is studied by a finite-difference analysis and by experiments for Rayleigh numbers from 10 to 104. The plate with uniform surface temperature or concentration on one side and insulated on the other is situated in an ‘infinite’ fluid medium. The buoyancy near the surface is directed either outward or inward normal to the active surface – equivalent to a heated plate facing upward or downward. The effect of insulated vertical and horizontal extensions to the plate are also examined.Finite-difference solutions are obtained for a heated strip in a two-dimensional domain for a Prandtl number of 0·7. Mass-transfer experiments are performed with square naphthalene plates in air. Both numerical and experimental results justify a 1/5-power law in the present range of Rayleigh number – i.e. Nusselt number or Sherwood number proportional to the Rayleigh number raised to the 1/5 power. The horizontal extensions cause a limited reduction in the transfer rate for the plate generating ‘outward buoyancy’, and a larger reduction with ‘inward buoyancy’. The vertical walls block the fluid flow directly, and thus greatly lower the transfer rate with either outward or inward buoyancy.

Numerical Study of High Rayleigh Number Convection in a Vertical Porous Enclosure

Abstract: The results of a numerical simulation of natural convection in a vertical rectangular porous enclosure subjected to a horizontal temperature differential are presented. By use of the stable exponential differencing computation scheme, values of the Darcy-Rayleigh number R have been obtained which are substantially larger than those in previous numerical studies. The present results provide a clear physical picture of the development process as R is increased toward asymptotically high values (R →). Correlations for the heat transfer rate are presented for four different aspect ratios and are compared with earlier experimental and theoretical results.

Effects of Free Convection Currents and Mass Transfer on Flow Past a Vertical Oscillating Plate

Abstract: An exact analysis of the flow caused by an oscillating vertical plate in the presence of free-convection currents and foreign mass has been presented. Solutions have been derived by Laplace-transform technique. Velocity profiles and leading edge effects have been shown for different gases present in air. During the course of discussion, the effects of Gr (Grashof number), Gm (modified Grashof number), Sc (Schmidt number), on the flow have been discussed. It has been observed that at all small values of Sc, transition from conduction to convection exists but at large values of Sc, such a transition is not present.

A Numerical Study of Transient Mixed Convection Flows in a Thermal Storage Tank

Abstract: Transient, two-dimensional, mixed convection flows in a thermal storage tank have been studied using a previously developed numerical technique based on the marker and cell method. The governing equations are the conservation equations for laminar, natural convection flow based on the Boussinesq approximation. Forced convection flow is superimposed through the use of appropriate boundary conditions (inflow and outflow conditions). The transient heat transfer and fluid flow characteristics are examined for different boundary conditions. Typical transient temperature and velocity distributions are presented. The effect of inflow and outflow configurations on the storage tank thermal performance is also investigated. It is found that the device can store energy at a faster rate when hot water is discharged into the tank from the top and colder water is extracted from the bottom. However, the discharge direction into and from the tank, which can be either vertical or horizontal, is found to have negligible effect on the thermal storage efficiency.

Planform of convection with strongly temperature-dependent viscosity

Abstract: This paper experimentally investigates the convective planform near critical in a fluid layer whose temperature-dependent viscosity varies from top to bottom by up to a factor of 1500. Convection occurs in three different planforms: rolls, hexagons and squares. The square planform, which appears only for fluids with viscosity variation greater than about 50, replaces the hexagonal convection pattern as the Rayleigh number increases much above critical. The large amplitude of hexagonal convection with strong viscosity variation precludes studying the hexagon-square transition with perturbation methods of the type used to study the hexagon-roll transitions at smaller viscosity variations.

Free and forced convection effects on evaporation

Abstract: The effects of free and forced convection mechanisms on evaporation rates from open water bodies is examined. Examination of measurements from seven water bodies (from very small to tens of square kilometers) indicates that evaporation resulting from forced convection progresses at its theoretical value for a wide range of ambient conditions. On the other hand, free convection effects are sensitive to the windspeed and water surface to air temperature difference. Based on the analysis presented, a new evaporation equation is obtained.

Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space

Abstract: This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK 1/2 ) / (k′ Ra1/4 ), where k, k′ , RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.

Vibrational thermal convection in a rectangular cavity

Abstract: Vibrational thermal convection in a rectangular cavity under conditions of weightlessness is studied. Some equilibrium configurations were obtained in earlier papers of two of the authors [1, 2] and their linear stability investigated. In the present paper, a numerical investigation is made of the developed vibrational convection which arises under conditions when equilibrium is impossible. The structure of the average vibrational-convective flows and the characteristics of the heat transfer are determined. The change of regimes and the connection with the stability problem are discussed.