Showing papers on "Natural convection published in 1987"

Handbook of single-phase convective heat transfer

Abstract: Basics of Heat Transfer (S. Kakac & Y. Yener) External Flow Forced Convection (R. Pletcher) Laminar Convective Heat Transfer in Ducts (R. Shah & M. Bhatti) Turbulent and Transition Flow Convective Heat Transfer in Ducts (M. Bhatti & R. Shah) Convective Heat Transfer in Curved Ducts (R. Shah & S. Joshi) Convective Heat Transfer in Cross Flow (A. Zukauskas) Convective Heat Transfer over Rod Bundles (K. Rehme) Convective Heat Transfer in Liquid Metals (C. Reed) Convective Heat Transfer with Electric and Magnetic Fields (F. Kulacki et al.) Convective Heat Transfer in Bends and Fittings (S. Joshi & R. Shah) Transient Forced Convection in Ducts (Y. Yener & S. Kakac) Basics of Natural Convection (Y. Jaluria) Natural Convection in Enclosures (K. Yang) Mixed Convection in External Flow (T. Chen & B. Armaly) Mixed Convection in Internal Flow (W. Aung) Convective Heat Transfer in Porous Media (A. Bejan) Enhancement of Single-phase Heat Transfer (R. Webb) The Effect of Temperature-dependent Fluid Properties on Convective Heat Transfer (S. Kakac) Interaction of Radiation with Convection (M. Ozisik) Non-Newtonian Fluid Flow and Heat Transfer (T. Irvine, Jr & J. Karni) Fouling with Convective Heat Transfer (W. Marner & J. Suitor) Thermophysical Properties (P. Liley) Index.

An enthalpy method for convection/diffusion phase change

Abstract: An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented. The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.

Natural Convection in a Vertical Porous Cavity: A Numerical Study for Brinkman-Extended Darcy Formulation

Abstract: A dimensional analysis of the Brinkman-extended Darcy formulation, which includes the transport and viscous terms, leads to four governing parameters for steady-state natural convection in a vertical porous cavity. They are: Rayleigh number, Darcy number, diffusion parameter {Omega}, and aspect ratio. Numerical results for 0 {le} Da {le} 10{sup {minus}1}, 10 {le} Ra* {le} 5 {times} 10{sup 3}, and A = 1 and 5, indicate that the temperature and velocity fields are significantly modified, the flow regimes are delayed, and the heat transfer rate is decreased when the Darcy number is increased beyond 10{sup {minus}5} for fixed Ra{sup {asterisk}} and A. The slope of the In (Nu) versus In (Ra*) curve in the boundary layer regime decreases from 0.53 at Da = 0 to 0.264 at Da = 10{sup {minus}1} when A = 5. The contribution of the transport term increases with {Omega}, Da, and Ra*, but the effect on the overall heat transfer is insignificant. However, the problem becomes ill formulated at high values of these parameters and may require the consideration of Forchheimer modifications. A scale analysis is also presented to show that the inertia term is of a low order of magnitude in comparison with the viscousmore » term at high Prandtl numbers.« less

Combined heat and mass transfer by natural convection in a vertical enclosure

Abstract: The phenomenon of natural convection caused by combined temperature and concentration buoyancy effects is studied analytically and numerically in a rectangular slot with uniform heat and mass fluxes along the vertical sides. The analytical part is devoted to the boundary layer regime where the heat and mass transfer rates are devoted to the boundary layer regime where the heat and mass transfer rates are ruled by convection. An Oseen-linearized solution is reported for tall spaces filled with mixtures characterized by Le = 1 and arbitrary buoyancy ratios. The effect of varying the Lewis number is documented by similarity solution valid for Le > 1 in heat-transfer-driven flows, and for Le < 1 in mass-transfer-driven flows. The analytical results are validated by numerical experiments conducted in the range 1 {le} H/L {le} 4, 3.5 {times} Ra {le} 7 {times} 10{sup 6}, {minus}11 {le} n {le} 9, 1 {le} Le {le} 40, and Pr = 0.7, 7. Massline patterns are used to visualize the convective mass transfer path and the flow reversal observed when the buoyancy ratio n passes through the value {minus}1.

Effects of non-Darcian and nonuniform porosity on vertical-plate natural convection in porous media

Abstract: This work examines analytically the effects of non-Darcian and nonuniform permeability conditions on the natural convection for a vertical plate in porous media. The non-Darcian effects, which include the no-slip and inertia effects, decrease the flow and heat transfer rate, while the nonhomogeneity effect enhances the heat transfer. For packed spheres, in particular, the nonhomogeneity in permeability due to the packing of spheres near the solid wall results in a strong flow-channeling effect that significantly increases the heat transfer. The effect of transverse thermal dispersion is also examined. This dispersion effect causes an increase in the heat transfer.

Compositional and thermal convection in magma chambers

Abstract: Magma chambers cool and crystallize at a rate determined by the heat flux from the chamber. The heat is lost predominantly through the roof, whereas crystallization takes place mainly at the floor. Both processes provide destabilizing buoyancy fluxes which drive highly unsteady, chaotic convection in the magma. Even at the lowest cooling rates the thermal Rayleigh number Ra is found to be extremely large for both mafic and granitic magmas. Since the compositional and thermal buoyancy fluxes are directly related it can be shown that the compositional Rayleigh number Rs (and therefore a total Rayleigh number) is very much greater than Ra. In the case of basaltic melt crystallizing olivine Rs is up to 106 times greater than Ra. However compositional and thermal buoyancy fluxes are roughly equal. Therefore thermal and compositional density gradients contribute equally to convection velocities in the interior of the magma. Effects of thermal buoyancy generated by latent heat release at the floor are included. The latent heat boundary layer at the floor of a basaltic chamber is shown to be of the order of 1 m thick with very low thermal gradients whereas the compositional boundary layer is about 1 cm thick with large compositional gradients. As a consequence, the variation in the degree of supercooling in front of the crystal-liquid interface is dominated by compositional effects. The habit and composition of the growing crystals is also controlled by the nature of the compositional boundary layer. Elongate crystals are predicted to form when the thickness of the compositional boundary layer is small compared with the crystal size (as in laboratory experiments with aqueous solutions). In contrast, equant crystals form when the boundary layer is thicker than the crystals (as in most magma chambers). Instability of the boundary layer in the latter case gives rise to zoning within crystals. Diffusion of compatible trace elements through the boundary layer can also explain an inverse correlation, observed in layered intrusions, between Ni concentration in olivine and the proportion of Ni-bearing phases in the crystallizing assemblage.

Thermal flow in porous media

Abstract: Thermal flows in porous media are important in a wide range of areas: oil recovery, geothermal development, chemical and nuclear industry, civil engineering, energy storage and energy conversion. This book uses a systematic, rigorous and unified treatment to provide a general understanding of the phenomena involved. General equations for single- or multiphase flows (including an arbitrary number of components inside each phase), diffusion and chemical reactions are presented. The boundary conditions which may be imposed, the non-dimensional para meters, the structures of the solutions, the stability of the finite amplitude solutions and many other related topics ae also studied. Although the treatment is basically mathematical, specific physical problems are also dealt with. There are two major fields of applications: natural convection and underground combustion. Both are discussed in detail. Various examples with exact or numerical solutions, for the case of bounded or unbounded domains, are presented, accompanied by extensive comment.

Mixed-Convection Flow and Heat Transfer in the Entry Region of a Horizontal Rectangular Duct

Abstract: Entry-region hydrodynamic and thermal conditions have been experimentally determined for laminar mixed-convection water flow through a horizontal rectangular duct with uniform bottom heating. Direct heating of 0.05 mm stainless steel foil was used to minimize wall conduction, and the foil was instrumented to yield spanwise and longitudinal distributions of the Nusselt number. Flow visualization revealed the existence of four regimes corresponding to laminar forced convection, laminar mixed convection, transitional mixed convection, and turbulent free convection. The laminar mixed-convection regime was dominated by ascending thermals which developed into mushroom-shaped longitudinal vortices. Hydrodynamic instability resulted in breakdown of the vortices and subsequent transition to turbulent flow. The longitudinal distribution of the Nusselt number was characterized by a minimum, which followed the onset of mixed convection, and subsequent oscillations due to development of the buoyancy-driven secondary flow.

Magnetic and Gravitational Natural Convection of Melted Silicon—Two-Dimensional Numerical Computations for the Rate of Heat Transfer : Heat Transfer, Combustion, Power, Thermophysical Properties

Abstract: The two-dimensional natural convection of fluid under both a magnetic and a gravitational field was modeled by conservation equations. Sample computations were carried out for the fluid in a square enclosure for Rayleigh number of from 104 to 106, for Hartman number of from 1 to 103 and for Prandtl number equal to 0.054, equivalent to melted silicon. The numerical computations converged successfully and the Nusselt numbers obtained were correlated to give an empirical equation for the rate of heat transfer. The steady state solutions were graphically visualized. At Ha=103 and Ra=106, the point at which the temperature profile was almost linear, the flow was almost suppressed and elongated in a regime with high wave numbers.

Effect of natural convection on growth velocity and morphology of dendritic ice crystals

Abstract: An experimental investigation of heat transfer by natural convection from a smooth, isothermal cubic cavity with a variety of side-facing aperatures is described in this paper. The study was motivated by the desire to predict the convective loss from large solar thermal-electric receivers and to understand the mechanisms which control this loss. Hence, emphasis is placed on the large Rayleigh number, Ra, regime with large ratios of the cavity wall temperature T{sub w} to the ambient temperature T{sub {infinity}}. A cryogenic wind tunnel with test section temperatures which are varied between 80 K and 310 K is used to facilitate deduction of the influences of the relevant parameters and to obtain large temperature ratios without masking the results by radiative heat transfer. A 0.4-m cubic cavity, which is mounted in the side wall of this tunnel, is used. The area of the aperture A{sub a} and its location are key variables in this study. The data which are presented cover the ranges: 1 < T{sub w}/T{sub {infinity}} < 3, L{sup 2}/18 {le} A{sub a} {le} L{sup 2}, and 3 {times} 10{sup 10}.

Natural Convection From Isothermal Cubical Cavities With a Variety of Side-Facing Apertures

Abstract: An experimental investigation of heat transfer by natural convection from a smooth, isothermal cubic cavity with a variety of side-facing aperatures is described in this paper. The study was motivated by the desire to predict the convective loss from large solar thermal-electric receivers and to understand the mechanisms which control this loss. Hence, emphasis is placed on the large Rayleigh number, Ra, regime with large ratios of the cavity wall temperature T{sub w} to the ambient temperature T{sub {infinity}}. A cryogenic wind tunnel with test section temperatures which are varied between 80 K and 310 K is used to facilitate deduction of the influences of the relevant parameters and to obtain large temperature ratios without masking the results by radiative heat transfer. A 0.4-m cubic cavity, which is mounted in the side wall of this tunnel, is used. The area of the aperture A{sub a} and its location are key variables in this study. The data which are presented cover the ranges: 1 < T{sub w}/T{sub {infinity}} < 3, L{sup 2}/18 {le} A{sub a} {le} L{sup 2}, and 3 {times} 10{sup 10}.

Electric field-induced flame convection in the absence of gravity

Abstract: Although chemical fuels uniquely provide a safe way of carrying large amounts of energy within a small mass and volume, their combustion in the absence of gravity raises major problems. Whenever flames are used for heating specific objects under gravity and in an oxygen-containing atmosphere, we rely on natural or forced convection to replenish reactants and direct the hot products. Forced convection requires a compressor or keeping fuel under pressure in cylinders, and thus entails a considerable weight penalty. Natural convection is not available under micro-gravity conditions, making heat transfer from flames difficult to achieve. Indeed, diffusion flames will tend to become spherical and will eventually extinguish as a result of blanketing by their own products. We report here an alternative method of controlling flames in zero gravity based on the application of electric fields, which can be achieved using compact, lightweight equipment.

Convective instability in porous media with throughflow

Abstract: In their study of the linear stability limits for free convection in layers of porous media or packed beds with throughflow, others found that throughflow was generally stabilizing, but there was an exception. In the case of flow toward a porous boundary, they found that the numerically calculated Rayleigh-Darcy number initially decreased and went through a minimum as the appropriate Peclet number increased from zero. It was stated that the origin of the minimum was not completely understood, but others had eliminated numerical inaccuracy as a possible cause. Thus a small amount of throughflow can have a destabilizing effect in at least one situation. The primary purpose of this note is to explain this effect. The opportunity is taken to provide some supplementary material.

A General Similarity Transformation for Combined Free and Forced-Convection Flows Within a Fluid-Saturated Porous Medium

Abstract: It is the purpose of the present paper to introduce a general transformation procedure appropriate to the problem of combined free and forced convection in a porous medium. It will be shown that particular transformations proposed in the previous papers by Cheng and Minkowycz and co-workers are simply the specific forms of the present general transformation. Pure forced convection will be treated first as a limiting case of combined free and forced convection. The analysis reveals that any two-dimensional or axisymmetric body of arbitrary shape possesses its corresponding class of wall temperature distributions which permit similarity solutions. Secondly, combined free and forced convection will be considered to seek similarity solutions. It is found that, unlike in pure forced convection, similarity solutions in mixed convection are possible only when the external free-stream velocity varies every where in proportion to the product of the streamwise component of the gravity force and the wall-ambient temperature difference.

Thermoelectric Conversion by Thin-Layer Thermogalvanic Cells with Soluble Redox Couples

Abstract: Thermogalvanic cells containing a redox couple of [Fe(CN)6]4−⁄3− or Fe2+⁄3+ as an electroactive species were built for thermoelectric conversion from low-grade heat with a temperature less than 100 °C. The distance between high- and low-temperature electrodes was set to 1 mm in order to produce a high power density. Thermoelectric powers, inner resistances, and heat fluxes of the cells, which were placed horizontally (i.e. in which the temperature gradient was vertical) were measured under steady state conditions. Natural convection, which was induced by a temperature difference and current flowing in appropriate directions, produced lower inner resistances than those with no convection by several times. It had only a small effect on thermoelectric powers and heat-transfer coefficients. Thus, both the power densities and the thermal efficiencies increased by nearly one order of magnitude due to the convection. A power density of 2.6 W m−2 was obtained during steady state using a cell containing an aqueous...

Numerical Modeling of Natural Convection Heating in Canned Liquid Foods

Abstract: Amathematical model was developed for the first time for predicting detailed flow patterns and temperature profiles during natural convection heating of canned liquids. Finite difference methods were used to solve the governing Navier-Stokes equations in axisymmetric cylindrical coordinates. A vorticity-stream function formulation of the equations was used. Details of the numerical techniques used are discussed. Plots of transient isotherms, streamlines and velocities are provided. From the standpoint of food processing, the slowest heating points migrated within the bottom 15% of the can with no particular pattern of migration.

Laminar Free Convection From a Sphere With Blowing and Suction

Abstract: The effect of mass transfer on free convection from a vertical plate has been studied by Eichhorn (1960), Sparrow and Cess (1961), Merkin (1972), and Parikh (1974). Recently, Merkin (1975) gave an asymptotic series solution for two-dimensional bodies. Minkowycz and Sparrow (1979) studied a vertical cylinder in a natural convective flow. According to their conclusions, the heat transfer rate increases with suction and decreases with blowing. The present note is concerned with the study of the influence of Prandtl number and surface mass transfer on a steady, laminar, free convective flow over a sphere with nonuniform surface temperature or heat flux.