Natural convection of a viscoelastic fluid

The influence of elasticity and shear thinning viscosity on the temperature distribution and heat transfer in natural thermal convection is discussed. The numerical investigations are based on a four-parameter Oldroyd constitutive equation, which represents the typical fluid response of dilute solutions and melts. It was found that especially the second normal-stress difference affects the heat transfer mechanism.     

Natural convection of a dusty gas

The natural convection of a gas-particle suspension inside a two-dimensional square region is investigated within the framework of a two-velocity two-temperature model of the medium with allowance for phase relaxation and particle deposition. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 46–52, March–April, 1994.     

Natural convection in inclined partitioned enclosures

The problem of steady, laminar, natural convective flow of a viscous fluid in an inclined enclosure with partitions is considered. Transverse gradient of temperature is applied on the two opposing regular walls of the inclined enclosure while the other walls are maintained adiabatic. The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on the finite volume method is obtained. Representative results illustrating the effects of the enclosure inclination angle and the degree of irregularity on the contour maps of the streamlines and temperature are reported and discussed. In addition, results for the average Nusselt number at the heated wall of the enclosure and the difference of extreme stream-function values are presented and discussed for various Rayleigh numbers, inclination angles and dimensionless partition heights.     

Natural convection in vertical permeable space

This article describes the natural convective heat transfer in a vertical space insulated with a permeable material. A numerical solution to the problem is given for Ra₀ ? 200, which is the range of interest to building technological applications. The variables and boundary conditions and their influence upon the convective heat transfer are discussed. Comparisons are made with previously published results.     

侧加热腔内的自然对流

开展侧加热腔内自然对流的研究具有重大的环境及工业应用背景. 总结侧加热腔内水平温差驱动的自然对流的最新研究进展, 并概述相应的流动性质、动力机制和传热特性以及对不同无量纲控制参数的依赖也有重要的科学价值. 已取得的研究结果显示突然侧加热的腔内自然对流的发展可包括初始阶段、过渡阶段和定常或准定常阶段. 不同发展阶段的流动依赖于瑞利数、普朗特数及腔体的高宽比, 且定常或准定常阶段的流态可以是定常层流流动、非定常周期性流动或者湍流流动. 此外, 回顾了对流流动失稳机制的研究成果以及湍流自然对流方面的新进展. 最后, 展望了侧加热腔内的自然对流研究的前景.      

Natural convection in unsteady MHD couette flow

 The combined effect of natural convection and uniform transverse magnetic field on the couette flow of an electrically conducting fluid between two parallel plates for impulsive motion of one of the plates in discussed. Under the assumption of negligible induced magnetic field and applied magnetic field being fixed relative to the fluid or plate, the governing equations have been solved exactly, and the expressions for velocity and temperature field have been presented for two different cases. A comparative study is made between the velocity field for magnetic field fixed with respect to plate and magnetic field fixed with respect to fluid. Received on 12 July 1999     

Natural convection in partially cooled tilted cavities

Two-dimensional numerical simulations of laminar natural convection in a partially cooled, differentially heated inclined cavities are performed. One of the cavity walls is entirely heated to a uniformly high temperature (heat source) while the opposite wall is partially cooled to a lower temperature (heat sink). The remaining walls are adiabatic. The tilt angle of the cavity is varied from 0° (heated from left) to −90° (heated from top). The fast false implicit transient scheme (FITS) algorithm, developed earlier by the same authors, is modified to solve the derived variables vorticity-streamfunction formulation. The effects of aspect ratio (AR), sink–source ratio and tilt angle on the average Nusselt number are examined through a parametric study; solutions are obtained for two Grashof numbers, 10⁵ and 10⁷. Flow patterns and isotherms are used to investigate the heat transfer and fluid flow mechanisms inside the cavity. © 1998 John Wiley & Sons, Ltd.     

Natural convection in partially heated vertical channels

A numerical analysis has been performed on laminar natural convection of air in open vertical channels partially heated at uniform wall temperature (UWT) or at uniform heat flux (UHF). The governing equations have been solved by means of a finite difference technique. Results showing axial velocity and temperature developments as well as heat transfer performances and correlations between non-dimensional groups, are presented.

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Natürliche Konvektion in teilweise erwärmten vertikalen Kanälen

Zusammenfassung Eine numerische Analyse wurde über die natürliche Luftkonvektion in vertikalen, mit gleichmäßiger Wandtemperatur (UWT) oder mit gleichmäßigem Wärmestrom (UHF) teilweise erwärmten Kanälen durchgeführt. Die analytischen Gleichungen des Problems wurden mit der Finit-Differenzen-Technik gelöst, und es werden Ergebnisse hinsichtlich der Geschwindigkeits- und Temperaturverteilungen im Inneren des Kanals sowie der thermischen Leistung des Systems aufgeführt.

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Nomenclature a thermal diffusivity of the fluid - c _p specific heat (at constant pressure) of the fluid - g acceleration due to gravity - Gr =[·g·S ³ ·(T₁-T₀)]/v²,Grashof number (UWT case) - Gr =[-g-S ⁴ -q ₁]/(v ²·k), Grashof number (UHF case) - Gr ^* =(S/H) Gr, modified Grashof number - H overall channel height - I, J X andY coordinate indexes - k thermal conductivity of the fluid - Nu mean Nusselt number of the channel - p difference between pressure inside the channel and pressureoutside, at the same heightx - P dimensionless difference pressure - Pr Prandtl number - q specific heat flux - q ₁ specific heat flux from heated plates (UHF case) - Q heat flux (per unit length in thez-direction) from walls - S channel width - T temperature - T _w reference wall temperature - T _o fluid temperature at the inlet section - T ₁ heated plates temperature (UWT case) - u, axial and transverse velocity of the fluid - u _o axial velocity of the fluid at the inlet section - U, V dimensionless axial and transverse velocity - U _o dimensionless axial velocity at the inlet section - x, y axial and transverse coordinate - X, Y dimensionless axial and transverse coordinate - X =H/(S·Gr), dimensionless overall channel height - thermal expansion coefficient of the fluid - dimensionless temperature - v kinematic viscosity of the fluid - density of the fluid     

Natural convection in cavities containing internal sources

 Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working fluid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar flow, and one well above it. In those latter cases, the long-term behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces. Received on 17 January 2000     

Natural convection heating of liquids in closed containers

Transport phenomena occurring during the heating of a non-agitated liquid in a closed cylindrical container were studied. Existing literature on this and analogous problems is briefly reviewed. Special attention is devoted to studies on natural convection in environments of non-uniform temperature. Our experimental work revealed the existence of a boundary layer flow at the vertical sidewall of the container, together with a stratified core in the upper part and a perfectly mixed, unstratified region in the lower part of the container. For the heat transfer rate a dimensionless correlation is found revealing Nu to be approximately proportional to (GrPr)^1/4. From the observed flow patterns and temperature profiles a simplified mathematical model is developed, with which the temperature stratification in the liquid during heating could be simulated. The model may be applied to conversion calculations of a first order chemical reaction (e.g. destruction of micro-organisms).     

Transient natural convection between horizontal concentric cylinders: Natural convection between concentric cylinders

The initial phase of transient natural convection between two horizontal concentric cylinders is investigated. Short-time solutions to the momentum and energy equations are obtained using the method of matched asymptotic expansions. The solutions for the velocity and temperature are expressed in terms of three expansions reflecting the existence of three distinct regions in the initial flow field, and four different patterns of motion may be distinguished, corresponding to four different types of thermal boundary conditions.     

Natural convection heat transfer along vertical rectangular ducts

Experimental investigations have been reported on steady state natural convection from the outer surface of vertical rectangular and square ducts in air. Seven ducts have been used; three of them have a rectangular cross section and the rest have square cross section. The ducts are heated using internal constant heat flux heating elements. The temperatures along the vertical surface and the peripheral directions of the duct wall are measured. Axial (perimeter averaged) heat transfer coefficients along the side of each duct are obtained for laminar and transition to turbulent regimes of natural convection heat transfer. Axial (perimeter averaged) Nusselt numbers are evaluated and correlated using the modified Rayleigh numbers for laminar and transition regime using the vertical axial distance as a characteristic length. Critical values of the modified Rayleigh numbers are obtained for transition to turbulent. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers and the area ratio for the laminar regimes. The local axial (perimeter averaged) heat transfer coefficients are observed to decrease in the laminar region and increase in the transition region. Laminar regimes are obtained at the lower half of the ducts and its chance to appear decreases as the heat flux increases.     

Natural convection heat transfer from sinusoidal wavy surfaces

This paper presents the results of an experimental study of the natural convection heat transfer characteristics of sinusoidal wavy surfaces on vertical plates maintained at a constant temperature. Local heat transfer coefficients were obtained with a Mach-Zehnder interferometer. The heat transfer from the wavy surfaces, compared to a plane plate of equal projected area, increased with increasing amplitude-to-wavelength ratio. The heat transfer was increased by about 15 percent at an amplitude-to-wavelength ratio of 0.3; for this case a flow instability was detected. A quantitative comparison with a previously published numerical investigation is also presented. In general, there is agreement between the two studies.     

Natural convection in inclined two dimensional rectangular cavities

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated. The channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. The field equations for a Newtonian Boussinesq fluid are solved numerically for three cavity height based Rayleigh numbers, Ra = 10⁴, 10⁵ and 10⁶, and several aspect ratios. The calculations are in excellent agreement with previously published benchmark results. The effect of the inclination of the cavity to the horizontal with the angle varying from 0° to 180° and the effect of the startup conditions on the flow pattern, temperature distribution and the heat transfer rates have been investigated. Flow admits different configurations at different angles as the angle of inclination is increased depending on the initial conditions. Regardless of the initial conditions Nusselt number Nu exhibits discontinuities triggered by gradual transition from multiple cell to a single cell configuration. The critical angle of inclination at which the discontinuity occurs is strongly influenced by the assumed startup field. The hysteresis effect previously reported is not always present when the calculations are reversed from 90° to 0°. A comprehensive study of the flow structure, the Nu variation with varying angle of inclination, the effect of the initial conditions and the hysteresis effect are presented.     

Natural convection from a buried elliptic heat source

Numerical solutions are presented for the natural convection heat transfer from an elliptic heat source buried beneath a semi-infinite, saturated, porous medium. The surface of the medium is assumed to be permeable. The governing equations for Darcy flow are solved using finite differences. The complicated geometry is handled through the use of a body-fitted curvilinear coordinate system. Results are presented for Ra values ranging from 10 to 200 and ellipse aspect ratio values from 1.0 (circular cylinder) to 0.167. Two body orientations have been considered. The slender orientation yields much higher hear transfer rates (especially at low ellipse aspect ratio values) than the blunt orientation. The numerical simulations indicate that the boundary-layer approximations cannot be employed for low ellipse aspect ratios. In addition, the heat loss does not depend on the burial depth.