Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×10⁶ and 1.43×10⁶. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.     

Transient natural convection of low-Prandtl-number fluids in a differentially heated cavity

The transient convective motion in a two-dimensional square cavity driven by a temperature gradient is analysed. The cavity is filled with a low-Prandtl-number fluid and the vertical walls are maintained at constant but different temperatures, while the horizontal boundaries are adiabatic. A control volume approach with a staggered grid is employed to formulate the finite difference equations. Numerically accurate solutions are obtained for Prandtl numbers of 0·001, 0·005 and 0·01 and for Grashof numbers up to 1 × 10⁷. It was found that the flow field exhibits periodic oscillation at the critical Grashof numbers, which are dependent on the Prandtl number. As the Prandtl number is decreased, the critical Grashof number and the frequency of oscillation decrease. Prior to the oscillatory flow, steady state solutions with an oscillatory transient period were predicted. In addition to the main circulation, four weak circulations were predicted at the corners of the cavity.     

Numerical investigation of transient laminar natural convection of air in a tall cavity

Transient laminar natural convection of air in a tall cavity has been studied numerically. The Navier-Stokes and Energy equations were solved by the accurate projection method (PmIII), in which the derived Poisson equation for pressure potential was solved by the approximate factorization one method (AF1). The aspect ratio of the tall cavity is 16, and the Prandtl number of air filled in the tall cavity is 0.71. To obtain the numerical results of heat transfer by natural convection of air in the tall cavity, the second order schemes for the space and time discretizations were utilized. The availability of the numerical algorithm was also assessed by considering the natural convection of air in a square cavity which is differentially heated from side walls. It was found that the overall Nusselt numbers for the Rayleigh numbers covering the range from 1000 to 100000 reveal a good agreement with measured data. When Ra takes the value in the range from 100000 to 600000, the overall Nusselt number have a relative deviation less than 18% from the experimental data. For the suddenly heating mode, the multicellular flow pattern occurs when Rayleigh number belongs to the range of Ra from 7000 to 20000. or greater than 115000. At the critical number of cats' eye instability, the cell distance is just twice of the cavity width. This is rather similar to the observed result for Bénard problem. When Ra is over 115000, a further increase of heat flux across the tall cavity causes serious cell-breaking. There are 8 cells when Ra = 600000.     

Transient natural convection cooling of a high Prandtl number fluid in a cubical cavity

This work presents a numerical analysis of the effects of thermal boundary conditions, fluid variable viscosity and wall conduction on transient laminar natural convection of a high Prandtl number (Pr=4×10⁴) fluid (Golden Syrup) in a cubical cavity. The simulations consider physical situations realizable at laboratory scale using a cavity with Plexiglas walls of 1 cm of thickness, and inside dimension of L=20 cm. The initial Rayleigh (Ra) number is 10⁶. The cavity is initially full of fluid at rest and at constant temperature (T _i =45°C) higher than the temperature of the walls (T _w =25°C). The time evolution of the flow patterns, the temperature contours, the mean temperature of the fluid and the Nusselt number (Nu) of eight different cases of cooling are presented and analyzed.     

Conjugate natural convection in a square porous cavity

 Steady-state conjugate natural convection in a square cavity filled with a porous medium is studied numerically in this paper. The enclosure consists of two horizontal conductive walls of finite thickness and two vertical walls at different uniform temperatures. The focus is on the role of solid-fluid conductivity ratio, k, on the flow and heat transfer characteristics and the average Nusselt number, , over the vertical hot and cold walls of the cavity for a limited set of particular parameters. It was shown that the interface temperature, θ_w, along the top of the solid wall decreases with the increase in the wall conductivity k. Also, the values of decreases with the increase of the values of the parameter k. Comparison with known results from the open literature when the wall thickness of the horizontal solid walls is neglected (non-conjugate problem) is excellent. Received on 4 April 2000     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

Transient conjugate mixed convection from a sphere in a porous medium saturated with cold pure or saline water

In this paper, a numerical investigation of the transient conjugate mixed convection flow about a sphere embedded in a porous medium saturated with pure or saline water is carried out. The effect of density extremum is considered by using the nonlinear dependence of density on the temperature. The salinity effects are considered by assuming uniform saline concentration over the domain considered. The direction of the natural convection is changed either to aiding or to opposing the upcoming flow direction simulating the sphere is either hot or cold relative to the surrounding temperature. Results show that the initial temperature differences as well as the saline concentration alter the transient heat transfer rate in conceivable degree. It was found that the heat capacity ratio between the sphere and the surrounding media has more significant effect on the calculated heat transfer rate than the thermal conductivity ratio. The study is performed by using six nondimensional parameters and results are discussed in detail. Received on 10 November 1997     

Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity

In this study, a transient heat transfer process of freezing water inside a two-dimensional square cavity has been investigated numerically. Water was used as a phase-change medium, and the numerical model has been created with control volume approach by using C++ programming language. To be able to accelerate the numerical calculations, CUT (Consistent-Update-Technique) algorithm has been implemented in the numerical code. Span-wise variations of the vertical component of the velocity have been represented in comparison with the experimental measurements from the literature at various vertical positions to examine the accuracy of the numerical scheme. The influence of natural convection has been considered by comparing the conduction and convection dominated solidification under same boundary conditions. Comparative results have been obtained regarding time-wise variations of the cold wall temperature and the dimensionless effectiveness. Moreover, the streamlines and isotherms have been represented to understand the differences between the conduction and convection driven phase change processes.Results indicate that natural convection becomes remarkable and has different forms at the initial periods of the phase change process. Increasing the effect of natural convection in the cavity increases the cooling rate of water. Near the density inversion temperature of water (4°C), temperature variations fluctuate and counter currents observed in the domain.     

Mass and heat transfer by natural convection in a vertical cavity

This paper reports a fundamental study of laminar natural convection in a rectangular enclosure with heat and mass transfer from the side, when the bouyancy effect is due to density variations caused by either temperature or concentration variations. In the first part of the study scale analysis is used to determine the scales of the flow, temperature and concentration fields in boundary layer flow for all values of Prandtl and Lewis numbers. In particular, scale analysis shows that in the extreme case where the flow is driven by bouyancy due to temperature variations, the ratio of mass transfer rate divided by heat transfer rate scales as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ only if (Pr > 1, Le < 1) or (Pr < 1, Sc < 1), and as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ if (Pr > 1, Le > 1) or (Pr < 1, Sc > 1). In the second part of the study, the boundary layer scales derived in the first part are used to determine the heat and mass transport characteristics of a vertical slot filled with fluid. Criteria for the existence of distinct thermal and concentration boundary layers in the slot are determined. Numerical solutions for the flow and concentration fields in a slot without distinct thermal boundary layers are reported. These solutions support further the method of scale analysis employed in the first part of the study     

Transient natural convection through vertical porous stratum

An analytical study is made to examine the flow behaviour of a fully developed transient free-convective flow of an incompressible viscous fluid between two heated vertical walls in a porous system. A Laplace transform technique has been employed to obtain the expression for velocity, temperature and skin-friction. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is discussed in detail. Received on 11 March 1997     

Transient natural convection flow of a nanofluid over a vertical cylinder

An analysis is performed to study unsteady free convective boundary layer flow of a nanofluid over a vertical cylinder. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme of the Crank-Nicolson type. The solutions at each time step have been found to reach the steady state solution properly. Numerical results for the steady-state velocity, temperature and nanoparticles volume fraction profiles as well as the axial distributions and the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.     

Transient laminar natural convection in a partitioned enclosure heated by uniform flux

Transient laminar natural convection in an enclosure partitioned by an adiabatic baffle is investigated numerically. The enclosure is heated by uniform heat flux from left wall and cooled from right wall which is kept at isothermal. A penalty finite element method with Newton-Raphson iteration algorithm and a backward difference scheme dealing with time term are adopted to solve governing equations. The effects of the baffle and Rayleigh number are found to be substantial on heat transfer mechanism during transient process. However, the variations of heat transfer mechanism occur mainly in the first one-third period of the time of transient, in spite of the present or not, or location of a baffle at the conditions of Rayleigh number being 10⁴ and 10⁶ in this study.Transiente, laminare freie Konvektion in einem von einer adiabaten Wand unterteilten Hohlraum wurde numerisch untersucht. Der Hohlraum wird von einem gleichmäßigen Wärmestrom von der linken Wand beheizt und von der rechten isothermen Wand gekühlt. Ein Finite-Element-Verfahren mit dem Newton-Raphson Iterationsalgorithmus und dem Differenzenverfahren mit Zeitterm sind übernommen worden, um bestehende Gleichungen zu lösen. Die Trennwand und die Rayleigh-Zahl sind für den Wärmeübergangsmechanismus während der transienten Phase von wesentlicher Bedeutung. Für den in dieser Studie untersuchten Bereich der Rayleigh-Zahl von 10⁴ und 10⁶ treten Veränderungen im Wärmeübergangsmechanismus hauptsächlich im ersten Drittel der transienten Phase auf und sind unabhängig von der Anwesenheit und Plazierung der Trennwand.     

Transient natural convection in a rectangular enclosure with one heated side wall

This paper describes a numerical and theoretical study of the transient natural convection heating of a two-dimensional rectangular enclosure filled with fluid. The heating is applied suddenly along one of the side walls, while the remaining three walls are maintained insulated. It is shown that the process has two distinct phases, an early period dominated by conduction and a late period dominated by convection. The scaling laws for the heat transfer rate and the effectiveness (energy storage fraction) are determined based on scale analysis. These theoretical results are confirmed by numerical experiments conducted in the domain Ra = 10³−10⁶, Pr = 7, A = 1, where Ra is the Rayleigh number based on height and initial temperature difference, Pr is the Prandtl number, and A is the height/length ratio of the enclosure. Correlations for heat transfer rate and effectiveness are constructed by comparing the theoretical scaling laws with the numerical results.     

Transient natural convection flow of a particulate suspension through a vertical channel

Continuum equations governing transient, laminar, fully-developed natural convection flow of a particulate suspension through an infinitely long vertical channel are developed. The equations account for particulate viscous effects which are absent from the original dusty-gas model. The walls of the channel are maintained at constant but different temperatures. No-slip boundary conditions are employed for the particle phase at the channel walls. The general transient problem is solved analytically using trigonometric Fourier series and the Laplace transform method. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the flow and thermal aspects of the problem.     

Three-dimensional conjugate natural convection in a vertical cylinder under heat transfer to the surroundings

Unsteady three-dimensional conjugate natural convection in a closed vertical cylinder with a local energy source under convective heat transfer to its surroundings is mathematically modeled in the “vector potential—velocity vorticity—temperature” variables. The temperature and velocity fields, together with the dependences of the mean Nusselt number at the energy source surface on a complex of the governing parameters controlling the formation of different regimes of mass, momentum, and energy transfer, are obtained.     

Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number

Finite element predictions of two-dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half-divider in water for Rayleigh number up to 10¹¹ and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.     

Melting process with solid-liquid density change and natural convection in a rectangular cavity

This paper presents a numerical method that simulates the melting process in the presence of solid-liquid density change and natural convection in the melt. The physical model concerned is two-dimensional melting of a phase-change material, initially at its fusion temperature, charged in a rectangular cavity with isothermally heated side walls and an adiabatic bottom wall. The presence of the density change brings no change into the basic form of governing equation, so it is considered through the reformulation of boundary conditions. Difficulties associated with the complex time-dependent melt region, whose shape is also a part of the solutions, are overcome by employing the boundary-fitted coordinate system. Comparison with other works validates the present numerical model and reveals the effects of density change qualitatively. Also, it is confirmed that the present method is preferable to others with natural convection only. Computed results for interesting cases are shown in forms of transient position of the interface, temperature distribution, flow pattern, heat transfer coefficient, and melting fraction as a function of time. Closer examination on melting patterns allows a correlation to be made between the melting fraction and a new independent variable Ste·Fo·Ra^1/4.