Numerical study of convection of a liquid heated from below

The equilibrium of a liquid heated from below is stable only for small values of the vertical temperature gradient. With increase of the temperature gradient a critical equilibrium situation occurs, as a result of which convection develops. If the liquid fills a closed cavity, then there is a discrete sequence of critical temperature gradients (Rayleigh numbers) for which the equilibrium loses stability with respect to small characteristic disturbances. This sequence of critical gradients and motions may be found from the solution of the linear problem of equilibrium stability relative to small disturbances. If the temperature gradient exceeds the lower critical value, then (for steady-state heating conditions) there is established in the liquid a steady convective motion of a definite amplitude which depends on the magnitude of the temperature gradient. Naturally, the amplitude of the steady convective motion cannot be determined from linear stability theory; to find this amplitude we must solve the problem of convection with heating from below in the nonlinear formulation. A nonlinear study of the steady motion of a liquid in a closed cavity with heating from below was made in [1]. In that study it was shown that for Rayleigh numbers R which are less than the lower critical value R_c steady-state motions of the liquid are not possible. With R>R_c a steady convection arises, whose amplitude near the threshold is small and proportional to (R–R_c)^1/2 (the so-called soft instability)-this is in complete agreement with the results of the phenom-enological theory of Landau [2, 3].Primarily, various versions of the method of expansion in powers of the amplitude [4–8] have been used, and, consequently, the results obtained in those studies are valid only for values of R which are close to R_c, i. e., near the convection threshold.It is apparent that the study of developed convective motion far from the threshold can be carried out only numerically, with the use of digital computers. In [9, 10] the numerical methods have been successfully used for the study of developed convection in an infinite plane horizontal liquid layer.The present paper undertakes the numerical study of plane convective motions of a liquid in a closed cavity of square section. The complete nonlinear system of convection equations is solved by the method of finite differences on a digital computer for various values of the Rayleigh number, the maximal value exceeding by a factor of 40 the minimal critical value R_c. The numerical solution permits following the development of the steady motion which arises with R>R_c in the course of increase of the Rayleigh number and permits study of the oscillatory motions which occur at some value of the parameter R. The heat transfer through the cavity is studied. The corresponding linear problem on equilibrium stability is solved approximately by the Galerkin method.     

FEM solution to natural convection flow of a micropolar nanofluid in the presence of a magnetic field

The two-dimensional, laminar, unsteady natural convection flow in a square enclosure filled with aluminum oxide (\(\hbox {Al}_{2} \hbox {O}_{3}\))–water nanofluid under the influence of a magnetic field, is considered numerically. The nanofluid is considered as Newtonian and incompressible, the nanoparticles and water are assumed to be in thermal equilibrium. The mathematical modelling results in a coupled nonlinear system of partial differential equations. The equations are solved using finite element method (FEM) in space, whereas, the implicit backward difference scheme is used in time direction. The results are obtained for Rayleigh (Ra), Hartmann (Ha) numbers, and nanoparticles volume fractions (\(\phi\)), in the ranges of \(10^3 \le Ra \le 10^7\), \(0\le Ha \le 500\) and \(0 \le \phi \le 0.2\), respectively. The streamlines and microrotation contours are observed to show similar behaviors with altering magnitudes. For low Ra values, when \(Ha=0\), symmetric vortices near the walls and a central vortex in opposite direction are observed in vorticity. As Ra increases, the central vortex splits into two due to the circulation in the effect of the buoyant flow. Boundary layer formation is observed when Ha increases for almost all Rayleigh numbers in both streamlines and vorticity. The isotherms have horizontal profiles for high Ra values owing to convective dominance over conduction. As Ha is increased, the convection effect is reduced, and isotherms tend to have vertical profiles. This study presents the first FEM application for solving highly nonlinear PDEs defining micropolar nanofluid flow especially for large values of Rayleigh and Hartmann numbers.     

Experimental study of free convective heat transfer in a liquid-saturated porous bed at high Rayleigh number

Experiments have been performed to investigate the heat transfer of a horizontal porous bed saturated by liquid heated from below. Attention was especially focussed on the heat-transfer characteristics at the high Rayleigh number where the observed data deviate to a great extent from the linear dependence of the Nusselt number on the Rayleigh number predicted by the previous investigators. The porous bed was made up of packed spherical glass beads with diameter ranging from 3.02 mm to 16.4 mm, while the depth of the bed was varied from 16.4 mm to 103.0 mm. Distilled water, ethylalcohol, fluorocarbon R-11 and transformer oil as testing liquids were used. The results revealed that the effects of particle diameter, depth of bed, and the Prandtl number on the heat-transfer characteristics at the high Rayleigh number are unexpectively large. It was also elucidated that the heat-transfer data which do not exhibit linear dependence of Nu on Ra with Pr_m ranging from 1.1 to 7.3 can well be correlated by the following equations: Nu= 0.10Pr_m ^0.132(d/H)^–0.655Ra^0.5 200 < Ra < 1400 Nu=0.88 Pr^0.132(d/H)^–0.655Ra^0.2 1400 < Ra < 40000

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Experimentelle Untersuchung des Wärmeübergangs bei freier Konvektion in einem flüssigkeits-gesättigten porösen Bett bei hohen Rayleigh-Zahlen

Zusammenfassung Die Versuche betrachten den Wärmeübergang in einem waagerechten porösen Bett, das mit Flüssigkeit gesättigt war und von unten beheizt wurde. Insbesondere wurde der Bereich hoher Rayleigh-Zahlen untersucht, wo die beobachteten Daten stark von der linearen Abhängigkeit der Nusselt-Zahl von der Rayleigh-Zahl abwichen, wie sie in der älteren Literatur behauptet wurde. Das poröse Bett bestand aus Glasperlen mit Durchmessern von 3,02 mm bis 16,4 mm bei einer Tiefe von 16,4 mm bis 103,0 mm. Destilliertes Wasser, Äthylalkohol, Fluorkohlenstoff R-11 und Transformatorenöl wurden verwendet. Die Versuche zeigen, daß die Einflüsse des Teilchendurchmessers, der Tiefe des Betts und der Prandtl-Zahl unerwartet hoch sind. Die Wärmeübergangsdaten, die keine lineare Abhängigkeit zwischen Nu und Ra im Bereich von Pr_m =1,1 bis 7,3 aufwiesen, ließen sich durch folgende Beziehungen wiedergeben: Nu=0,10 Pr_m ^0,132(d/H)^–0,655Ra^0.5 200 < Ra < 1400 Nu=0,88 Pr_m ^0,132(d/H)^0,655Ra^0.2 1400 < Ra < 40000.

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Nomenclature Cp_f specific heat of liquid - d diameter of spherical particles - g gravitational acceleration - H depth of porous bed - k permeability of porous bed - Nu Nusselt number for porous bed, defined in Eq.(4) - Pr_m modified Prandtl number for porous bed, as defined in Eq. (3) - q rate of heat transfer per unit cross-sectional area of porous bed - Ra Rayleigh number for porous bed, as defined in Eq.(1) - T_c temperature of cold wall - T_h temperature of hot wall - T temperature of environment Greek symbols coefficient of volumetric expansion of liquid - temperature difference between hot wall and cold wall - porosity of porous bed - _m modified thermal diffusivity for porous bed - _f thermal conductivity of liquid - _m modified thermal conductivity for porous bed - _f kinematic viscosity of liquid - _f density of liquid     

Interaction between a distributed source and the free surface of a viscous fluid

A self-similar solution of the Navier-Stokes equations describing steady-state axisymmetric viscous incompressible fluid flow in a half-space is investigated. The motion is induced by sources or sinks distributed over a vertical axis with a constant density. The horizontal plane bounding the fluid is a free surface. It is found that in the presence of sources a solution of the above type exists and is unique for any value of the Reynolds numberR > 0, but in the case of sinks only on the interval –2 R < 0. The results of calculating the self-similar solutions are presented. The asymptotics of the solutions are found asR 0 andR .Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–65, March–April, 1996.     

Multiple Steady State Solutions Resulting From Coupling Between Mixed Convection And Radiation In An Inclined Channel

In this work, we present a numerical study of mixed convection coupled with radiation in an inclined channel with an aspect ratio B = L/H=10, and locally heated from one side. Convective, radiative and total Nusselt numbers, evaluated on the cold surface and at the exit of the channel, are presented for different combinations of the governing parameters namely, the surface emissivity (0 1), the Reynolds number (10 Re 50), the inclination of the channel with respect to the horizontal surface (0° 90°) and the Rayleigh number (Ra = 10⁵). The ratio, R = Q_C/Q_E, of the heat quantities, leaving the channel through the cold wall, Q_C, and through the exit, Q_E, is presented to identify the most favorable issue to the heat transfer in the studied configuration. The results obtained show that the flow structure is significantly altered by radiation which contributes to reduce or to enhance the number of the solutions obtained.     

Natural convection in shallow enclosures with multiple conducting partitions

Laminar natural convection and conduction in shallow enclosures having multiple partitions with finite thickness and conductivity have been studied. An approximate analytical solution is obtained by using the parallel flow approximation in horizontal shallow enclosures heated isothermally at two vertical ends while adiabatic on horizontal end walls. The same problem is solved also using a finite difference formulation and the control volume method. The study covers the range ofRa from 105 to 107,A=H/L0.2, C=1/L from 0 to 0.15, and the thermal conductivity ratio of partition to fluidk _r from 10^–4 to 10¹¹. The partition numberN was varied from 0 to 5. The Prandtl number was 0.72 (for air). The results are reduced in terms ofNu as a function ofRa, k, and various geometrical parameters (A, C). The streamlines and isotherms are produced to visualize the flow and temperature fields.Es wird der kombinierte Einfluß von laminarer Naturkonvektion und Leitung in flachen Behältern mit mehreren Trennwänden endlicher Dicke und Leitfähigkeit untersucht. Eine analytische Näherungslösung läßt sich über die Parallelstromapproximation bezüglich horizontaler flacher Behälter finden, deren zwei vertikale Begrenzungswände isotherm beheizt sind, während die Horizontalflächen adiabat sein sollen. Das selbe Problem wird unter Verwendung eines Differenzverfahrens und der Kontrollvolumen-Methode gelöst und zwar für die Parameterbereiche 105 Ra 10⁷;A=H/L<0.2;>C=1/L 0.15; 10^–4k_r 1011, wobei der letzte Parameter das Verhältnis der Leitfähigkeit von Trennwand und Fluid bezeichnet. Die Zahl der TrennwändeN variierte Zwischen 0 und 5, die Prandtl-Zahl betrug 0.72 (Luft). Die Ergebnisse werden in dimensionsloser Form gemäß der BeziehungNu =f (Ra, k _r ,A, C) mitgeteilt bzw. durch Diagrammdarstellungen der Stromlinien- und Isothermenfelder veranschaulicht.Financial support from the Natural Sciences and Engineering Council Canada is acknowledged. Financial support to A. Kangni from Canadian Fellowship Program For French Speaking Countries is also acknowledged.     

Rayleigh-Benard convection: experimental study of time-dependent instabilities

The transition from steady thermal convection to turbulent thermal convection in a horizontal layer of water (Prandtl number=5.8) contained by a square cavity of large aspect ratio (48.5) has been studied using laser Doppler velocimetry. Power spectra of the horizontal velocity fluctuations were measured in the Rayleigh number range from 30,000 and 99,000, wherein periodic, quasi-periodic, and broad-band time-dependent instabilities coexist. At Rayleigh numbers greater than 32,000 a narrow-band spectrum emerges. The frequency of this motion scales with x/d ² modified by a Prandtl number factor for intermediate values of the Prandtl number. Between 10 Ra _c and 30 Ra _i the frequency undergoes three abrupt jumps while increasing along an Ra ^2/3 power law. A different frequency mode that occurs above 30 Ra _c appears to be associated with fully turbulent convection.List of symbols c heat capacity - d depth of fluid layer - f frequency - g gravitational acceleration - H heat flux - k thermal conductivity - Nu Nusselt number=Hd/k T - Pr Prandtl number=v/x - Ra Rayleigh number - Ra _c critical Rayleigh number=1708 - T temperature difference across the fluid layer - thermal coefficient of expansion - _v aspect ratio=width/depth - x thermometric conductivity=k/ - kinematic viscosity - density A version of this paper was presented at the Tenth Symposium of Turbulence, University of Missouri-Rolla, September 22–24, 1986     

Nusselt-Rayleigh correlations for free convection in 2D air-filled parallelogrammic enclosures with isothermal active walls

In the present study Nu-Ra-α correlations are proposed to calculate the steady-state natural convection heat transfer taking place in 2D air-filled cavities of parallelogrammic section. The thermal conditions and the dimensions of the enclosures permit to cover a large range of Rayleigh numbers, 1.7 × 10³  ≤ Ra ≤ 3.0 × 10⁹, suitable for diverse engineering applications. The two active walls of the cavities are kept vertical and isothermal at hot and cold temperatures T _h and T _c respectively. Separated by a horizontal distance H, they have the same height H and are connected by a closed adiabatic channel whose upper and lower walls can be inclined at an angle α with respect to the horizontal, varying between −60° to +60°. That gives rise to a conducting or insulating cavity, in the convective sense of the term (diode cavity). A computational model based on the finite volume method is used to solve the governing equations. The large number of treated configurations led to propose Nu-Ra-α correlations for large ranges of Ra and α which can be applied to many engineering areas. The results of this numerical study have been successfully compared with calculated and measured available data.     

Low power laser Rayleigh probe for flow mixing studies

A laser Rayleigh correlation probe was constructed, which allows the application of low cost, low power (milliwatt) laser sources. It was tested for basic mixing studies in isothermal binary gas flows. Here, it can be used for the time and space resolved measurement of the concentration mean value and of all important statistical quantities, which give information on the distribution around the concentration mean value (rms, skewness, kurtosis) and on the relation of adjecent fluctuations in time or space (autocorrelation function, power spectral density).List of symbols c concentration (mole fraction) of investigated gas species - c time averagered mean concentration - c instantaneous fluctuating concentration - rms concentration - D Rayleigh intensity difference of two gas species (I _R1–I _R2) - d width of the rectangular channels (x-direction), see Fig. 3 - f frequency - G() Rayleigh autocorrelation function (ACF) - I ₀ intensity of irradiated laser light - I _Ri intensity of Rayleigh signal of gas species i - K, k calibration constant of Rayleigh probe - l lenght of observed scattering volume - n(t) temporally fluctuating number density of gas molecules - R() normalized ACF - S Rayleigh intensity of gas components 2 in a binary mixture (I _R2) - T gas temperature - t time - u exit velocity - skewness of the concentration distribution around the mean value - kurtosis of the concentration distribution around the mean value - (d/d)_eff effective scattering cross section of the binary gas mixture - solid angle of collection optics - delay time - sample time     

Single-phase heat transfer characteristics of concentric-tube thermosyphon

An experimental study has been conducted to evaluate the influence of the presence of inner tube and the Rayleigh number on free convective heat transfer in an open thermosyphon. Water and fluorocarbon R-11 refrigerant as the working fluids were utilized. Heat transfer results using the concentric geometry were given for modified Rayleigh number from 3.6×10² to 4.1 × 10⁷ which encompasses the regions of similarity, impeded and boundary layer flow conditions. It was found that the presence of the inner tube markedly increases the overall heat transfer coefficient of open thermosyphon by a factor as large as 2 to 10 in the turbulent impeded and boundary layer regimes.

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Wärmeübergang in einem Thermosyphon aus konzentrischem Rohr bei einphasiger Strömung

Zusammenfassung Es wurde experimentell untersucht, wie der Einbau eines Innenrohres und wie die Rayleigh-Zahl auf die freie Konvektion in einem offenen Thermosyphon, gefüllt mit Wasser oder dem Kältemittel R 11, einwirkt. Der untersuchte Bereich bei konzentrischer Geometrie lag bei modifizierten Rayleigh-Zahlen von 3,6 · 10² bis 4,1 · 10⁷ und umfaßte damit die Regionen der Grenzschichtströmung. Es ergab sich, daß der Einbau eines Innenrohres den Gesamtwärmeübergang eines offenen Thermosyphons im Bereich der behinderten turbulenten Strömungen und Grenzschichtströmungen um den Faktor 2 bis 10 steigert.

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Nomenclature a inner radius of heated tube, D/2 - A_in sectional space area of inner tube, d _i ² /4 - A_an sectional space area of annulus, (D^2-d ₀ ² )/4 - C_p specific heat - d_i inner diameter of inner tube - d₀ outer diameter of inner tube - D inner diameter of heated tube - g gravitational acceleration - L tube length of thermosyphon - Nu_a Nusselt number based on inner radius of heated tube - Nu_r Nusselt number based on equivalent heattransfer radius - Nu_x Nusselt number, defined in equation (1) - Pr Prandtl number, defined in equation (3) - q heat flux from heated tube - r equivalent heat-transfer radius, defined in equation (4) - Ra_a modified Rayleigh number based on inner radius of heated tube - Ra_r modified Rayleigh number based on equivalent heat-transfer radius - Ra_x modified Rayleigh number, defined in equation (2) - T_e temperature of entrance-fluid - T_w temperature of heated surface - T temperature difference between heated wall and entrance-fluid, T_w-T_e Greek Symbols coefficient of volumetric expansion - thermal diffusivity - thermal conductivity - viscosity - kinematic viscosity     

Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses

Across traveling autocatalytic fronts, density differences due to composition and temperature changes can lead to buoyancy-driven hydrodynamic instabilities deforming the front by convective motions. We study here the influence of heat losses through the walls of the reactor on the stability of such exothermic fronts in the gravity field. The stability domain is computed numerically in a parameter space spanned by the solutal R_c and thermal R_T Rayleigh numbers of the problem for various values of the Newton's coefficient α quantifying the intensity of heat losses.     

A generating function for the yield criterion of isotropic and anisotropic polycrystalline materials

Summary A yield criterion for elastic pure-plastic polycrystalline materials is generated under simplified conditions by assuming that for yielding a certain fraction Q _c of the total number of slip planes in the material has to be active. This fraction Q _c is called the critical active quantity. We suppose Q _c to be independent of the state of stress. The yield criterion is mathematically expressed as an integral, which is a function of Q _c. This criterion can also be used for anisotropic materials.For isotropic materials the ratio (r) of the yield stress in torsion to that in tension is calculated as a function of Q _c. We find 0.5r0.61.The value r=0.5 (Tresca's criterion) is obtained for Q _c=0 and Q _c=1. The value r=0.577 (von Mises criterion) is obtained for Q _c=0.34 and Q _c=0.79. The difference between two criteria with the same r is the magnitude of the yield stress. We think the value Q _c=0.79 corresponds to the experiments for f.c.c. materials, since a rough estimation gives Q _c>0.75 for yielding.The independence of Q _c on the state of stress brings on that r>0.5 is more probable. This is caused by the slower increase to Q _c in torsion compared with the case of tension.From the theory follows that in the general case (Q _c0) the middle principal stress has influence on yielding.In this paper we don't determine Q _c, but adapt its value to the experimental results. However, a rough estimation of Q _c is given for isotropic materials.     

Distinctive Features of the Flow past a Flight Vehicle Integrated with an Air-Breathing Engine at High Supersonic Velocities

The aerodynamic characteristics and distinctive features of the flow past hypersonic integral-layout flight vehicles with air-breathing engines intended for cruising atmospheric flight are experimentally investigated. The experiments were conducted on a simplified model designed with regard for the general principles of integration for vehicles of the class considered. The tests were run in a high-speed supersonic wind tunnel over the Mach and Reynolds number ranges 4 M 9 and 10⁵ Re₀ 10⁶.Balance testing was conducted, the pressure distributions over the vehicle surface were measured, the flowfield parameters were determined using a moving total-pressure tube, and flow shadowgraphs were obtained. The measured data are compared with the results of the calculations for three-dimensional inviscid flows. The effects of mounting a nacelle and contouring the internal duct are considered. The effect of the corrections on the duct flow in the absence of jet modeling is estimated.     

Kinematic regimes of convection at high Prandtl number in a shallow cavityRégimes cinématiques de la convection à haut nombre de Prandtl dans une cavité allongée.

We consider free convection in a horizontal shallow cavity with different end temperatures, filled with a high Prandtl number fluid. From scaling analysis, we find two kinematic regimes resulting from the competition of heat transfer by conduction and by convection. Numerical simulations realized for a large range of Rayleigh number and aspect ratio confirm the phenomenological analysis and provide the threshold between the two regimes. The conductive and convective regimes occur at $\mathit{Ra}{A}^2$ smaller and larger than 443 respectively, where Ra is the Rayleigh number and A is the aspect ratio. In the convective regime, the characteristic velocity is independent of depth of the cavity. To cite this article: J.-M. Flesselles, F. Pigeonneau, C. R. Mecanique 332 (2004).     

Influence of inclination angle on buoyancy-driven convection in triangular enclosure filled with a fluid-saturated porous medium

The present investigation deals with the numerical analysis of steady-state laminar buoyancy-driven convection in an inclined triangular enclosure filled with fluid saturated porous media using the Darcy law equation. One wall of the enclosure is isothermally heated and the other is cooled, while the remaining wall is adiabatic. The effect of inclination angle on natural convection is investigated by varying the angle of inclination (φ) between 0° and 360°. The governing transformed equations are solved numerically using a finite-difference method. Obtained results are shown in the form of streamlines, isotherms, mean Nusselt numbers and dimensionless stream function for different values of the Rayleigh number Ra in the range 100 ≤ Ra ≤ 1,000. It is found that the values of the maximum and minimum mean Nusselt number are reached for φ = 330° and φ = 210° , respectively. However, the lowest flow strength is formed at φ = 240° for all values of Ra.     

Bounds on convective heat transport in a rotating porous layer

Using the background field variational method, bounds on convective heat transport in a rotating porous layer heated from below are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the dimensionless temperature difference across the layer (the Rayleigh number Ra) according to

This rigorous upper bound shows that rotation has a retarding effect on convective heat transport.     

Torsion of two bonded layers by a rigid disk

The problem considered in this paper describes the torsion of a homogeneous isotropic elastic layer (0zd ₁) of finite thickness d ₁, perfectly bonded to another elastic layer (-d ₂z0) of finite thickness d ₂. The problem is reduced to the solution of a Fredholm integral equation of the second kind. The solutions are given for some particular cases.

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Sommario In questo lavoro si considera il problema della torsione di uno strato elastico omogeneo ed isotropo (0zd ₁) di spessore finito d ₁, perfettamente incollato ad un altro strato elastico (-d ₂z0) di spessore finito d ₂. II problema é ricondotto alla soluzione di una equazione integrale di Freedholm del secondo ordine. Le soluzioni sono ottenute per alcuni casi particolari.

     

A MEMS skin-friction sensor for time resolved measurements in separated flows

A MEMS surface fence sensor for skin-friction measurements in separated flows has been developed and tested successfully in low-speed flows. The new sensor is able to distinguish between forward and reverse flow and features a temporal resolution of up to 1 kHz. Calibrations of the sensor have been obtained in the range of –0.7 N m^-2_w0.7 N m^-2 with a resolution of 0.02 N m^-2. Comparative measurements with the wall-pulsed wire technique in a reverse-flow region show excellent agreement with respect to the mean skin-friction coefficient c_f but also reveal some discrepancies for the fluctuating part c_f.     

Non-Darcian and Anisotropic Effects on Free Convection in a Porous Enclosure

The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement (SAR) scheme have been obtained for 100 ≤ Ra ≤ 1000, 0.5 ≤ AR ≤ 5, 0.5 ≤ K* ≤ 5, 0.5 ≤ k* ≤ 5, and 0 ≤ Da ≤ 0.1. It has been found that [`(Nu)]{\overline {Nu}}, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in [`(Nu)]{\overline {Nu}} depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow.     

The Onset and Nonlinear Regimes of Convection in a Two-Layer System of Fluid and Porous Medium Saturated by the Fluid

The onset of convection and its nonlinear regimes in a heated from below two-layer system consisting of a horizontal pure fluid layer and porous medium saturated by the same fluid is studied under the conditions of static gravitational field. The problem is solved numerically by the finite-difference method. The competition between the long-wave and short-wave convective modes at various ratios of the porous layer to the fluid layer thicknesses is analyzed. The data on the nature of convective motion excitation and flow structure transformation are obtained for the range of the Rayleigh numbers up to quintuple supercriticality. It has been found that in the case of a thick porous layer the steady-state convective regime occurring after the establishment of the mechanical equilibrium becomes unstable and gives way to the oscillatory regime at some value of the Rayleigh number. As the Rayleigh number grows further the oscillatory regime of convection is again replaced by the steady-state convective regime.