Development of Multicellular Solutions in Natural Convection in an Air-Filled Vertical Cavity

1997 ◽  
Vol 119 (1) ◽  
pp. 97-101 ◽  
Author(s):  
S. Wakitani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Multiple Solutions ◽  
Initial Condition ◽  
Two Dimensional ◽  
Reverse Transition ◽  
Wide Range ◽  
Flow Through ◽  
Rayleigh Numbers ◽  
Vertical Cavity

Consideration is given to the multiple solutions of two-dimensional natural convection in a vertical air-filled tall cavity with differentially heated sidewalls. Numerical simulations are carried out for a wide range of Rayleigh numbers from the onset of the steady multicellular flow, through the reverse transition to the unicellular pattern, to the unsteady multicellular flow. The dependence of the flow structure on the initial condition is clarified from the simulations by means of starting from a motionless and isothermal state, and gradually increasing or decreasing the Rayleigh number.

scholarly journals Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2788
Author(s):  
Hyun-Sik Yoon ◽  
Yoo-Jeong Shim
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Circular Cylinder ◽  
Flow Structures ◽  
Two Dimensional ◽  
Square Enclosure ◽  
Wide Range ◽  
Secondary Vortices ◽  
Rayleigh Numbers

The present study investigated the natural convection for a hot circular cylinder embedded in a cold square enclosure. The numerical simulations are performed to solve a two-dimensional steady natural convection for three Rayleigh numbers of 103, 104 and 105 at a fixed Prandtl number of 0.7. This study considered the wide range of the inner cylinder positions to identify the eccentric effect of the cylinder on flow and thermal structures. The present study classifies the flow structures according to the cylinder position. Finally, the present study provides the map for the flow structures at each Rayleigh number (Ra). The Ra = 103 and 104 form the four modes of the flow structures. These modes are classified by mainly the large circulation and inner vortices. When Ra = 105, one mode that existed at Ra = 103 and 104, disappears in the map of the flow structures. The new three modes appear, resulting in total six modes of flow structures at Ra = 105. New modes at Ra = 105 are characterized by the top side secondary vortices. The corresponding isotherms are presented to explain the bifurcation of the flow structure.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

Effects of magnetic field on the liquid gallium thermosyphon fluid flow; a numerical study

2019 ◽  
Vol 30 (2) ◽  
pp. 681-703
Author(s):  
Hamid Teimouri ◽  
Amin Behzadmehr
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Liquid Gallium ◽  
Two Dimensional ◽  
Left Wall ◽  
Content Type ◽  
Wide Range

Purpose This paper aims to numerically study the laminar natural convection in a thermosyphon filled with liquid gallium exposed to a constant magnetic field. The left wall of the thermosyphon is at an uniformed hot temperature, whereas the right wall is at a uniform cold temperature. The top and bottom walls are considered to be adiabatic. All walls are electrically insulated. The effects of Hartmann number, in a wide range of Rayleigh number and aspect ratio combinations, on the natural convection throughout the thermosyphon, are investigated and discussed. Furthermore, different forces that influence the natural flow structure are studied. Design/methodology/approach A Fortran code is developed based on the finite volume method to solve the two-dimensional unsteady governing equations. Findings Imposing a magnetic field improves the stability of the fluid flow and thus reduces the Nusselt number. For a given Hartmann and Rayleigh number, there is an optimum aspect ratio for which the average velocity becomes maximum. Research limitations/implications This paper is a two-dimensional investigation. Originality/value To the best of the authors’ knowledge, the effect of the magnetic field on natural convection of liquid gallium in the considered thermosyphon has not been studied numerically in detail. The results of this paper would be helpful in considering the application of the low Prandtl number’s liquid metals in thermosyphon MHD generators and certain cooling devices.

Interaction of temperature- and salinity-driven natural convection in homogeneous porous media

2020 ◽  
Author(s):  
Márk Szijártó ◽  
Attila Galsa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Simulations ◽  
Theoretical Models ◽  
Time Dependent ◽  
Two Dimensional ◽  
Thermohaline Convection ◽  
Rayleigh Numbers

<p>Onset of thermal and haline convection was studied separately by Lapwood (1948) and Wooding (1956) in theoretical models using analytical methods. They established that the buoyancy force caused by difference in temperature (Δ<em>T</em>) or concentration (Δ<em>c</em>) can induce natural convection depending on the model properties (e.g. geometry, permeability, etc.). In the course of further numerical simulations, the thermal (<em>Ra<sub>T</sub></em>) and the haline Rayleigh number (<em>Ra<sub>H</sub></em>) proved itself useful to characterise the type, the intensity and the form of the natural convection (e.g. Diersch and Kolditz, 2002). The main purpose of our study was to examine numerically the combined effect of temperature- and salinity-driven natural convection in a two-dimensional homogeneous porous medium.</p><p>Two-dimensional finite element base model was set up in agreement with the Elder problem (Wooding, 1956) in order to verify the numerical calculation. First, it was established that (1) the critical Rayleigh numbers are mathematically equivalent in the two separated cases (<em>Ra</em><sub><em>Tcr</em></sub>=<em>Ra<sub>Hcr</sub></em>=4π<sup>2</sup>), and (2) time-dependent thermal or haline natural convections evolve, when the Rayleigh number lies within the range of 300–600. Numerical simulations were accomplished to investigate the interaction of the temperature- and salinity-driven natural convection. Non-dimensional thermal expansion and haline concentration were increased from αΔ<em>T</em>=0.01 to 1 and from βΔ<em>c</em>=10<sup>-5</sup> to 10<sup>-3</sup>, respectively, while the variation of the Darcy flux, the temperature, the concentration, the Nusselt and the Sherwood numbers was computed. The main points of this study were that (1) how the onset of the thermohaline convection is facilitated by the positive interaction of the thermal and haline effects (<em>Ra<sub>THcr</sub></em>); (2) under what conditions time-dependent flow evolves in the theoretical models; (3) whether a new non-dimensional number can be defined instead of the two separated Rayleigh numbers in order to characterise the behaviour of the thermonaline convection. These simulations draw attention to the importance of understanding the physical background of thermohaline convection, for instance, at the margin of confined and unconfined carbonate systems (e.g. Buda Thermal Karst), or in the case of groundwater flow induced by water pumping/injection of deep geothermal power plants.</p><p>The project was supported by the ÚNKP-19-3 and ÚNKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology, the Hungarian Research Fund (K 129279) and the János Bolyai Scholarship of the Hungarian Academy of Science. This research is a part of a project that has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 810980.</p><p>References:</p><p>Diersch, H.-J.G., Kolditz, O. (2002), Variable-density flow and transport in porous media: approaches and challenges. Advances in Water Resources, 25, 899-944.</p><p>Lapwood, E.R. (1948), Convection of a fluid in a porous medium. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 508-521.</p><p>Wooding, R.A. (1956), Steady state free thermal convection of liquid in a saturated permeable medium. Journal of Fluid Mechanics, 2, 273-285.</p>

A Numerical Solution for Natural Convection in Cylindrical Annuli

1971 ◽  
Vol 93 (2) ◽  
pp. 210-220 ◽  
Author(s):  
R. E. Powe ◽  
C. T. Carley ◽  
S. L. Carruth
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Unsteady Flow ◽  
Numerical Solution ◽  
Numerical Technique ◽  
Secondary Flows ◽  
Pronounced Increase ◽  
Wide Range ◽  
Rayleigh Numbers

The results of a finite-difference solution for natural convection within horizontal cylindrical annuli for Prandtl numbers near 0.7 (air) are presented. The ranges of Rayleigh number and inverse relative gap width over which such a solution yields valid results are investigated. It is shown that this solution, though formulated for steady flow, can be used to obtain an indication of the Rayleigh number at which transition from a steady to an unsteady flow will occur for a wide range of inverse relative gap widths (2.8–12.5). A recent experimental investigation has shown that steady secondary cellular flows occur immediately prior to transition for this range of inverse relative gap widths, and the Rayleigh number at which these secondary flows occur is accurately predicted by the numerical solution, thereby yielding a good indication of the Rayleigh number at which transition to an unsteady flow occurs. Flow patterns predicted by the numerical solution near transition are compared with photographs of the flow, and excellent qualitative agreement is noted. It is thus shown that this numerical technique gives, at least qualitatively, valid results for all Rayleigh numbers at which the flow is steady for the range of inverse relative gap widths under consideration. Heretofore unavailable data on temperature profiles, radial and angular velocity components, and local Nusselt numbers for Rayleigh numbers near the transition value are presented. It is found that the foregoing parameters (velocity, temperature, and Nusselt number) are little affected by the appearance of the secondary flow for the smaller inverse relative gap widths considered, whereas for the larger inverse relative gap widths a pronounced increase in magnitude of temperatures and velocity components is noted. The overall or mean Nusselt number is not affected by the appearance of these secondary flows for any of the inverse relative gap widths considered.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

scholarly journals Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 363 ◽  
Author(s):  
Jong Hwi Lee ◽  
Jong-Hyeon Shin ◽  
Se-Myong Chang ◽  
Taegee Min
Keyword(s):  
Natural Convection ◽  
Heat Exchanger ◽  
Rayleigh Number ◽  
Numerical Method ◽  
Stokes Equations ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Tube Heat Exchanger ◽  
Fin Tube ◽  
Rayleigh Numbers

In this research, unsteady three-dimensional incompressible Navier–Stokes equations are solved to simulate experiments with the Boussinesq approximation and validate the proposed numerical model for the design of a circular fin-tube heat exchanger. Unsteady time marching is proposed for a time sweeping analysis of various Rayleigh numbers. The accuracy of the natural convection data of a single horizontal circular tube with the proposed numerical method can be guaranteed when the Rayleigh number based on the tube diameter exceeds 400, which is regarded as the limitation of numerical errors due to instability. Moreover, the effective limit for a circular fin-tube heat exchanger is reached when the Rayleigh number based on the fin gap size ( Ra s ) is equal to or exceeds 100. This is because at low Rayleigh numbers, the air gap between the fins is isolated and rarely affected by natural convection of the outer air, where the fluid provides heat resistance. Thus, the fin acts favorably when Ra s exceeds 100.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103<Ra<4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

scholarly journals Thermally Optimum Spacing between Inner Plates in Natural Convection Flows in Cavities by Numerical Investigation

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 554 ◽  
Author(s):  
Blas Zamora
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Numerical Investigation ◽  
Thermophysical Properties ◽  
Electronic Equipment ◽  
Passive Devices ◽  
Wide Range ◽  
Optimum Spacing ◽  
Rayleigh Numbers ◽  
Wall Spacing

Buoyancy-driven airflow that included two isothermal inner plates established in a vented cavity is investigated numerically. The thermally optimum wall-to-wall spacing of the immersed channel, as well as its dependence with respect to the relevant governing parameters, are determined. Results are presented as a function of the aspect ratio b/H for a wide range of Rayleigh numbers RaH. A logarithmic correlation for the optimum (b/H)opt as a function of RaH is presented. In addition, since the outlined configuration might be subject to intense heating conditions, the influence of considering variable thermophysical properties is also included in the analysis. In fact, an appreciable influence of the variation of properties on (b/H)opt is also detected for a representative value of RaH = 109. Obtained results can be directly applied to the optimization of electronic equipment cooling, or even to thermal passive devices in buildings.

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