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Rayleigh Number (rayleigh + number)
Selected AbstractsExperimental study on heat transfer enhancement on natural convection in a vertical plate by using longitudinal vortex generators arranged in rowsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2006JingAn Long Abstract Longitudinal vortices are capable of producing beneficial effects in heat transfer enhancement. Experiments in natural convection heat transfer enhancement were done on a vertical flat heating plate using delta-winglet longitudinal vortex generators (LVGs) arranged in rows. In an experimental range of Rayleigh number, the height and width of the winglet of the longitudinal vortex generator (LVG), the array form of the longitudinal vortex generators on the heat transfer performance were experimentally investigated, and the best height of the winglet of the longitudinal vortex generator was obtained. The results showed the change of the array form of the longitudinal vortex generators could affect the heat transfer effect. Finally by arranging some longitudinal vortex generator arrays with the appropriate interval, the whole heat transfer effect of the interval could reach a prime value. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 351,358, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20119 [source] Fluid flow and heat transfer in the transition process of natural convection over an inclined plateHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2001Katsuo Komori Abstract The present study deals with fluid flow and heat transfer in the transition process of natural convection over an inclined plate. In order to examine the mechanism of the transition process, experiments on the flow and heat transfer were performed for various plate inclination angles in the range of 20 to 75°. The wall temperature and fluid flow fields were visualized using a liquid crystal sheet and fluorescent paint, respectively. The visualization confirmed that separation of a boundary layer flow took place, and the onset point of streaks appeared over the plate wall when the modified Rayleigh number exceeded a characteristic value for each inclination angle. The local Nusselt number in the transition range was proportional to the one-third power of the local modified Rayleigh number. By introducing a nondimensional parameter, a new correlation between visualizations of the flow and temperature fields and heat transfer was proposed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 648,659, 2001 [source] Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2001Hideki Tokanai Abstract Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier,Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485,502, 2001 [source] Improvement of the basic correlating equations and transition criteria of natural convection heat transferHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2001Shi-Ming Yang Abstract In this paper, improvements in the basic physical laws of natural convection heat transfer were implemented in two major respects by incorporating recent research findings in this field. A preferred transition criterion was adopted in this paper to correlate all of the experimental data. Since transition correlations are primarily flow stability problems, the Grashof number, instead of the Rayleigh number, was found to be the preferred criterion. Furthermore, in the case of natural convection heat transfer from a horizontal cylinder, a series of experimental data in the high-Rayleigh-number regions recently became available. These data made it possible to establish new reliable correlations and also to test the validity of previous correlations. It is concluded that the previous correlation for a horizontal cylinder in high-Rayleigh-number regions was based on unreliable experimental results. The transition correlation for a horizontal cylinder occurred at much higher values of Rayleigh number than the previous recommendation. In the case of natural convection heat transfer from a vertical plate, more accurate property values for air under pressurized conditions are now available. This made it possible to replot the reliable data of Saunders. From this result and the experimental result of Warner and Arpaci, a new set of basic correlations in natural convection heat transfer for laminar, transitional, and turbulent regimes are recommended. These recommendations reflect a better understanding of the basic physical laws in the field of heat convection. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 293,300, 2001 [source] Density-dependent surface water,groundwater interaction and nutrient discharge in the Swan,Canning EstuaryHYDROLOGICAL PROCESSES, Issue 13 2001Anthony J. Smith Abstract Salinity in the Swan,Canning Estuary, Western Australia, varies seasonally from freshwater conditions in winter up to the salinity of seawater in summer. Field observations show that the resulting seasonal density contrasts between the estuary and the adjacent fresh groundwater system are sufficient to drive mixed-convection cells that give rise to circulation of river water in the aquifer. In this study, we examine the role of steady density-driven convection as a mechanism that contributes to the exchange of dissolved nutrients, particularly ammonium, between the Swan,Canning Estuary and the local groundwater system. We present results from two-dimensional (section) and three-dimensional density-coupled flow and mass transport modelling, in comparison with Glover's abrupt-interface solution for saltwater intrusion. The modelling is focused on developing an understanding of the physical processes that influence the long-term or mean convective behaviour of groundwater beneath the estuary. It is shown that the convective stability depends fundamentally on the interplay between two factors: (1) the downward destabilizing buoyancy effect of density contrasts between the estuary and aquifer; and (2) the upward stabilizing influence of regional groundwater discharge. The structure of convection cells beneath the estuary and recirculation rates of estuary water within the groundwater system are shown to be related to a flow-modified Rayleigh number that depends critically on the aquifer anisotropy and estuary meander pattern. The recirculation of estuary water by these mechanisms is responsible for transport of high concentrations of ammonium, observed in pore fluids in the estuary bed sediments, into groundwater and its eventual return to the estuary. Copyright © 2001 John Wiley & Sons, Ltd. [source] PID adaptive control of incremental and arclength continuation in nonlinear applicationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009A. M. P. Valli Abstract A proportional-integral-derivative (PID) control approach is developed, implemented and investigated numerically in conjunction with continuation techniques for nonlinear problems. The associated algorithm uses PID control to adapt parameter stepsize for branch,following strategies such as those applicable to turning point and bifurcation problems. As representative continuation strategies, incremental Newton, Euler,Newton and pseudo-arclength continuation techniques are considered. Supporting numerical experiments are conducted for finite element simulation of the ,driven cavity' Navier,Stokes benchmark over a range in Reynolds number, the classical Bratu turning point problem over a reaction parameter range, and for coupled fluid flow and heat transfer over a range in Rayleigh number. Computational performance using PID stepsize control in conjunction with inexact Newton,Krylov solution for coupled flow and heat transfer is also examined for a 3D test case. Copyright © 2009 John Wiley & Sons, Ltd. [source] Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002Mark A. Christon Abstract This paper summarizes the results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001. The primary objectives for the special session were to: (1) determine the most accurate estimate of the critical Rayleigh number above which the flow is unsteady, (2) identify the correct, i.e. best time-dependent benchmark solution for the 8: 1 differentially heated cavity at particular values of the Rayleigh and Prandtl numbers, and (3) identify those methods that can reliably provide these results. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical investigation of the first instabilities in the differentially heated 8:1 cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002F. Auteri Abstract We present a new Galerkin,Legendre spectral projection solver for the simulation of natural convection in a differentially heated cavity. The projection method is applied to the study of the first non-stationary instabilities of the flow in a 8:1 cavity. Statistics of the periodic solution are reported for a Rayleigh number of 3.4×105. Moreover, we investigate the location and properties of the first Hopf bifurcation and of the three successive bifurcations. The results confirm the previous finding in the range of Rayleigh numbers investigated that the flow instabilities originate in the boundary layer on the vertical walls. A peculiar phenomenon of symmetry breaking and symmetry restoring is observed portraying the first steps of the transition to chaos for this flow. Copyright © 2002 John Wiley & Sons, Ltd. [source] LS-DYNA and the 8:1 differentially heated cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002Mark A. Christon Abstract This paper presents results computed using LS-DYNA's new incompressible flow solver for a differentially heated cavity with an 8:1 aspect ratio at a slightly super-critical Rayleigh number. Three Galerkin-based solution methods are applied to the 8:1 thermal cavity on a sequence of four grids. The solution methods include an explicit time-integration algorithm and two second-order projection methods,one semi-implicit and the other fully implicit. A series of ad hoc modifications to the basic Galerkin finite element method are shown to result in degraded solution quality with the most serious effects introduced by row-sum lumping the mass matrix. The inferior accuracy of a lumped mass matrix relative to a consistent mass matrix is demonstrated with the explicit algorithm which fails to obtain a transient solution on the coarsest grid and exhibits a general trend to under-predict oscillation amplitudes. The best results are obtained with semi-implicit and fully implicit second-order projection methods where the fully implicit method is used in conjunction with a ,smart' time integrator. Copyright © 2002 John Wiley & Sons, Ltd. [source] A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001E. Gadoin Abstract This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier,Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] The destabilizing effect of boundary slip on Bénard convectionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2006Mark Webber Abstract We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev-tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] The long-time behaviour of the thermoconvective flow in a porous mediumMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2004M. A. Efendiev Abstract For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd. [source] Natural Convection in Heat Generating Oval Porous Enclosures: A Non-Darcian ModelTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2003Subrat Das Abstract This paper presents a series of numerical simulations dealing with the problem of natural convection flows and associated heat transfer in an enclosure filled with a fluid-saturated porous medium. The analysis is based on the finite element technique and incorporates the Brinkman-extended Darcy model for an oval enclosure. The numerical results obtained for a modified Rayleigh number, Ra, Darcy number, Da, offset, E, and eccentricity, e, are presented and discussed. The numerical predictions for a square enclosure compared well with published data. It is found that any increase in Da or Ra results in a higher fluid velocity that is responsible for shifting the core of the flow. Moreover, at higher ovality (E = 0.5), asymmetric flow is observed even at the lower range of Rayleigh number (Ra , 20), which may be attributed to the effect of curved isothermal wall. On présente dans cet article une série de simulations numériques des écoulements avec convection naturelle et du transfert de chaleur associé, dans une enceinte remplie d'un milieu poreux saturé en fluide. L'analyse repose sur la technique des éléments finis et fait appel à un modèle généralisé de Darcy-Brinkman pour une enceinte de forme ovale. Les résultats numériques obtenus pour le nombre de Rayleigh modifié, Ra, le nombre de Darcy, Da, le décentrement, E, et l'eccentricité, e, sont présentés et analysés. Les prédictions numériques pour une enceinte carrée se comparent bien aux données publiées. On trouve que toute augmentation de Da ou Ra entraîne une plus grande vitesse de fluide qui est responsable du déplacement du c,ur de l'écoulement. En outre, à une plus grande ovalité (E = 0,5), un écoulement asymétrique est observé même dans la gamme inférieure de nombre de Rayleigh (Ra" 20), ce qui peut être l'effet de la paroi isotherme courbée. [source] Fronts in reactive convection: Bounds, stability, and instabilityCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2003Peter Constantin This paper examines a simplified active combustion model in which the reaction influences the flow. We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. Nonlinear stability of planar fronts is established for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be linearly unstable with respect to long-wavelength perturbations if the Rayleigh number is sufficiently large. We also prove uniform bounds on the bulk burning rate and the Nusselt number in the KPP reaction case. © 2003 Wiley Periodicals, Inc. [source] Fluid flow and heat transfer of opposing mixed convection adjacent to downward-facing, inclined heated platesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 1 2009Kenzo Kitamura Abstract Experimental investigations were carried out for opposing mixed convective flows of air adjacent to downward-facing, inclined heated plates. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers from ReL=400 to 4600 and RaL*=1.0×107 to 5.4×108, and the inclination angles from ,=15 to 75° from horizontal. The flow fields over the plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the bottom edge of the plate, and then the separation point shifts toward upstream with increasing wall heat flux, and finally, reaches the top edge of the plates. It was found that the separations at the bottom and top edges are predicted with a non-dimensional parameter (GrL,*/ReL2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the minimum coefficients appear in the separation region. Moreover, it was revealed that forced, natural, and combined convective flows can be classified by the non-dimensional parameter (GrL,*/ReL2.5). © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Pub- lished online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20233 [source] Heat transfer of combined forced and natural convection from horizontal cylinder to airHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2007Kenzo Kitamura Abstract Experimental investigations have been carried out for combined convective flows of air induced around uniformly heated, horizontal cylinders. Three cases of aiding, opposing, and cross flows were examined. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers of Red=50 to 900 and Rad*=5×104 to 3×106. The flow fields around the cylinders were visualized with smoke. The results showed that separation points gradually shift from those of the forced convection to the top edge of the cylinder with increasing wall heat fluxes. The local heat transfer coefficients of the cylinders were also measured. Although the local coefficients show complex variations with the forced flow velocities and the wall heat fluxes, the overall coefficients become higher than those estimated from pure forced and natural convections throughout the cases of aiding, opposing, and cross flows. Moreover, it was confirmed that the overall Nusselt numbers as well as the separation points can be predicted with the non-dimensional parameter (Grd*/NudRed2). © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 474,488, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20180 [source] Experimental study on heat transfer enhancement in the vertical nature convection by using delta-winglet longitudinal vortex generatorsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2006Taowang Abstract This paper focuses on the study of heat transfer enhancement in natural vertical convection by using delta-winglet longitudinal vortex generators. In the experimental range of Rayleigh numbers, the effect of attack angle, height, and width of the winglet of longitudinal vortex generator (LVG) on heat transfer performance was experimentally investigated. The results showed that there was an optimal attack angle and that the height and width can affect the heat transfer. In terms of array performance, it was shown that initial arrays could enhance the performance of later arrays. Moreover, the effects of LVG and low rectangular fins were compared. The results showed that the effect of LVGs was greater than that of low rectangular fins. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(6): 402,409, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20126 [source] Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003Ge Lin Abstract Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright © 2003 John Wiley & Sons, Ltd. [source] Stabilized finite element formulation of buoyancy driven incompressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2002S. Aliabadi Abstract Streamline-upwind/Petrov,Galerkin finite element method is developed for buoyancy-driven incom-pressible flows with heat and mass transfer. The stabilized finite element formulations are implemented in parallel using message passing interface libraries. To measure the accuracy of the method, we solve a 2D numerical example of natural convection flows at moderate to high Rayleigh numbers. The 3D applications include the dispersion of smoke from a chimney and within a stadium. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical investigation of the first instabilities in the differentially heated 8:1 cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002F. Auteri Abstract We present a new Galerkin,Legendre spectral projection solver for the simulation of natural convection in a differentially heated cavity. The projection method is applied to the study of the first non-stationary instabilities of the flow in a 8:1 cavity. Statistics of the periodic solution are reported for a Rayleigh number of 3.4×105. Moreover, we investigate the location and properties of the first Hopf bifurcation and of the three successive bifurcations. The results confirm the previous finding in the range of Rayleigh numbers investigated that the flow instabilities originate in the boundary layer on the vertical walls. A peculiar phenomenon of symmetry breaking and symmetry restoring is observed portraying the first steps of the transition to chaos for this flow. Copyright © 2002 John Wiley & Sons, Ltd. [source] A coupled lattice BGK model for the Boussinesq equations,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2002Zhaoli Guo Abstract In this paper, a thermal lattice BGK model is developed for the Boussinesq incompressible fluids. The basic idea is to solve the velocity field and the temperature field using two independent lattice BGK equations, respectively, and then combine them into one coupled model for the whole system. The porous plate problem and the two-dimensional natural convection flow in a square cavity with Pr=0.71 and various of Rayleigh numbers are simulated using the model. The numerical results are found to be in good agreement with the analytical solutions or those of previous studies. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||