Showing papers on "Natural convection published in 1990"
TL;DR: In this article, a finite volume multigrid procedure for the prediction of laminar natural convection flows is presented, enabling efficient and accurate calculations on very fine grids, which is fully conservative and uses second-order central differencing for convection and diffusion fluxes.
Abstract: A finite volume multigrid procedure for the prediction of laminar natural convection flows is presented, enabling efficient and accurate calculations on very fine grids. The method is fully conservative and uses second-order central differencing for convection and diffusion fluxes. The calculations start on a coarse (typically 10 × 10 control volumes) grid and proceed to finer grids until the desired accuracy or maximum affordable storage is reached. The computing times increase thereby linearly with the number of control volumes.
Solutions are presented for the flow in a closed cavity with side walls at different temperatures and insulated top and bottom walls. Rayleigh numbers of 104, 105 and 106 are considered. Grids as fine as 640 × 640 control volumes are used and the results are believed to be accurate to within 0–01%. Second-order monotonic convergence to grid-independent values is observed for all predicted quantities.
445 citations
TL;DR: In this paper, the free convection boundary layer flow with simultaneous heat and mass transfer in a porous medium is studied when the boundary wall moves in its own plane with suction, and asymptotic approximate solutions are obtained for the flow variables for various values of the activation energy.
Abstract: The free convection boundary layer flow with simultaneous heat and mass transfer in a porous medium is studied when the boundary wall moves in its own plane with suction. The study also incorporates chemical reaction for the very simple model of a binary reaction with Arrhenius activation energy. For large suction, asymptotic approximate solutions are obtained for the flow variables for various values of the activation energy.
262 citations
TL;DR: In this paper, the effect of a centered, square, heat-conducting body on natural convection in a vertical square enclosure was examined numerically and the analysis revealed that the fluid flow and heat transfer processes are governed by the Rayleigh and Prandtl numbers, the dimensionless body size, and the ratio of the thermal conductivity of the body to that of the fluid.
Abstract: The effect of a centered, square, heat-conducting body on natural convection in a vertical square enclosure was examined numerically. The analysis reveals that the fluid flow and heat transfer processes are governed by the Rayleigh and Prandtl numbers, the dimensionless body size, and the ratio of the thermal conductivity of the body to that of the fluid. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of streamlines, isotherms, and the overall heat transfer across the enclosure as described by the Nusselt number. Heat transfer across the enclosure, in comparison to that in the absence of a body, may be enhanced (reduced) by a body with a thermal conductivity ratio less (greater) than unity. Furthermore, the heat transfer may attain a minimum as the body size is increased. These and other findings are justified through a careful examination of the local heat and fluid flow phenomena.
226 citations
TL;DR: In this paper, a comparison of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid is presented.
Abstract: Comparisons of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid are presented. The good comparisons indicate that the simulation is capturing the important features of the flow. Several features are identified and discussed in detail; in particular, the presence of travelling wave instabilities on the vertical-wall boundary layers and horizontal intrusions, the existence of a rapid flow divergence in the region of the outflow of the intrusions, and the presence of cavity-scale oscillations, caused by the interaction of the intrusions with the opposing vertical boundary layer. The utilization of both numerical and experimental investigations has allowed a more complete exploitation of the available resources than would have been possible had each been conducted separately.
174 citations
TL;DR: In this article, a new temperature-based fixed-grid formulation is proposed, and the reason that the original equivalent heat capacity model is subject to such restrictions on the time step, mesh size and the phase-change temperature range is discussed.
Abstract: Fixed grid solutions for phase-change problems remove the need to satisfy conditions at the phase-change front and can be easily extended to multidimensional problems. The two most important and widely used methods are enthalpy methods and temperature-based equivalent heat capacity methods. Both methods in this group have advantages and disadvantages. Enthalpy methods (Shamsundar and Sparrow, 1975; Voller and Prakash, 1987; Cao et al., 1989) are flexible and can handle phase-change problems occurring both at a single temperature and over a temperature range. The drawback of this method is that although the predicted temperature distributions and melting fronts are reasonable, the predicted time history of the temperature at a typical grid point may have some oscillations. The temperature-based fixed grid methods (Morgan, 1981; Hsiao and Chung, 1984) have no such time history problems and are more convenient with conjugate problems involving an adjacent wall, but have to deal with the severe nonlinearity of the governing equations when the phase-change temperature range is small. In this paper, a new temperature-based fixed-grid formulation is proposed, and the reason that the original equivalent heat capacity model is subject to such restrictions on the time step, mesh size, and the phase-change temperature range will alsomore » be discussed.« less
167 citations
TL;DR: In this article, the effects of operating conditions, reactor geometry, and heat transfer characteristics on flow patterns and growth rate uniformity in vertical, axisymmetric reactors for metalorganic vapor phase epitaxy (MOVPE) are described.
149 citations
TL;DR: The behavior of power spectra in a Rayleigh-Berard convection experiment in a helium-gas cell is reported.
Abstract: The behavior of power spectra in a Rayleigh-Berard convection experiment in a helium-gas cell is reported
148 citations
TL;DR: In this article, a two-dimensional direct numerical simulation of the natural convection flow of air in a differentially heated square cavity was performed for a Rayleigh number of 10 10, and the simulation was commenced from isothermal and quiescent conditions and was allowed to proceed to a statistical steady state.
Abstract: A two-dimensional direct numerical simulation of the natural convection flow of air in a differentially heated square cavity was performed for a Rayleigh number of 10 10 . The simulation was commenced from isothermal and quiescent conditions and was allowed to proceed to a statistical steady state. Two-dimensional turbulence resulted without the introduction of random forcing. Good agreement of mean quantities of the statistically steady flow is obtained with available experimental results. In addition, the previously proposed (George & Capp 1979) − $\frac{1}{3}$ and $+\frac{1}{3}$ temperature and velocity variations in the buoyant sublayer are confirmed. Other statistics of the flow are consistent with available experimental data. Selected frames from a movie generated from the computational results show very clearly turbulence production via the sequence from initial instability, proceeding through transition, and eventually reaching statistical steady state. Prominent large-scale structures are seen to persist at steady state.
128 citations
TL;DR: In this paper, three fundamental combinations of thermal boundary conditions on the respective wall surface (i.e., isoflux-isoflux, isoftluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern.
Abstract: The present analysis is concerned with flow reversal phenomena and heat transfer characteristics of the fully developed laminar combined free and forced convection in the heated vertical channels. Three fundamental combinations of thermal boundary conditions on the respective wall surface (namely isoflux-isoflux, isofluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern. Results of the velocity distribution and temperature distribution as well as the Nusselt number in terms of bulk mean temperature are carried out. Based on the analytical solutions obtained, flow reversal adjacent to the relatively colder wall is found to exist within the channel as Re/Gr is below than a threshold value, which is related to the thermal boundary conditions. Parameter zones for the occurrence of reversed flow are presented. Comparisons and verification are made using the existing numerical solutions at locations far downstream of developing flow.
124 citations
TL;DR: In this paper, an axisymmetric case was solved and plots of temperature, velocity and streamlines were provided for natural convection heating and isotherms compared with pure conduction contour plots.
Abstract: Sterilization of a thick viscous liquid food in a metal can sitting in an upright position and heated from the side wall (Tw= 394 K) only in a still retort was simulated. The liquid had temperature dependent viscosity but constant specific heat and thermal conductivity. Equations of mass, motion and energy conservation for an axisymmetric case were solved and plots of temperature, velocity and streamlines were provided for natural convection heating and isotherms compared with pure conduction contour plots. Results indicated that the natural convection moved the slowest heating point to the bottom center. The bottom of the can heated up slower than predicted by pure conduction heating. The magnitude of the axial velocity was found to be of the order of 10−5 m/sec which varied with time and position in the can.
108 citations
TL;DR: In this paper, the authors describe the combined heat and mass-transfer natural convection mechanisms, which are considered an important subfield in contemporary heat andmass transfer research, and consider the phenomena of convection through fluid-saturated porous media generally in terms of volume-averaged quantities.
Abstract: Publisher Summary The chapter describes the combined heat and mass-transfer natural convection mechanisms, which are considered an important subfield in contemporary heat and mass-transfer research. This subfield essentially brings together the studies concerned with the combined heat and mass-transfer or double-diffusive processes that are driven by buoyancy through porous media saturated with fluid. The density gradients that provide the driving buoyancy effect are induced by the combined effects of temperature and species concentration nonuniformities present in the porous medium. The chapter considers the phenomena of convection through fluid-saturated porous media generally in terms of volume-averaged quantities. There are four conservation principles considered in the study of convection with more than one buoyancy effect. These include conservation of mass, energy, species, and momentum. Heat and mass transfer in the vertical direction and in horizontal direction are discussed in detail. Another category of studies of combined buoyancy effects in porous media deals with the local fields around buried sources of heat and mass. The recent work in this field focuses on the multilayer structure of flows of the boundary-layer or concentrated-source type.
TL;DR: In this article, the authors used an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc).
Abstract: A review of the literature on natural convection in a horizontal layer heated from below shows the need for reliable data at high Rayleigh number (Ra) to determine the asymptotic Nusselt number (Nu) variation with Rayleigh number. The present study expands the data base by the use of an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc). The results of the present study give Sh = 0.0659 for Sc ≈ 2750, 3 × 109 < Ra < 5 × 1012. Using the heat-mass transfer analogy, this indicates the high Prandtl number variation of Nu with Ra.
TL;DR: In this paper, a general formulation to treat mixed boundary conditions using the spline approximation has been presented, where numerical solutions have been obtained by solving the Navier-Stokes and energy equations.
Abstract: The present work is devoted to the numerical study of laminar natural convection flow from a heated horizontal cylinder under diverse surface boundary conditions using the spline fractional step method. A general formulation to treat mixed boundary conditions using the spline approximation has been presented. Numerical solutions have been obtained by solving the Navier-Stokes and energy equations. The results for the isothermal boundary condition as well as for the uniform heat flux are in good agreement with published experimental data and with other solutions presently available in the literature. Some new computations at very high Rayleigh numbers indicate the existence of attached separation vortices in the downstream plume region, the appearance of these vortices being dependent on the values of the Biot number. All results were computed on a personal computer using unequally spaced grids that provided good results with a minimum number of computational points. The numerical scheme presented here app...
TL;DR: In this paper, the interaction of free convection with thermal radiation of the oscillatory flow past a vertical plate is studied and the Rosseland approximation is used to describe the radiative heat flux in the energy equation.
Abstract: The interaction of free convection with thermal radiation of the oscillatory flow past a vertical plate is studied. The Rosseland approximation is used to describe the radiative heat flux in the energy equation.
TL;DR: In this article, the error in finite element methods in approximating, so-called, free or natural convection problems was analyzed under a uniqueness condition on the Rayleigh and Prandtl numbers.
Abstract: We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (u p T), which we also establish.
TL;DR: In this paper, the critical heat flux (CHF) of subcooled flow boiling is analyzed based on the liquid sublayer dryout mechanism, assuming that it is a similar phenomenon to CHF in pool boiling except for apparent differences between forced and natural convection.
TL;DR: In this paper, the authors derived critical Rayleigh numbers for the onset of convection and examined the steady flow patterns at moderately supercritical Rayleigh number for horizontal rectangular channels filled by isotropic and anisotropic porous media.
Abstract: This paper is an analytical study on natural two-dimensional convection in horizontal rectangular channels filled by isotropic and anisotropic porous media. The channel walls, assumed to be impermeable and perfectly heat conducting, are nonuniformly heated to establish a linear temperature distribution in the vertical direction. The authors derive the critical Rayleigh numbers for the onset of convection and examine the steady flow patterns at moderately supercritical Rayleigh numbers. The stability properties of these flow patterns are examined against two-dimensional perturbations using a weakly nonlinear theory.
01 Jan 1990
TL;DR: In this paper, the authors derived critical Rayleigh numbers for the onset of convection and examined the steady flow patterns at moderately supercritical Rayleigh number for horizontal rectangular channels filled by isotropic and anisotropic porous media.
Abstract: This paper is an analytical study on natural two-dimensional convection in horizontal rectangular channels filled by isotropic and anisotropic porous media. The channel walls, assumed to be impermeable and perfectly heat conducting, are nonuniformly heated to establish a linear temperature distribution in the vertical direction. The authors derive the critical Rayleigh numbers for the onset of convection and examine the steady flow patterns at moderately supercritical Rayleigh numbers. The stability properties of these flow patterns are examined against two-dimensional perturbations using a weakly nonlinear theory.
TL;DR: In this article, a high-purity copper sphere was plunged into cooling baths without boiling and the sphere was instrumented with several interior thermocouples for measuring the transient temperature response during quenching.
Abstract: Methodological and experimental aspects of the estimation of transient heat transfer coefficients in quenching experiments, using inverse heat transfer methods, were addressed and investigated. Beck's method was used for the estimation of the transient heat transfer coefficient history from interior transient temperature measurements during quenching. Experiments involved plunging a high-purity copper sphere into cooling baths without boiling. The sphere was instrumented with several interior thermocouples for measuring the transient temperature response during quenching. Water and ethylene glycol were investigated. The early transient values of the heat transfer coefficient history were found to be about 100-120% higher than the values predicted using well-known empirical correlations for free convection. The later time values were in good agreement with those predicted with empirical correlations. The transient inverse technique has the capability of estimating early transients and subsequent quasi-steady-state values of heat transfer coefficient in a single transient experiment.
TL;DR: In this paper, a simulation of two-dimensional high Rayleigh (Ra) number, base-heated thermal convection in large aspect ratio boxes is presented for infinite Prandtl number fluids, as applied to the Earth's mantle.
Abstract: Direct numerical simulations of two‐dimensional high Rayleigh (Ra) number, base‐heated thermal convection in large aspect‐ratio boxes are presented for infinite Prandtl number fluids, as applied to the Earth’s mantle. A transition is characterized in the flow structures in the neighborhood of Ra between 107 and 108. These high Ra flows consist of large‐scale cells with strong intermittent, boundary‐layer instabilities. For Ra exceeding 107 it is found that the heat‐transfer mechanism changes from one characterized by mushroom‐like plumes to one consisting of disconnected ascending instabilities, which do not carry with them all the thermal anomaly from the bottom boundary layer. Plume–plume collisions become much more prominent in high Ra situations and have a tendency of generating a pulse‐like behavior in the fixed plume. This type of instability represents a distinct mode of heat transfer in the hard turbulent regime. Predictions of this model can be used to address certain issues concerning the mode of time‐dependent convection in the Earth’s mantle.
TL;DR: In this paper, a numerical analysis is carried out to investigate the effects of latent heat transfer, in association with the evaporation of a finite liquid film on the channel wall, on the natural convection heat and mass transfer.
TL;DR: In this paper, the authors investigated two-dimensional natural convection in a vertical differentially heated air-filled cavity and found several branches of solutions characterized by different numbers of cells in the flow structure.
Abstract: Two-dimensional natural convection in a vertical differentially heated air-filled cavity is investigated numerically from the onset of the multicellular flow structure to the return of the unicellular pattern. Several branches of solutions characterized by different numbers of cells in the flow structure are found. The return to the unicellular flow structure occurs through a gradual decrease in the number of cells and each change in the number of cells is characterized by hysteresis. Also, unsteady solutions are found.
TL;DR: In this article, the authors investigated the structure of laminar wakes and heat transfer in the presence of thermal buoyancy art in a two-dimensional horizontal channel with a built-in square cylinder and showed that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone.
Abstract: Structures of laminar wakes and heat transfer in the presence of thermal buoyancy art investigated from the numerical solution of complete Navier-Stokes and energy equations in a two-dimensional horizontal channel with a built-in square cylinder. Results show that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone. For a given Reynolds number, the heating of the fluid in the channel is improved by mixed convection up to a certain Grashof number and deteriorates if the Grashof number is further increased.
TL;DR: In this article, a finite difference method is proposed to remove the need for staggered grids in fluid dynamic computations, which can be applied to free convection in a square cavity, one-dimensional flow through an actuator disk and plane stagnation flow.
Abstract: A new finite difference method, which removes the need for staggered grids in fluid dynamic computations, is presented. Pressure checkerboarding is prevented through a differencing scheme that incorporates the influence of pressure on velocity gradients. The method is implemented in a SIMPLE-type algorithm, and applied to three test problems: one-dimensional flow through an actuator disk, plane stagnation flow, and free convection in a square cavity. Good agreement is obtained between the numerical solutions and the corresponding analytical or benchmark solutions
TL;DR: In this paper, critical Rayleigh numbers for both linear instability and nonlinear energy stability were found for convection in a fluid saturated porous layer, and numerical findings indicate that for the heat sources and gravity fields chosen, the growth rate of linear theory is real at criticality.
TL;DR: In this article, heat transfer enhancement in mixed convection flow between parallel plates heated uniformly from below is investigated, and the onset of secondary flow is found to precede appreciable heat transfer enhancements.
TL;DR: In this paper, a set of condensation models for forced and natural convection in the presence of a non-condensable gas was proposed, and the effects of a wavy interface are implemented in this model by using correlations for a rough wall surface.
TL;DR: In this article, the effect of wall conduction on laminar free convection between asymmetrically heated vertical plates was investigated. But the authors used an implicit finite difference scheme to solve the governing equations.