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Showing papers on "Natural convection published in 2006"


Book
01 Dec 2006
TL;DR: In this paper, the authors present an overview of the basic concepts in Heat Conduction Equation (HCE) and its application in the context of refrigeration and freezing of foods.
Abstract: 1 Introduction and Basic Concepts 2 Heat Conduction Equation 3 Steady Heat Conduction 4 Transient Heat Conduction 5 Numerical Methods in Heat Conduction 6 Fundamentals of Convection 7 External Forced Convection 8 Internal Forced Convection 9 Natural Convection 10 Boiling and Condensation 11 Heat Exchangers 12 Fundamentals of Radiation 13 Radiation Heat Transfer 14 Mass Transfer Appendix 1 Property Tables and Charts (SI Units) Appendix 2 Property Tables and Charts (English Units) Appendix 3 Introduction to EES Online Chapters 15 Cooling of Electronic Equipment 16 Heating and Cooling of Buildings 17 Refrigeration and Freezing of Foods

816 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of Rayleigh number (Ra) and aspect ratio (AR) on the flow pattern and energy transport within the thermal boundary layer were investigated for various pertinent parameters.

381 citations


Journal ArticleDOI
TL;DR: In this article, the interpolation supplemented lattice Boltzmann method has been used to simulate high Rayleigh number natural convection in a square cavity and the results were shown to be in very good agreement with the benchmark results available in the literature.

381 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed.

297 citations


Journal ArticleDOI
TL;DR: In this paper, the Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium and numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers.

275 citations


Journal ArticleDOI
TL;DR: In this paper, the electrostatic repulsion mechanism was used to stabilize nanoparticles and the resulting stable nanofluids were then used for both the transient and steady-state heat transfer experiments under natural convection conditions.
Abstract: This paper reports an experimental study on the natural convective heat transfer of nanofluids, an area in which little work has been carried out in the past. Aqueous-based titanium-dioxide nanofluids of various concentrations are formulated by using the two-step method and a high shear homogenizer is used to break large aggregates. Instead of the use of dispersant and/or surfactant, the electrostatic repulsion mechanism is adopted to stabilize nanoparticles. The resulting nanofluids are found to be very stable, although the actual measured particle size is much larger than the primary nanoparticle size. The stable nanofluids are then used for both the transient and steady-state heat transfer experiments under natural convection conditions. The results show that the presence of nanoparticles systematically decreases the natural convective heat transfer coefficient under the conditions of this study, which is an observation that contrasts with the previous expectation. Discussion of the results suggests that changes in the nanofluids' thermal conductivity and viscosity could not explain the observed decrease in the heat transfer coefficient, and particle-surface interactions may play an important role.

196 citations


Journal ArticleDOI
TL;DR: In this article, a tilted heated square cylinder kept in an enclosure has been studied in the range of 10 3 ǫ⩽ Ra ⩽ 10 6, where the stream function-vorticity formulation of the Navier-Stokes equation is solved numerically using finite-difference method in non-orthogonal body-fitted coordinate system.

183 citations


Journal ArticleDOI
TL;DR: In this article, the melting behavior of paraffin wax as a phase change material (PCM) encapsulated in a cylindrical capsule, used in a latent heat thermal energy storage system with a solar water heating collector, is analyzed.

170 citations


Journal ArticleDOI
TL;DR: In this paper, the mass transfer of CO2 into a reservoir brine sample is studied experimentally at high pressures and elevated temperatures, and it is found that the density of the brine with dissolved CO2 increases linearly with CO2 concentration.
Abstract: In this paper, the mass transfer of CO2 into a reservoir brine sample is studied experimentally at high pressures and elevated temperatures. The equilibrium concentration of CO2 in the reservoir brine and the density of CO2-saturated brine are measured by saturating the brine with CO2. The mass-transfer rate of CO2 into the brine is determined by monitoring the pressure decay inside a closed, visual, high-pressure PVT cell. It is found that the density of the brine with dissolved CO2 increases linearly with CO2 concentration. As CO2 gradually dissolves into the brine by molecular diffusion, a concentration-induced density gradient is generated near the CO2−brine interface. Under the influence of gravity, this concentration-induced density gradient causes natural convection, which accelerates the mass-transfer rate of CO2 into the brine. The modified diffusion equation with an effective diffusivity is applied to model the mass-transfer process. It is found that the determined effective diffusivities of CO2...

158 citations


Journal ArticleDOI
TL;DR: In this paper, a two-dimensional thermal model is developed to establish a standard for the simulation of spirally wound cells, which properly deals with the geometric characteristics and the boundary conditions to avoid the distorted simulation results due to improper approximation of the spiral geometry.
Abstract: A two-dimensional thermal model is developed to establish a standard for the simulation of spirally wound cells. It properly deals with the geometric characteristics and the boundary conditions to avoid the distorted simulation results due to improper approximation of the spiral geometry. Furthermore, the flexible architecture makes it possible that the precision of the numerical solutions can be elevated by spending more time on calculation. According to the simulation of lithium batteries under natural convection, the hottest temperatures are in a circular region near the liquid-filled hollow core but not at the exact center. Furthermore, radiation contributes as much as 53.6% to the heat dissipation if the surface emissivity approaches unity. Adopting an air flow parallel to the cylinder axis is effective to suppress the surface temperature, but the hottest temperature inside a battery remains high if a battery has a large radius. The heat dissipation rate of an air flow perpendicular to the cylinder axis is slightly lower than that of a parallel flow, and a battery case with high thermal conductivity is suggested to maintain the temperature uniformity of a battery.

156 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the effect of the orientation and the aspect ratio of the enclosure and the strength and direction of the magnetic field on the flow and temperature fields in an inclined rectangular enclosure heated from one side and cooled from the adjacent side.

Journal ArticleDOI
TL;DR: The effect of temperature dependent viscosity on laminar mixed convection boundary layer flow and heat transfer on a continuously moving vertical surface is studied in this article, where the fluid viscosities are assumed to vary as an inverse linear function of temperature.

Journal ArticleDOI
TL;DR: The preliminary computational results support the argument that the micro-heat-convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids.

Journal ArticleDOI
TL;DR: In this article, the authors focused on the study of coupled heat and mass transfer by boundary-layer free convection over a vertical flat plate embedded in a fluid-saturated porous medium.

Journal ArticleDOI
TL;DR: This paper confirms the reliability and the computational efficiency of the lattice Boltzmann method in simulating natural convection in porous media at the representative elementary volume scale with good quantitative agreement for the whole range of Darcy and Rayleigh numbers.

Journal ArticleDOI
TL;DR: In this paper, the effects of the following operating parameters on the thermal performance of the NDWCT have been investigated: droplet diameter, inlet water temperature, number of nozzles, water flow rate and number of tracks per nozzle.

Journal ArticleDOI
TL;DR: In this article, the effects of the pertinent parameters on the local skin friction coefficient and rate of the heat transfer in terms of the local Nusselt number are discussed, and the local similarity solutions of the transformed dimensionless equations for the flow, microrotation, and heat transfer characteristics are evaluated using Nachtsheim- Swigert shooting iteration technique.
Abstract: Magnetohydrodynamic convective flow and heat transfer of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption with constant suction has been analyzed numerically. With appropriate transformations the boundary layer equations are transformed into nonlinear ordinary differential equa- tions. The local similarity solutions of the transformed dimensionless equations for the flow, microrotation, and heat transfer characteristics are evaluated using Nachtsheim- Swigert shooting iteration technique. Numerical results are presented in the form of velocity, microrotation, and temperature profiles within the boundary layer for different parameters entering into the analysis. Also the effects of the pertinent parameters on the local skin friction coefficient and rate of the heat transfer in terms of the local Nusselt number are also discussed. DOI: 10.1115/1.2136918

Journal ArticleDOI
TL;DR: In the majority of magnetohydrodynamic (MHD) natural-convection simulations, the Lorentz force due to the magnetic field is suppressed into a damping term resisting the fluid motion as discussed by the authors.
Abstract: In the majority of magnetohydrodynamic (MHD) natural-convection simulations, the Lorentz force due to the magnetic field is suppressed into a damping term resisting the fluid motion. The primary benefit of this hypothesis, commonly called the low-R m approximation, is a considerable reduction of the number of equations required to be solved. The limitations in predicting the flow and heat transfer characteristics and the related errors of this approximation are the subject of the present study. Results corresponding to numerical solutions of the full MHD equations, as the magnetic Reynolds number decreases to a value of 10−3, are compared with those of the low-R m approximation. The influence of the most important parameters of MHD natural-convection problems (such as the Grashof, Hartmann, and Prandtl numbers) are discussed according to the magnetic model used. The natural-convection heat transfer in a square enclosure heated laterally, and subject to a transverse uniform magnetic field, is chosen as a c...

Journal ArticleDOI
TL;DR: In this paper, the authors have proposed a method for the computation of natural convection flow in a square enclosure with a centered internal conducting square block both of which are given an inclination angle.

Journal ArticleDOI
TL;DR: In this article, a series of numerical models designed to compare and then couple thermally and mechanically driven fluid flow (and incorporate temperature-dependent fluid properties), starting with generic problems and then using a simulation of coupled deformation, heat transfer, and fluid flow that may be applicable to the formation of Mount Isa-style Pb-Zn ores and other extension-related basinal deposits.
Abstract: Fluid circulation within low-permeability basement rocks has been proposed to occur beneath many sediment-hosted mineral deposits, in some cases contributing substantial metals or sulfur to the deposits in overlying cover sequences. However, mechanisms proposed for fluid transport and mass transfer within and through basement rocks are diverse, some models appealing to thermal circulation but others appealing more to deformation- or topography-driven flow. We address some of these issues here by a series of numerical models designed to compare and then couple thermally and mechanically driven fluid flow (and incorporate temperature-dependent fluid properties), starting with generic problems and then using a simulation of coupled deformation, heat transfer, and fluid flow that may be applicable to the formation of Mount Isa-style Pb-Zn ores and other extension-related basinal deposits. Results from deformation-only models show that downward penetration of near-surface fluids into relatively low permeability basement rocks may occur along fault zones at high strain rates during extension, because local deformation rates may exceed the capacity for fluid to move through the basement rocks due to their low permeability, leading to periods of underpressure. For our thermal fluid-flow models, in the absence of deformation and with elevated basal heat flows, large differences in basement and cover permeability tend to restrict thermal convection to the permeable units. Downflow into low-permeability basement may occur by a reduction of the permeability of cover sequences, because larger convection cells are possible as permeability approaches common, optimal values throughout the rock mass. The normal reduction in porosity and permeability of cover sequences with burial may thus lead to progressively deepening convection cells and an enhanced potential for extraction of components from basement rocks. Long-lived, stable convection is generated with ≤2 order of magnitude permeability difference between basement and cover. Such convection has the potential to lead to near-surface mineralization (e.g., sediment-hosted syngenetic or diagenetic deposits), particularly if an initial overpressure stimulates convection cells toward upflow along basin-bounding faults. These models also serve to indicate the inadequacy of models that do not incorporate thermal dependencies of fluid viscosity and density, because the upward fluid velocity generated by buoyancy is of the same order of magnitude as the downward fluid velocity generated by extension-related underpressure in models that do not incorporate these properties. In numerical models of coupled deformation, heat transfer and fluid flow in which high basal heat flow is coupled with extensional deformation, the effects of the deformation dominate flow regimes, rather than the thermal structure. A model with initial heating and fluid flow established large convection cells with basement fluid circulation, prior to deformation being incorporated. The convection cells are effectively destroyed by extension at geologically reasonable strain rates around 10−14s−1, with surface fluids driven downward and meeting remnants of the decaying convection deep in the system. This simulation provides a possible solution for mixing of near-surface and deep fluids in unconformity-related U deposits and Olympic Dam-style iron oxide Cu-Au deposits. Geological models for shale-hosted base metal deposits (e.g., Mount Isa Zn-Pb) appeal to transitions from active rifting to blanketing by mineralized sag-phase shales, requiring reduction or cessation of extension with time. We simulate this here by stopping the deformation component of the coupled model and allowing the heating and fluid-flow parts to continue. Initial or periodic fluid overpressures (140% of hydrostatic) applied at the base of our coupled numerical models during extension (rift phase) cause initial upflow along faults and sufficient heat advection to generate steep near surface thermal gradients. When deformation ceases, convection progressively deepens with time, but upflow continues along faults, producing perfect conditions for exhalation of fluids that have circulated through basement. From all of the coupled models, we infer that active extension or extensional reactivation of basin-bounding faults is generally destructive with respect to potential fluid upflow and generation of near-surface deposits. Exhalative or other near-surface ores are likely to form when extension ceases and the thermal structure becomes the driver of fluid flow.

Journal ArticleDOI
TL;DR: In this article, the authors present experimental results on buoyancy-induced convection in aluminum metal foams of different pore densities and porosities and show that compared to a heated surface, the heat transfer coefficients in these heat sinks are five to six times higher.
Abstract: In this paper, we present our recent experimental results on buoyancy-induced convection in aluminum metal foams of different pore densities [corresponding to 5, 10, 20, and 40 pores per in. (PPI)] and porosities (0.89-0.96). The results show that compared to a heated surface, the heat transfer coefficients in these heat sinks are five to six times higher. However, when compared to commercially available heat sinks of similar dimensions, the enhancement is found to be marginal. The experimental results also show that for a given pore size, the heat transfer rate increases with porosity, suggesting the dominant role played by conduction in enhancing heat transfer. On the other hand, if the porosity is held constant, the heat transfer rate is found to be lower at higher pore densities. This can be attributed to the higher permeability with the larger pores, which allows higher entrainment of air through the porous medium. New empirical correlations are proposed for the estimation of Nusselt number in terms of Rayleigh and Darcy numbers. We also report our results on novel finned metal foam heat sinks in natural convection. Experiments were conducted on aluminum foams of 90% porosity with 5 and 20 PPI with one, two, and four aluminum fins inserted in the foam. All of these heat sinks were fabricated in-house. The results show that the finned metal foam heat sinks are superior in thermal performance compared to the normal metal foam and conventional finned heat sinks. The heat transfer increases with an increase in the number of fins. However, the relative enhancement is found to decrease with each additional fin. The indication is that there exists an optimum number of fins beyond which the enhancement in heat transfer, due to increased surface area, is offset by the retarding effect of overlapping thermal boundary layers. Similar to normal metal foams, the 5 PPI samples are found to give higher values of h compared to the 20 PPI samples due to higher permeability of the porous medium. Future work is planned to arrive at the optimal heat sink configuration for even larger enhancement in heat transfer.

Journal ArticleDOI
TL;DR: In this paper, a quasi-geostrophic approximation of the Prandtl-number dependence of rapidly rotating convection in spherical geometry outside the tangent cylinder is investigated using quasi geostrophic approximations.
Abstract: Rapidly rotating convection in spherical geometry outside the tangent cylinder is investigated using the quasi-geostrophic approximation. The validity of the approximation is discussed, and numerical simulations using these equations are performed, reaching Ekman numbers, E, down to 10 -6 . The results are compared with experiments and fully three-dimensional numerical simulations. We find that the inertial scaling developed to study rapidly rotating convection does not represent the Prandtl-number dependence of our results adequately. Instead, we find that even in strongly supercritical situations the dominant wavenumbers at the onset of convection still have a strong influence on the behaviour. We find that the local Peclet number, the product of the typical convective velocity and local convective length scale divided by the thermal diffusivity, is helpful for understanding the dynamics of rapidly rotating convection. We explore the zonal flows driven by Reynolds stresses with no-slip boundaries and explore their Prandtl-number dependence. We also study the convective heat transport at low E, and consider the boundary layer structures that can form at large Rayleigh number, slowing down the rate of growth of the Nusselt number with Rayleigh number.

Journal ArticleDOI
TL;DR: In this paper, the authors have analyzed natural convection heat transfer in a triangle enclosure with flush mounted heater on vertical wall using finite difference method in solution of governing equations in stream function-vorticity form and linear algebraic equations were solved via Successive Under Relaxation (SUR).

Journal ArticleDOI
TL;DR: The result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.
Abstract: We present an experimental study of the azimuthal motion of the mean wind in turbulent thermal convection. The experiments were conducted with cylindrical convection cells of unity aspect ratio and over the range of the Rayleigh number from $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{10}$. The azimuthal angle of the circulation plane of the mean wind was measured using both the particle image velocimetry and flow-visualization techniques. It is found that the azimuthal motion consists of erratic fluctuations and a time-periodic oscillation. The orientation of the wind is found to be ``locked,'' i.e., it fluctuates about a preferred direction most of the time with all other orientations appearing as ``transient states,'' and large excursions of the azimuthal angle often result in a net rotation which takes the wind back to the preferred orientation. The rate of erratic rotation of the circulation plane is found to have a strong dependence on Ra. Our result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.

Journal ArticleDOI
TL;DR: Clark et al. as discussed by the authors examined the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium.
Abstract: The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

Journal ArticleDOI
TL;DR: In this paper, the effect of radiation and natural convection in a saturated porous medium embedded in a vertical annular cylinder has been investigated, and the influence of aspect ratio (A) and radius ratio (R) on Nusselt number is presented.

Journal ArticleDOI
TL;DR: In this paper, a numerical investigation of steady, laminar, natural convective fluid flow in a square enclosure with an inclined heated thin fin of arbitrary length attached to the hot wall is considered.
Abstract: A numerical investigation of steady, laminar, natural convective fluid flow in a square enclosure with an inclined heated thin fin of arbitrary length attached to the hot wall is considered. A transverse temperature gradient is applied on two opposing walls of the enclosure, while the other two walls are adiabatic. Attachment of highly conductive inclined thin fins with lengths equal to 20%, 35%, and 50% of the side, positioned in the middle of the hot left wall of the enclosure, is examined. The problem is formulated in terms of the vorticity–stream function procedure. A numerical solution based on the finite-volume method is obtained. Representative results illustrating the effects of the thin-fin inclination angle and length on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers at the heated wall of the enclosure are presented and discussed for various parametric conditions. It is found that the Rayleigh number and ...

Journal ArticleDOI
TL;DR: In this article, a differentially heated, partitioned, square cavity containing heat generating fluid has been studied numerically, and two distinct regimes have been observed and studied with various geometrical parameters, depending on the ratio of the internal and external Rayleigh numbers.

Journal Article
TL;DR: In this article, the Nusselt number in turbulent thermal convection in a cylindrical container of aspect ratio 4 was measured and the data showed that the log Nu-log Ra slope saturates at a value close to 1/3, as observed previously by us in experiments with smaller aspect ratios.
Abstract: We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra=2×10 13 . Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the log Nu-log Ra slope saturates at a value close to 1/3, as observed previously by us in experiments with smaller aspect ratios. The increasing slope over the last half a decade of Ra is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and Ra that collapses data for different aspect ratios.

Journal ArticleDOI
TL;DR: In this paper, a study of natural convection, in a vertical rectangular cavity filled with a non-Newtonian fluid and subjected to uniform heat flux along the vertical side walls, is carried out numerically by solving the full governing equations.
Abstract: A study of natural convection, in a vertical rectangular cavity filled with a non-Newtonian fluid and subjected to uniform heat flux along the vertical side walls, is carried out numerically by solving the full governing equations. In the limit of a tall enclosure, these equations are considerably reduced by using the parallel flow approximation. Solutions for the flow and temperature fields, and the heat transfer rate, are obtained as functions of the governing parameters. Good agreement is found between the results of the two approaches for a wide range of governing parameters.