Lattice Boltzmann simulation of natural convection in an open ended cavity

Natural convection in an open ended cavity is simulated using Lattice Boltzmann Method (LBM). The paper is intended to address the physics of flow and heat transfer in open end cavities and close end slots. The flow is induced into the cavity by buoyancy force due to a heated vertical wall. Also, the paper demonstrated that open boundary conditions used at the opening of the cavity is reliable, where the predicted results are similar to conventional CFD method (finite volume method, FVM) predictions. Prandtl number (Pr) is fixed to 0.71 (air) while Rayleigh number (Ra) and aspect ratio (A) of the cavity are changed in the range of 10⁴–10⁶ and of 0.5–10, respectively. It is found that the rate of heat transfer deceases asymptotically as the aspect ratio increases and may reach conduction limit for large aspect ratio. The flow evaluation in the cavity starts with recirculation inside the cavity, as the time proceeds the flow inside the cavity communicates with the ambient.     

Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

Numerical simulation of natural convection in an open-ended square cavity filled with porous medium by lattice Boltzmann method

In the present work, natural convection in an open-ended square cavity packed with porous medium is simulated. The double-population approach is used to simulate hydrodynamic and thermal fields, and the Taylor series expansion and the least-squares-based lattice Boltzmann method has been implemented to extend the thermal model. The effect of a porous medium is taken into account by introducing the porosity into the equilibrium distribution function and adding a force term to the evolution equation. The Brinkman–Forchheimer equation, which includes the viscous and inertial terms, is applied to predict the heat transfer and fluid dynamics in the non-Darcy regime. The present model is validated with the previous literature. A comprehensive parametric study of natural convective flows is performed for various values of Rayleigh number and porosity. It is found that these two parameters have considerable influence on heat transfer.     

Natural convection investigation in square cavity filled with nanofluid using dispersion model

A cooling achieved with compact and efficient device is one of the major challenges encountered in the promising technique of fuel cell stacks. The safe and reliable use of such a system is highly dependent on the efficiency of the assured heat transfer and consequently on the quality of the coolant used. To test the possible improvement of the coolant performances, laminar natural convection in square cavity filled with copper-water nanofluid is numerically carried out taking into account the thermal dispersion effect on the heat transfer intensity. The finite element method is used to solve the governing equations. The hydrodynamic structure of the flow and its thermal behavior are studied for a wide range of Rayleigh numbers. The obtained results showed an enhancement of heat transfer with an increase in nanoparticle volume fraction for all examined Rayleigh numbers. However, it is found that an increase in nanoparticle diameter enhances heat transfer only when thermal dispersion is significant. Correlation with 99.94% confidence coefficient is proposed to quantify the heat transfer intensity according to the Rayleigh number and particle diameter and concentration.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Numerical modeling of natural convection in partially open square cavities under electric field

Numerical modeling of the electric field effect on natural convection in the partially open square cavities is investigated. The interactions between electric, flow, and temperature fields are analyzed by using a computational fluid dynamics technique. The results indicate that the flow and heat transfer enhancements are the decreasing function of Rayleigh number. Moreover, the volume flow rate and heat transfer coefficient are substantially improved by the electric field effect, especially at the low aperture size and high aperture position. The effect of number of electrodes and inclined angle to the flow and heat transfer enhancements are also achieved.     

Natural convection of water-CuO nanofluid in a cavity with two pairs of heat source-sink

Natural convection in a two-dimensional square cavity filled with a water-CuO nanofluid is numerically studied. Two pairs of heat source-sink are considered to cover the entire length of the bottom wall of the cavity while the other walls are thermally insulated. The nanofluid is assumed to be homogenous and Newtonian. The governing differential equations are discretised by the control volume approach and the coupling between velocity and pressure is solved using the SIMPLE algorithm. A comparison study is presented between two cases with different arrangements of the two pairs on the bottom wall. The effects of Rayleigh number and solid volume fraction of the nanofluid on the heat transfer rate have also been examined. The results show that regardless of the position of the pairs of source-sink, the heat transfer rate increases with an increase of the Rayleigh number and the solid volume fraction.     

Numerical study of mixed convection on jet impingement cooling in an open cavity filled with porous medium

The present study numerically investigates the opposing mixed convection arises from jet impingement cooling of a heated bottom surface of an open cavity in a horizontal channel filled with porous medium. The FeCrAlY foam is considered in the present study with a porosity of 0.867. The heat transfer characteristics are investigated with governing parameters in the range of Rayleigh number (50 ≤ Ra ≤ 150), Péclet number (1 ≤ Pe ≤ 1000) and dimensionless cavity depth (0 ≤ H ≤ 0.4). The results show that, the average Nusselt numbers decreases with the increase in dimensionless cavity depth. The opposing mixed convection is demonstrated to cause deterioration in average Nusselt number for fluid at certain Peclet number. The average Nusselt number for fluid is found to increase with the increase in Rayleigh number but the effect of Rayleigh number become insignificant at high Peclet number (Pe > 500).     

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Conjugate natural convection heat transfer in an inclined square cavity containing a conducting block

The present work is concerned with computation of natural convection flow in a square enclosure with a centered internal conducting square block both of which are given an inclination angle. Finite volume method through the concepts of staggered grid and SIMPLE algorithm have been applied. Deferred QUICK scheme has been used to discretize the convective fluxes and central difference for diffusive fluxes. The problem of conjugate natural convection has been taken up for validating the code. The abrupt variation in the properties at the solid/fluid interface are taken care of with the harmonic mean formulation. Solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been performed for Ra = 10³–10⁶, angle of inclination varying from 15° to 90° in steps of 15° and ratio of solid to fluid thermal conductivities of 0.2 and 5.0. Results are presented in terms of streamlines, isotherms, local and average Nusselt number.     

Natural convection in metal foams with open cells

This paper presents a combined experimental and numerical study on natural convection in open-celled metal foams. The effective thermal conductivities of steel alloy (FeCrAlY) samples with different relative densities and cell sizes are measured with the guarded-hot-plate method. To examine the natural convection effect, the measurements are conducted under both vacuum and ambient conditions for a range of temperatures. The experimental results show that natural convection is very significant, accounting for up to 50% of the effective foam conductivity obtained at ambient pressure. This has been attributed to the high porosity (ε > 0.9) and inter-connected open cells of the metal foams studied.Morphological parameters characterizing open-celled FeCrAlY foams are subsequently identified and their cross-relationships are built. The non-equilibrium two-equation energy transfer model is employed, and selected calculations show that the non-equilibrium effect between the solid foam skeleton and air is significant. The study indicates that the combined parameter, i.e., the porous medium Rayleigh number, is no longer appropriate to correlate natural convection by itself when the Darcy number is sufficiently large as in the case of natural convection in open-celled metal foams. Good agreement between model predictions and experimental measurements is obtained.     

Free convection in a square cavity filled with a bidisperse porous medium

The classical problem of steady Darcy free convection in a square cavity filled with a porous medium has been extended to the case of a bidisperse porous medium (BDPM) by following the recent model proposed by Nield and Kuznetsov [D.A. Nield, A.V. Kuznetsov, Natural convection about a vertical plate embedded in a bidisperse porous medium, Int. J. Heat Mass Transfer 51 (2008) 1658–1664] and Rees et al. [D.A.S. Rees, D.A. Nield, A.V. Kuznetsov, Vertical free convective boundary-layer flow in a bidisperse porous medium, ASME J. Heat Transfer 130 (2008) 1–9]. The transformed partial differential equations in terms of the dimensionless stream function and temperature are solved numerically using a finite-difference method for some values of the governing parameters when the Rayleigh number Ra is equal to 10² and 10³. Results are presented for the flow field with streamlines, temperature field by isotherms and heat transfer by local and mean Nusselt numbers are presented for both the f- and p-phases. It is found that the most important parameters that influence the fluid flow and heat transfer are the inter-phase heat transfer parameter H and the modified thermal conductivity ratio parameter γ.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Analysis of mixed convection in an inclined square cavity using nanofluids with Vajjha and Das' nanofluid model

In this article, the effects of angle of inclination on heat transfer by mixed convection have been analyzed numerically in a square cavity packed with a CuO nanofluid. Cavity boundaries are constructed by having sinusoidal varying temperature on sidewalls, inactive horizontal walls, and the hot passing plate at the center of the cavity. The transport equations for fluid and heat are solved using the finite-volume method with SIMPLE algorithm. The Richardson number (Ri) varying from 0.01 to 100, inclination angle (γ) from 0° to 90°, wall speed ratios (λ) from 0 to 3 and volume fraction of nanoparticles (φ) from 0.0 to 0.1 are given and represented in the form of flow fields, temperature fields, and mean heat transfer graphs. It is detected that the principal flow constraints have a substantial impact on the flow lines and thermal lines. Specifically, the structures of cavity inclination, existence of copper nanoparticles, and the hot wall in motion at the midpoint of the cavity are established to enrich the overall rate of heat transfer. Correspondingly, in the present study, the Vajjha and Das model is taken into account for the effective thermal conductivity and viscosity of the nanofluid; application of this model is beneficial for the industries working in a high-temperature environment.     

Magneto hydrodynamic buoyant convection of an electrically conducting fluid in a tilted square cavity

A numerical investigation of steady‐natural convection of an electrically conducting fluid, enclosed in a tilted square cavity, subjected to a uniform magnetic field applied perpendicular to the plane of cavity is presented. A comprehensive understanding of the effects of controlling parameters on the flow and heat transfer is delineated for a wide range of parameters. Correlations for the average Nusselt number are presented specifically for fluids with low Prandtl numbers pertaining to liquid metals. It is made known that when the applied magnetic field is perpendicular to the plane of the cavity, the magneto hydrodynamic drag is greatest as compared to any other direction of the applied magnetic field and consequently the suppression of convection is also at its maximum, irrespective of all other controlling parameters. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20326     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。