Natural Convection in a Square Enclosure with Two Horizontal Cylinders

This study investigates natural convection in a cooled square enclosure with two inner heated circular cylinders with the same diameter. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively. The immersed boundary method (IBM) to model the inner circular cylinders based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh numbers varying in the range of 10³ ≤ Ra ≤ 10⁵. The effect of the radius of inner circular cylinders in an enclosure on heat transfer and fluid flow at different Rayleigh numbers has been examined. As the Rayleigh number increases, the horizontal symmetry is broken and the asymmetry occurred from the smaller radius. As the radius decreases, the dependence of the convection on the Rayleigh number is considerable. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.     

Natural Convection in a Square Enclosure with a Square Heat Source at Different Horizontal and Diagonal Eccentricities

The present article aims to extend a previous numerical study on the natural convection process in a square enclosure with a vertical eccentric square heat source (cylinder) [1]. Here, we investigated buoyancy-induced convective flow and heat transfer for horizontal and diagonal eccentric displacement in a square cylinder. Numerical studies are performed for Rayleigh numbers in the range 10³–10⁶, using our recently developed flexible forcing IB–thermal lattice Boltzmann method scheme [1 S. M. Dash, T. S. Lee, and H. Huang Natural Convection from an Eccentric Square Cylinder Using a Novel Flexible Forcing Ib-Lbm Method, Numer. Heat Transfer, Part A: Appl., vol. 65, pp. 531–555, 2013.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Detailed analysis of isotherms, streamlines, and Nusselt number distribution as functions of Rayleigh number and eccentricity is provided in this paper.     

Numerical Simulation of Steady Mixed Convection Around Two Heated Circular Cylinders in a Square Enclosure

In this paper, a numerical study has been carried out to investigate the steady-state mixed convection around two heated horizontal cylinders in a square two-dimensional enclosure. The cylinders are located at the middle of the enclosure height and the walls of the cavity are adiabatic. Streamlines and isotherms are produced and the effects of cylinder diameter, Reynolds number, and Richardson number on the heat transfer characteristics are numerically analyzed. The average Nusselt number over the surface of cylinders and average nondimensional temperature in the enclosure are also presented. The results show that both heat transfer rates from the heated cylinders and the dimensionless fluid temperature in the enclosure increase with increasing Richardson number and cylinder diameter. However, the trend of average Nusselt number and nondimensional temperature variation is completely opposite when Reynolds number increases. In addition, by increasing the cylinders diameter and Richardson number, the left cylinder is less affected by the inlet flow than right one.     

Natural Convection in Power-Law Fluids in a Square Enclosure from Two Differentially Heated Horizontal Cylinders

Laminar natural convection has been numerically investigated from two differentially heated horizontal cylinders in a square enclosure filled with power-law fluids. Two basic configurations, namely, vertical- and diagonal-alignment of the cylinders at various locations have been considered. The coupled continuity, momentum and energy equations have been solved numerically to elucidate the effect of the Grashof number (10²–10⁴), Prandtl number (0.7–100) and power-law index (0.2–2) for a range of symmetric and asymmetric locations of the cylinders. The velocity and temperature fields are visualized in terms of streamlines, isothermal contours and plots of the local and average Nusselt number for different positions of the cylinders. The occurrence of the power-law index in the definitions of the Grashof and Prandtl numbers accentuates the interplay between the viscous, inertial and buoyancy forces thereby leading to nonlinearity in the observed trends. The presence of the dead zones coupled with the dominance of conduction under certain conditions strongly influences the overall heat transfer. All else being equal, it is possible to improve heat transfer for asymmetric positioning of the cylinders, especially at high values of the Prandtl number and Grashof number in shear-thinning fluids. A predictive correlation has been developed thereby enabling the estimation of the heat transfer coefficient in a new application in terms of the geometric and kinematic parameters.     

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10² to 10⁶, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10⁵. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number, and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.     

Inverse Natural Convection Problem with Radiation in Rectangular Enclosure

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas temperature measurements in the flow field. The inverse problem is solved through a minimization of an objective function using the conjugate gradient method with adjoint problem. The effects of functional form of bottom wall temperature profile, the number and the position of measurement points, and the measurement errors are investigated and discussed. The conjugate gradient method is found to work well in estimating the bottom wall temperature, even when natural convection with radiation phenomena is involved.     

Natural Convection from a Heated Elliptic Cylinder with a Different Axis Ratio in a Square Enclosure

A detailed study about the free convection over a heated elliptic cylinder, placed at the center of a square cavity having cooled walls, is performed. Simulations are carried out for three Rayleigh numbers (10⁴, 10⁵, and 10⁶) and two cavity aspect ratios (CR = 2.5 and 5.0) for different axis ratio (AR). The effect of AR on fluid flow and heat transfer characteristics for varying Rayleigh number and cavity aspect ratio are analyzed. The influence of AR is phenomenal at higher Ra and lower CR. At higher Ra, thermal plumes are observed above the cylinder for different ARs. Bicellular vortices are formed at low Ra by changing CR. The surface-averaged Nusselt number (Nu _avg ) increases with increasing AR and Ra. The value of Nu _avg increases with decreasing CR, and a correlation for Nu _avg in terms of AR is obtained for each CR.     

Numerical Investigation of Natural Convection in a Partitioned Rectangular Enclosure

This work presents a numerical analysis using the finite-element method of natural-convection heat transfer and flow patterns in a square partitioned enclosure with two partitions protruding centrally from the end walls of the enclosure. The enclosure has opposite isothermal walls at different temperatures. The length of the partitions is fixed and equal to one-fourth the height of the enclosure. Three partition positions and thicknesses are considered. Computation of Nusselt numbers for Rayleigh numbers in the range 10⁴–10⁶ is done. “Standard” boundary conditions are introduced as being more appropriate to simulate situations of practical engineering interest. Results clearly demonstrate that partition location and thickness have a significant effect on heat transfer.     

Natural Convection of Al2O3 Nanofluid Between Two Horizontal Cylinders Inside a Circular Enclosure

Natural convection heat transfer within horizontal annuli has many engineering applications such as heat exchangers like fire tube heaters. In this paper numerical methods were used for the computational analysis of heat transfer from the fire tube/hot tube to the gas tube/cold tube inside the water medium using alumina nanoparticles. Because of eccentricities of both hot and cold cylinders and different diameters, the geometry is asymmetric. The mathematical model is based on two-dimensional continuity, momentum, energy, and volume fraction equations, which are solved numerically. The simulation was done for different values of particle loading, 1%, 2%, and 5%, at Rayleigh numbers 10³, 10⁴, and 10⁵. The results show that nanoparticles enhance the heat transfer by increasing the volume concentrations of particles. It was observed that the maximum and minimum augmentation of the average Nusselt number are about 30% and 14% at the Ra = 10³ and Ra = 10⁵, respectively. Although the average Nusselt number rises by increasing the Rayleigh number, the ratio of heat transfer using nanofluid to that by pure fluid decreases. Using 5% volume fraction of alumina nanoparticles at Rayleigh number of 10³ increases the heat transfer to cold tube by about 23% compared to the pure water. The effect of nanolayer formation around particles was considered in a thermal conductivity model, which shows approximately 5% increase in the Nusselt number. To verify the solution results, comparisons with previously published work on the basis of special cases are performed.     

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 10⁷; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.     

Effect of Prandtl Number on Free Convection from Two Cylinders in a Square Enclosure

This study explores the effect of Prandtl number on the laminar natural convection heat transfer to Newtonian fluids in a square enclosure consisting of one hot circular cylinder and one cold circular cylinder. The walls of the square enclosure are maintained isothermal and at the same temperature as the cold cylinder and the fluid medium. The governing partial differential equations have been solved numerically over the following ranges of conditions: Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100 (or the range of Rayleigh numbers as 7 to 10⁷); and relative positioning of the cylinders, ?0.25 to 0.25. However, the ratio of the radius of the cylinder to the side of the enclosure is held fixed at 0.2. Extensive results on the streamline and isotherm contours, the local Nusselt number distribution, and the average Nusselt number are discussed to delineate the influence of Grashof and Prandtl numbers on them for a given location with respect to the horizontal center line. The surface-averaged Nusselt number shows a positive dependence on Grashof and Prandtl numbers for a fixed location of the two cylinders. The heat transfer results have been correlated as a function of the Rayleigh number and geometric parameters, thereby enabling its prediction in a new application.     

Influence of Heater Aspect Ratio on Natural Convection in a Rectangular Enclosure

Analysis of natural convection with heating source protruding from the nonheated lower surface of a rectangular enclosure has been performed using experimental apparatus of a two-dimensional particle image velocimetry system. Results obtained from the experiments are used to validate the numerical simulations. Extensive numerical simulation is carried out using in-house code based on the finite-volume method and the SIMPLE algorithm. Heat transfer and entropy generation are estimated numerically for a protruding heater of different perimeters and aspect ratios, Rayleigh number, and Prandtl number. It is found that the Rayleigh number, Prandtl number, and heater sizes have strong influence on the flow fields, thermal mixing, heat transfer characteristics, and entropy production rate in the enclosure. The analysis indicates that a high thermal mixing may not be the most favorable situation for achieving higher degree of temperature uniformity. The effect of Bejan number is discussed.     

Natural Convection Heat Transfer of a Rectangular Block within a Vertical Enclosure

A numerical solution of the natural convection heat transfer between two cold and hot isolated vertical plates is presented for different horizontal and vertical location ratios of an enclosure. Results show that: a) flow configurations of cold and hot plates are different; b) the increase of vertical location ratio, toward that corresponding to the enclosure middle value, is considerably diminishing the temperature differences between heating and cooling conditions; c) the effect of vertical location ratio variation is more prominent on heat transfer for cold and hot plates than that of the horizontal location ratio variation; d) the average Nusselt number, obtained from the hot isolated plate, is 20–39% larger than that of the cold plate under the same conditions when the isolated plate varies horizontally; e) for a narrow distance between the inner plate and the bounding wall, the inner plate Nusselt number is enhanced, but aside from this, the plate average Nusselt number is insensitive to the plate position; and f) different trends are found to affect heat transfer for cold and hot plates when the isolated plate varies vertically. The optimal vertical location can be found at specific Rayleigh number for the hot plate and cold plate.     

Numerical Investigation of Transient Magnetohydrodynamic Mixed Convection in a Ventilated Cavity Containing Two Heated Circular Cylinders

A two-dimensional finite volume computation is performed to analyze the transient magnetoconvective transport in a ventilated cavity containing two inner heated circular cylinders with identical shape. An electrically conducting fluid (Prandtl number 0.01) enters the cavity through an opening at the middle of the left wall and is taken away by a similar opening at the middle of the right wall. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. Simulations are performed for the parameters, Richardson number (0, 0.25, 0.5, and 1), Reynolds number (380–550), Hartmann number (0, 10, 20, and 50) and dimensionless gap between the cylinders 0.1, 0.2, and 0.3. The analysis indicates that the transport process is a complex function of the magnetic field strength, mixed convective strength and the cylinder distance. Some typical combinations of these controlling parameters may produce three different transport characteristics such as the steady state, periodic oscillatory, and chaotic. With a lower cylinder distance and higher mixed convective strength, the flow instability increases causing periodic and even chaotic oscillations, whereas the magnetic field due to its damping nature imparts stability to the flow resulting in a steady state flow condition.     

Natural Convection Heat Transfer of Liquid Metal Gallium Nanofluids in a Rectangular Enclosure

A new mixed nanofluid (Cu/diamond–gallium [Cu/diamond–Ga] nanofluid) is proposed, and the mass ratio of Cu nanoparticles and diamond nanoparticles in the new mixed nanofluid is 10:1. The natural convection heat transfer of Cu/diamond–Ga nanofluid, Cu–gallium (Cu–Ga) nanofluid, and liquid metal gallium with different volume fractions in a rectangular enclosure is investigated by a single‐phase model in this paper. The effects of temperature difference, nanoparticle volume fraction and the kinds of nanofluid on the natural convection heat transfer are discussed. The natural convection heat transfer of the three kinds of fluids is compared. It is found that Nusselt numbers of the Cu/diamond–Ga nanofluid along with X direction increases with the nanoparticle volume fraction and temperature difference. Cu/diamond–Ga nanofluid can enhance the heat transfer by 73.0% and 9.7% at low‐temperature difference (ΔT = 1 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively. It also can enhance the heat transfer by 85.9% and 5.2% at high‐temperature difference (ΔT = 11 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively.     

Natural Convection in a Square Cavity with Discrete Heating at the Bottom with Different Fin Shapes

Numerical study is carried out to investigate the effect of different fin shapes on heating a square cavity by small heating strip located at the bottom wall. The natural convection of air is considered with constant heat flux from heat source which is located at the center of the bottom wall. The width of the heating strip is assumed to be 20% of the total width of the bottom wall. The remaining (non-heated) part of the bottom wall and the top wall are adiabatic and the side walls are maintained at constant temperature. The investigation considered four shapes of aluminum fins with equal area and equal base width. The easy to fabricate fin shapes are considered as: rectangular, one triangular, two opposite triangular and two isosceles triangular shape. Other parameters considered are the total area of the fin (or the height of the fin) and the Grashof number in the laminar flow range. It is found that the heat transfer can be enhanced by either increasing the Grashof number or the height of the fins. In most of the investigated cases the heat transfer in the case of the two opposite triangular fins shape is found to be higher than that of the other shapes under the same conditions.     

Coupled Natural Convection and Radiation in a Horizontal Rectangular Enclosure Discretely Heated from Below

A numerical study is carried out to investigate the interaction between natural convection and thermal radiation in a horizontal enclosure filled with air and heated discretely from below. The results are presented for a cavity having an aspect ratio A _r  = L′/H′ = 10, while the Rayleigh number and the emissivity of the walls are varied in the ranges 10³ ≤ Ra ≤ 10⁶ and 0 ≤ ε ≤ 1, respectively. The results of the study, presented in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, evaluated on the cold wall, show that the problem has multiple solutions. Each of these solutions is characterized by a specific flow structure, and its appearance and range of existence depend strongly on the parameters Ra and ε. The amount of heat evacuated through the cold surface is dependent on the type of solution.     

含热源方腔的耦合自然对流换热的三维数值模拟

对具有内热源方腔的稳态层流耦合自然对流换热进行了三维的数值模拟，采用的模拟代码基于连续介质计算力学的开源库OpenFoam，解决了自然对流换热与固体传热的耦合问题。对外壁面为常温、方腔内充满含体积热源流体的自然对流计算结果表明，温度场、速度场与非耦合的工况有很大差异。     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.