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.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Natural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle Mounted on Its Upper Inclined Surface

A numerical investigation examined the effects on heat transfer of mounting baffles to the upper inclined surfaces of trapezoidal cavities. Two thermal boundary conditions are considered. In the first, the left, short vertical wall is heated while the right, long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right, long vertical wall is heated while the left, short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). For each boundary condition, computations are performed for three baffle heights, two baffle locations, four Rayleigh number values, and three Prandtl number values. Results are displayed in terms of streamlines, isotherms, and local and average Nusselt number values. For both boundary conditions, predictions reveal a decrease in heat transfer in the presence of baffles, with its rate generally increasing with increasing baffle height and Prandtl number. For a given baffle height, a higher decrease in heat transfer is generally obtained with baffles located close to the short vertical wall. Average Nusselt number correlations for both boundary conditions are presented.     

Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

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。     

Numerical Study of Laminar Natural Convection in a Side-Heated Trapezoidal Cavity at Various Inclined Heated Sidewalls

Steady natural convection of air flow in a two-dimensional side-heated trapezoidal room was investigated numerically using a non-orthogonal, collocated finite-volume grid system. The considered geometry has an inclined left heated sidewall, a vertical right cooled sidewall, and two insulated horizontal upper and lower walls. Computations are performed for seven values of the heated sloping wall angle, three different values of aspect ratio, and five Rayleigh number values. Results are displayed in terms of streamlines, isotherms, and both local and average Nusselt number values. The principal result of this work is the great dependence of the flow fields and the heat transfer on the inclination angle, the aspect ratio, and the Rayleigh number. A correlation between the average Nusselt number, Rayleigh number, heated sloping wall angle, and aspect ratio is proposed.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.     

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.     

Numerical Investigation on Natural Convection Inside the Side Ventilated Square Enclosure with Vertical Mid-Partition

A finite volume-based computational study of steady laminar natural convection inside the square enclosure with cold partition wall centrally placed on top and bottom is presented. The fluid considered is air with Prandtl number 0.71. Except the partition walls, all other walls were assumed as hot. The heights of inlet and outlet ports are constantly fixed as 20% of height of the enclosure. The height of the opening in the partition walls were 10%, 20%, and 30% of height of enclosure. The buoyancy-driven heat transfer mechanism inside the domain is influenced by the percentage of opening in the partition, Rayleigh number, and geometrical position of inlet and outlet. The cold partition walls attract the flow that subsequently influences the thermal modifications around the partition. The fluid flow and heat transfer were investigated for 81 cases with different positions of inlet and outlet and varying height of openings for Ra = 10³, 10⁴, and 10⁵. The cross flow between the vertical walls through the opening in the central partition wall was considered in this study. The formation of vortices and their sizes depends on the configuration of inlet and outlet ports. The higher temperature gradient occurs near the inlet and outlet port of vertical walls. Local Nusselt number is maximum just below the inlet for all cases. Due to the dominance of buoyancy forces, heat transfer rate increases when Rayleigh number increases for all the cases. The hydrodynamic block effect by the openings on the partition wall has significant effect on the velocity profile than on the heat transfer.     

Numerical Simulation of Natural Convection and Radiation Heat Transfer in Two-Dimensional Enclosure on Hybrid Grids

Natural convection and radiation heat transfer interaction commonly exists in engineering problems, and a numerical method for combined natural convection and radiation heat transfer is very important in practical engineering applications. In this article, the finite-volume method (FVM) for radiation is formulated and implemented in the fluid flow solver GTEA on hybrid grids. For comparison and validation, three test cases, an equilateral triangular enclosure and a square enclosure with/without baffles, are chosen. Then, natural convections in a cavity with/without baffles are simulated with the present FVM to take into account the radiation heat transfer effects. All the results obtained by the presented FVM agree very well with the exact solutions as well as results obtained by the zone method. Natural convection under low gravity is researched with Gr = 0.7 and 700, and the radiation effects on the temperature distribution are also studied with variation conduction-radiation numbers, Nr = 0.06, 0.1, and 0.15. It is found that the solutions are sensitive to the conduction-radiation number but do not change very much with the Grashof number.     

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 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.     

Natural Convection in an Enclosure with a Partially Active Magnetic Field

Chaotic natural convection flow of a molten gallium in a square enclosure with the upper and lower surfaces being insulated was studied by two-dimensional numerical simulation. Constant temperatures are imposed along the left and right walls of the enclosure with a volumetrically heated enclosure. In addition, a nonuniform partially active magnetic field is applied in a vertical direction. The flux lines spread out into a fringing field so the effective cross-sectional area of the gap is larger than that of the pole face. A chaotic regime is considered under steady state boundary condition. This study was done for an internal Rayleigh number of 10⁷, external Rayleigh number of 10⁵, and Prandtl number of 0.024. The study covers various magnet pole effect widths of 1/4, 1/2, and 3/4 from enclosure width and the magnetic field strength ranges 0.0 ≤ B _o  ≤ 10 Tesla. The transport equations for continuity, momentum, and energy are solved. The numerical results are reported for the effect of the partially active magnetic field on the velocity vectors, counters of temperature, streamline, and heat transfer coefficient. The numerical study shows that a magnetic field is damping chaotic oscillation behavior and decreases the amplitude of oscillation. Also, at a certain magnetic field strength the chaotic flow tend to becomes periodic flow at certain amplitude and frequency, and at high magnetic field strength the flow in the square enclosure flow tends to become steady laminar flow with stable average Nusselt number values; so, the random oscillation behavior disappeared. The effect of a nonuniform magnetic field tends to push the fluid to flow away from magnetic field region.     

The Influence of Baffles on the Natural Convection in Trapezoidal Cavities

This article presents an investigation into natural convection in trapezoidal cavities. It examines a cavity whose floor and upper inclined walls are both adiabatic, while the vertical walls are isothermal. For these isothermal walls, we consider two thermal boundary conditions. Under the first condition, the short wall on the left side is heated as the tall one on the right side is cooled. The second condition is the reverse of the first—the short wall is cooled as the tall one is heated. Considering laminar conditions and a two-dimensional system, steady-state computations are carried out to assess the effects of one and two baffles, the baffle's height (H _b ), Rayleigh number, 10³ ≤ Ra ≤ 10⁶, and three Prandtl number values. To demonstrate the various effects, the results from several designed case studies are shown in terms of isotherms, streamlines, and local and average Nusselt numbers in order. Predictions reveal that the second baffle decreases the cavity's fluid flow and heat transfer. As the height of the baffle rises, the heat transfer drops drastically. Also, two baffles produce more pronounced thermal stratification than only one.     

Patterns of Natural Convection in an Irregular Arc-Shaped Enclosure

Abstract

The current article deals with laminar natural convection in an irregular arc-shaped enclosure with a heated base and cooled upper top. The domain is filled with a liquid with Prandtl number of 4.0. This two-dimensional study focuses attention to understand changes in flow and temperature field development due to variation in aspect ratio from 0.1 to 0.4 for each case of Grashof number varies from 10⁴ to 10⁷. The paper also addresses the effect of orientation by placing the enclosure at an inclined position with angles of 45° and 90°. The flow behavior and thermal characteristics have been investigated through streamlines and isotherms, respectively. Complete domain has been chosen for analysis. Asymmetric solutions are also observed for some of the cases. These results are confirmed by the development of the corresponding convection loops and also by the variation of local Nusselt number. Finally, the paper summarizes the effects of different parameters on the rate of heat transfer.     

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.     

Numerical Investigation of Natural Convection in an Enclosure Filled with Porous Medium Under Magnetic Field

In this study, natural convection in an enclosure filled with a fluid-saturated porous medium in a strong magnetic field is investigated numerically. Two physical models are considered. One is heated from the bottom and cooled from the top (Model A), and the other is heated from the left side vertical wall and cooled from the opposite wall (Model B). An electric coil is set below this enclosure to generate a magnetic field. The Brinkman-Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for the fluid and solid are solved with the local thermal nonequilibrium (LTNE) model. The linkage between velocity and pressure is handled with the SIMPLE algorithm. Computations are performed for a range of Darcy number from 10^?5 to 10^?1, Rayleigh number from 10³ to 10⁵, and magnetic force parameter γ from 0 to 100. The results show that the magnetic force has significant effect on the flow field and heat transfer in the fluid-saturated porous medium.     

Heatlines for Visualization of Heat Transport for Natural Convection within Porous Trapezoidal Enclosures with Various Wall Heating

A detailed study on natural convection heat transfer within porous trapezoidal enclosures has been carried out for two different cases. The effect of linearly heated side walls on flow pattern is investigated in case 1; whereas, the effect of linearly heated left wall and cold right wall is studied in case 2. In both cases, the bottom wall of the cavity is uniformly heated and the upper wall is adiabatic. The results are analyzed for a wide range of parameters such as Rayleigh number, Ra(10³ ≤ Ra ≤ 10⁶), Prandtl number, Pr(0.015 ≤Pr ≤ 988.24), and Darcy number, Da(10^?5 ≤ Da ≤ 10^?3).     

Modeling of Unsteady Natural Convection for Double-Pipe in a Partially Cooled Enclosure

In this article, a model is developed for unsteady natural convection heat transfer and fluid flow in a partially cooled enclosure with a hollow cylinder through it. The right vertical wall of the enclosure is cooled partially. The location of the partial cooling is set up in three different configurations; namely, bottom (P ₁), middle (P ₂), and top (P ₃). A hollow cylinder is located at the middle of the enclosure to simulate a double-pipe heat exchanger. Three values of Grashof number are applied in this work, i.e., 10⁴, 10⁵ and 10⁶, and three lengths of the cooler, i.e., 0.2, 0.4 and 0.6. Finite element method was utilized to solve the unsteady dimensionless conservation equations of mass, momentum and energy. It is found that the length and location of cooler does not have a significant effect on the natural convection for the case of the low Grashof number. The maximum heat transfer rate is reached when the cooler is located at the middle of the vertical wall.     

有内热源的肋片散热数值分析

利用流体区域与固体区域温度场耦合的方法求解含内热源肋片的稳态自然对流换热问题,讨论了肋片材料、肋片间距和内热源强度对整个散热的影响。得出各种情况下流场和温度场的变化和不同情况下散热效果的标志性参数——最高温度的变化规律如下：内热源越强,最高温度越高;肋片间距增加,最高温度降低;提出了具体的计算式;导热系数大于10W／（m·K）的金属材料,肋片最高温度不受材料热物理性质的影响。