NATURAL CONVECTION IN A TWO-DIMENSIONAL DIFFERENTIALLY HEATED SQUARE ENCLOSURE UNDERGOING ROTATION

A numerical study of two-dimensional natural convection in a rotating and differentially heated square enclosure has been presented by solving the conservation equations of mass, momentum, and energy in a rotating coordinate system using the finite difference method. Considering air to be the fluid medium in the cavity, the results are presented for a wide range of Rayleigh numbers (Ra), Taylor numbers (Ta), and rotational Rayleigh numbers (Ra _w). It is found that a significant enhancement in heat transfer can be achieved due to rotational effects. At a particular Ra, increase in Ta results in an increase in frequency of oscillations of the dynamical variables and also gives rise to formation of a mushroom-shaped plume in the core of the cavity. For constant Ta, an increase in Ra results in formation of thinner thermal boundary layers at the isothermal walls and stable thermal stratification in the core of the cavity. The stratification becomes unstable when the Ta     

NATURAL CONVECTION HEAT TRANSFER AROUND HEATED CYLINDERS INSIDE A CAVITY WITH CONDUCTING WALLS

A numerical study has been conducted for natural convection heat transfer for air around two vertically separated horizontal heated cylinders placed inside a rectangular enclosure having finite wall conductances. The interaction between convection in the fluid-filled cavity and conduction in the walls surrounding the cavity is investigated. Results have been obtained for Rayleigh numbers Ra between 10 ³ I. Tokura , H. Saito , K. Kishinami , and K. Muramoto , An Experimental Study of Free Convection Heat Transfer from a Horizontal Cylinder in a Vertical Arcay Set in Free Space between Parallel Walls , J. Heat Transfer , vol. 105 , pp. 102 – 107 , 1993 . [Google Scholar] and 10 ⁶ M. Lacroix , Natural Convection Heat Transfer around Two Heated Horizontal Cylinders inside a Rectangular Cavity Cooled from Above , Numer. Heat Transfer Part A , vol. 21 , pp. 37 – 54 , 1992 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], dimensionless wall-fluid thermal conductivity ratio α between 0.2 and 1000.0, and different thermal boundary conditions. The results indicate that wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer around the cylinders. Heat removal through the vertical wall is significant even when its outer surface is insulated. The overall heat transfer coefficient for both cylinders is correlated with C Raⁿ for different α and thermal boundary conditions.     

HYDROMAGNETIC COMBINED CONVECTION FLOW IN A VERTICAL LID-DRIVEN CAVITY WITH INTERNAL HEAT GENERATION OR ABSORPTION

The problem of unsteady, laminar, combined forced-free convection flow in a square cavity in the presence of internal heat generation or absorption and a magnetic field is formulated. Both the top and bottom horizontal walls of the cavity are insulated while the left and right vertical walls are kept at constant and different temperatures. The left vertical wall is moving in its own plane at a constant speed while all other walls are fixed. A uniform magnetic field is applied in the horizontal direction normal to the moving wall. A temperature-dependent heat source or sink is assumed to exist within the cavity. The governing equations and conditions are solved numerically by the finite-volume approach along with the alternating direct implicit (ADI) procedure. Two cases of thermal boundary conditions corresponding to aiding and opposing flows are considered. Comparisons with previously published work are performed and the results are found to be in excellent agreement. A parametric study is conducted and a set of representative graphical results is presented and discussed to illustrate the influence of the physical parameters on the solution.     

NUMERICAL EVALUATION OF WEAKLY TURBULENT FLOW PATTERNS OF NATURAL CONVECTION IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED SIDE WALLS

This article presents the results of numerical evaluation of weakly turbulent natural convection of air in a rectangular enclosure with differentially heated side walls and adiabatic horizontal walls. The turbulence in the natural convection was described by k–ε equations, which were solved by Strang splitting, while average thermal and fluid flow fields were described by statistically averaged equations, which were solved by the projection method PmIII. The combined application of projection method and the Strang splitting characterizes the numerical method in this study. Numerical results for Rayleigh number 1.58 × 10⁹ have revealed reasonable agreement with the existing experimental ones, with some discrepancy attributable to the adiabatic boundary conditions on the horizontal walls. The results are also in good agreement with some published numerical results, particularly at higher Rayleigh numbers. However, comparison with the latest experimental data reveals that the turbulent heat flux model is not quite capable of giving satisfactory temperature distribution.     

HYDROMAGNETIC NATURAL CONVECTION FROM AN INCLINED POROUS SQUARE ENCLOSURE WITH HEAT GENERATION

The problem of unsteady, laminar, two-dimensional hydromagnetic natural convection heat transfer in an inclined square enclosure filled with a fluid-saturated porous medium in the presence of a transverse magnetic field and fluid heat generation effects is studied numerically. The walls of the enclosure are maintained at constant temperatures. The flow in the porous region is modeled using the Brinkman-extended Darcy's law to account for the no-slip conditions at the walls. The control volume method is used to solve the governing balance equations for different values of the Darcy number, Hartmann number, and the inclination angle. Favorable comparisons with previously published work are performed. These comparisons confirmed the correctness of the numerical results. The obtained numerical results are presented graphically in terms of streamlines and isotherms as well as velocity and temperature profiles at midsections of the cavity to illustrate interesting features of the solution.     

NUMERICAL SIMULATION OF NATURAL CONVECTION WITH DENSITY INVERSION IN A SQUARE CAVITY

Water has its density maximum at 4^oC, and natural convection around the temperature is complicated. In this study, natural convection with density inversion in a two-dimensional vertical square cavity is investigated numerically. To express the average Nusselt number nondimensionally, some parameters are chosen by observing the calculated flow-temperature fields. Then a simple expression of heat transfer correlation as a function of Galilei number, wall temperature ratio, and density function is proposed. The present correlation has a deviation of about 10%.     

CONJUGATE NATURAL CONVECTION HEAT TRANSFER IN A VERTICAL ANNULUS WITH INTERNAL CIRCUMFERENTIAL FINS

A numerical investigation is carried out to study natural convection heat transfer in a vertical annular enclosure with circumferential fins mounted on the inner cylinder. Heat is generated within the inner solid cylinder, while the top, the bottom, and the outer walls are exposed to convection. The results show that, even though the presence of fins does not alter the main features of the flow in the large-scale recirculation zone, it reduces the mean temperature of the inner cylinder by a maximum of 9.6% at low Rayleigh numbers. Also, the number and length of fins have a pronounced effect on the mean temperature.     

UNSTEADY FREE CONVECTION IN A VERTICAL CHANNEL WITH A BUILT-IN HEATED SQUARE CYLINDER

The cause of high operating temperatures experienced by grate blocks in a waste-to-energy power plant is investigated. A three-dimensional numerical analysis is performed to assess convection from the grate to the underfire air supply and conduction within the grate. A number of geometric complexities, including variable solid thickness, extended surfaces, sharp curvatures, and narrow passages, are accounted for via a finite element approach. The grate temperature is found to be very sensitive to the flow characteristics beneath the grates. Analysis of a modified grate structure was performed, showing a 14% reduction in maximum grate temperature.     

二维方腔自然对流熵产模拟分析

利用热和流体流动控制方程,同时考虑了粘性耗散效应,以温差驱动的二维方腔内自然对流换热为对象,分析讨论了熵产的分布以及随着Ra在10~5～10~7之间的变化关系。分析结果表明:熵产主要发生在高温壁面和低温壁面,最大熵产出现在高温壁面的下侧和低温壁面的上侧;熵产的面积加权平均(?)随着Ra呈指数形式变化;(?)与Ra之间呈线性关系;在总熵产中,传热熵产占绝对比重,且随着Ra的增大,其占总熵产的比例也越来越大。     

TRANSIENT NATURAL CONVECTION IN A CAVITY WITH WALLS OF FINITE THICKNESS

Numerical studies are made of transient natural convection in a square cavity. The top and bottom end walls are thermally insulated. The vertical solid side walls are of finite thickness and of finite thermal conductivity. Flow is driven, from the motionless isothermal initial state, by impulsively increasing (decreasing) the temperature at the outer surface of one (the other) vertical side wall. Numerical solutions art sought to the time-dependent Navier-Stokes equations for the fluid and the solid regions. The ratios of thermophysical properties between solid and fluid are the significant parameters. As the thermal capacity ratio increases, the development of flow in the fluid region is retarded. The conductive and convective timescales are estimated. The effects of the thermal conductivity ratio and of the thickness of the side wall are delineated. The effect of the system Rayleigh number on transient heat transport is analyzed. The applicability of the approximate one-dimensional thermal conductance model to the transient features is scrutinized.     

BUOYANT CONVECTION IN A SQUARE CAVITY PARTIALLY FILLED WITH A HEAT-GENERATING POROUS MEDIUM

Steady-state buoyant convection in a rectangular cavity, partially filled with a fluid-saturated porous medium with spatially uniform internal heat generation, is considered. The Brinkman-extended Darcy model in the porous region is adopted. The overall Rayleigh number is large to render a boundary-layer-type global flow pattern. Scale analysis is performed to obtain a rudimentary understanding of the flow characteristics. In parallel with the theoretical endeavors, numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that there exists an asymptotic convection regime where the flow is nearly independent of the permeability and conductivity of the porous medium. The effect of the thermal conductivity of porous material is appreciable in the intermediate regime. In the conduction-dominant regime, the porous region acts like a heat-generating solid block. The numerical study gives credence to the reliability of the theoretical arguments.     

NATURAL-CONVECTIVE HEAT TRANSFER IN A SQUARE CAVITY WITH TIME-VARYING SIDE-WALL TEMPERATURE

ABSTRACT

The natural-convective heat transfer in an inclined square enclosure is studied numerically. The top and bottom horizontal walls are adiabatic, and the right side wall is maintained at a constant temperature T ₀. The temperature of the opposing vertical wall varies by sine law with time about a mean value T ₀. The system of Navier–Stokes Equations in Boussinesq approximation is solved numerically by the control-volume method with SIMPLER algorithm. The enclosure is filled with air (Pr = 1) and results are obtained in the range of inclination angle 0° ≤ α ≤ 90° for two values of Grashof number (2 × 10⁵ and 3 × 10⁵). It can be noted that there is a nonzero time-averaged heat flux through the enclosure at α ≠ 0°. The dependencies of time-averaged heat flux on oscillation frequency and inclination angle are depicted. It is found that the maximal heat transfer corresponds to the values of inclination angle α = 54^○ and dimensionless frequency f = 20π for both Grashof numbers studied (2 × 10⁵ and 3 × 10⁵).     

HEAT TRANSFER FROM THE COLD WALL OF A SQUARE CAVITY TO THE HOT ONE BY OSCILLATORY NATURAL CONVECTION

ABSTRACT

The periodic natural convection in an inclined square enclosure is studied numerically. One of the cavity sides is maintained at a constant temperature, and the temperature of the opposite wall is varied by the sine law. The mean value of this temperature in a period was lower than the given constant temperature. The other two walls of the enclosure were adiabatic. The system of Navier–Stokes Equations in Boussinesq approximation is solved numerically by the control-volume method with the SIMPLER algorithm. Solutions are obtained for Grashof number equal to 5 × 10⁵ and Prandtl number equal to unity in a wide range of oscillation frequency variation. The heat transfer dependency on oscillation frequency is studied for different values of inclination angle. It is found that there is a possibility of heat transferring from the colder wall to the hotter one in the whole range of problem parameters. The possible causes of such a phenomenon are analyzed.     

NAVIER-STOKES STUDY OF NATURAL CONVECTION AND HEAT TRANSFER IN VERTICAL SYMMETRICALLY HEATED PLATE-FIN HEAT SINKS

A numerical study was performed on buoyant flow and heat transfer in vertical plate-fin heat sinks. As a result of the problem's importance, a number of semiempirical correlations have been proposed to determine the Nusselt number along the wetted surfaces and establish the optimum fin spacing. This article aims to assess the accuracy and range of applicability of such correlations. A CFD program Coolit^TM specifically designed for modeling electronic equipment, was used to predict heat transfer over a wide range of Raleigh numbers and geometrical parameters. The computed results are presented and compared with semiempirical correlations. Ranges of validity of the correlations and three-dimensional flow mechanisms responsible for the observed discrepancies are discussed.     

NATURAL CONVECTION AND RADIATION IN A SQUARE ENCLOSURE

Natural convection of a radiating fluid in a square enclosure is studied numerically. The coupled momentum, energy, and radiative transfer equations are solved by an iterative procedure. The solutions to the equation of radiative transfer are obtained by the discrete ordinates method using S4 and S8 quadratures. The method is based on control volume formulation and is fully compatible with the SIMPLER algorithm used to solve the momentum and energy equations. The effects of optical thickness and scattering on the flow and temperature fields and heat transfer rates are analyzed. The changes in the buoyant flow patterns and temperature distributions due to the presence of radiation in inclined or heat generating enclosures are also studied. Comparative results obtained by the P-I differential approximation are presented.     

TWO-DIMENSIONAL AND UNSTEADY NATURAL CONVECTION IN A HORIZONTAL ENCLOSURE WITH A SQUARE BODY

A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 103 to 106. When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is high, the flow and temperature fields become time dependent, and their time-averaged shapes approach the symmetric pattern again. The Rayleigh number for the fluid flow and temperature fields to become nonsymmetrical and time dependent depends on the thermal boundary conditions of a body. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls and at the body surfaces for different Rayleigh numbers and thermal boundary conditions are also presented to show the overall heat transfer characteristics in the system.     

EFFECT OF HEATED WALL POSITION ON MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY

Mixed convection in an open cavity with a heated wall bounded by a horizontally insulated plate is studied numerically. Three basic heating modes are considered: (a) the heated wall is on the inflow side (assisting flow); (b) the heated wall is on the outflow side (opposing flow); and (c) the heated wall is the horizontal surface of the cavity (heating from below). Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of streamlines, isotherms, wall temperature, and the velocity profiles in the cavity for Ri=0.1 and 100, Re=100 and 1000, and the ratio between the channel and cavity heights (H/D) is in the range 0.1-1.5. The present results show that the maximum temperature values decrease as the Reynolds and the Richardson numbers increase. The effect of the H/D ratio is found to play a significant role on streamline and isotherm patterns for differentheating configurations. The present investigation shows that the opposing forced flow configuration has the highest thermal performance in terms of both maximum temperature and average Nusselt number.     

SOLUTION OF TRANSIENT LAMINAR NATURAL CONVECTION IN A SQUARE CAVITY BY AN EXPLICIT FINITE ELEMENT SCHEME

This paper discusses the application of a finite element method based on the first-order projection scheme, which is an extension ofChorin's algorithm, to transient laminar natural convection in a square cavity. Results have been presented for a fluid of Prandtl number 0.71 in the Rayleigh number range of 10³-10⁶ in terms of the variation of vertical velocity component, nondimensional temperature, and average Nusselt number with time. Various features of the scheme that render it economical in terms of CPU time and storage requirements are discussed. The steady state results have been compared with benchmark solutions, and the agreement appears to be good.     

NUMERICAL INVESTIGATION OF CONVECTION HEAT TRANSFER IN A HEATED ROOM

We describe numerical investigation of airflow and temperature field in a room with a convective heat source. The simulation involves using computational fluid dynamics (CFD) to validate different turbulence models, i.e., the standard k- k model and the low Reynolds number k- k model. The comparisons between computations and experiments show good and acceptable agreement. It can be concluded that the CFD simulations can capture the main flow features and provide satisfactory results. It can be seen that the thermal wall jet created by the heat source greatly influences airflow pattern and temperature field in the room. It can also be seen that the advanced turbulence model may produce better results than the standard one under a suitable mesh scheme.