Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Conjugate natural convection in air filled tube inserted a square cavity

Numerical analyses of fluid flow and heat transfer due to buoyancy forces in a tube inserted square cavity filled with fluid were carried out by using control volume method in this study. The cavity was heated from the left wall and cooled from the right isothermally and horizontal walls were adiabatic. A circular tube filled with air was inserted into the square cavity. The case that the inside and outside of the tube were filled with the same fluid (air) was examined. Varied solid materials were chosen as the tube wall. Results were obtained for different Rayleigh numbers (Ra = 10⁴, 10⁵ and 10⁶), thermal conductivity ratio of the fluid to the tube wall (k = 0.1, 1 and 10) and different location centers of the tube (c (0.25 ≤ x ≤ 0.75, 0.25 ≤ y ≤ 0.75)). Comparison with benchmark solutions of the natural convection in a cavity was performed and numerical results gave an acceptable agreement. It was found that varied location of the tube center can lead to different flow fields and heat transfer intensities which are also affected by the value of Rayleigh number.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection 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 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Investigation of buoyancy-driven flow and heat transfer in a trapezoidal cavity filled with water–Cu nanofluid

A numerical study is conducted to investigate the transport mechanism of free convection in a trapezoidal enclosure filled with water–Cu nanofluid. The horizontal walls of the enclosure are insulated while the inclined walls are kept at constant but different temperatures. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for a wide range of the aspect ratio (AR) and Prandtl number (Pr) with Rayleigh number (Ra = 10⁵) and solid volume fraction (? = 0.05). The streamlines, isotherm plots and the variation of the average Nusselt number at the left hot wall are presented and discussed. It is found that both AR and Pr affect the fluid flow and heat transfer in the enclosure. A correlation is also developed graphically for the average Nusselt number as a function of the Prandtl number as well as the cavity aspect ratio.     

Computation of combined natural-convection and radiation heat-transfer in a cavity having a square body at its center

This paper describes a numerical study of the radiation-natural convection interactions in a differentially-heated cavity with an inner body. A specifically developed numerical model, based on the finite-volume method, is used for the solutions of the governing differential-equations. The SIMPLER algorithm for the pressure–velocity coupling is adopted. The fluid (air) is perfectly transparent to the radiation. The surface emissivity ε, the Rayleigh number Ra, and the thermal conductivity ratio R_k were varied parametrically. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of isotherms, streamlines, average Nusselt-numbers across the enclosure, local Nusselt-numbers at the hot and cold walls, vertical and horizontal median velocities and horizontal walls, temperature distributions. It is found that: (i) the radiation exchange homogenizes the temperature inside the cavity and produces an increase in the average Nusselt-number, particularly when R_k and Ra are high and (ii) the average Nusselt-number increases with increasing surface emissivity, especially at high Rayleigh numbers.     

Natural convection in an air-filled cavity: Experimental results at large Rayleigh numbers

A large-scale experimental setup is built and instrumented. It consists in a 4 m-high cavity with a horizontal cross-section equal to 0.86 × 1.00 m². Two opposite vertical walls are heated and cooled down; other walls (lateral walls, ceiling and floor) are made of insulating medium covered with a thin and low-emissivity film designed to minimize radiative effects into the cavity. The temperatures of active walls are imposed, constant and equally distributed around the ambient temperature in order to reduce heat losses. The temperature difference between the hot and cold walls is chosen to respect the Boussinesq approximation. Under these assumptions, Rayleigh number values up to 1.2 × 10¹¹ (ΔT = 20 °C) can be obtained. The centre-symmetry is verified on the thermal stratification. Influence of the temperature difference and of wall emissivities on the stratification parameter (dimensionless vertical temperature gradient) is discussed. Velocity measurements allow the velocity field to be obtained and provide information on flows encountered in the cavity. Temperature measurements are also carried out in the whole cavity. In the paper, a complete experimental characterization is provided: airflow inside the cavity is analyzed and the Nusselt number along the hot and the cold wall is presented.     

Natural convection in an open square cavity with slots

In this paper, we investigate heat transfer by natural convection in an open cavity in which a uniform heat flux is applied to the inside active wall facing the opening with slots. Conservation equations are solved by finite difference–control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to 10⁶, the Prandtl number, Pr = 0.7, constant for air, the cavity aspect ratio, A = L/H = 1. Number of slots N is varied from 2 to 8 and the dimensionless opening ratio OR from 0.1 to 0.6. We found that the Nusselt number and the volume flow rate are both increasing functions of the Rayleigh number; they are a decreasing function of the number of slots and increasing function of the opening ratio, though there is an optimum opening ratio at high Rayleigh numbers.     

Effects of inclination angle on conduction—natural convection in divided enclosures filled with different fluids

Laminar natural convection in inclined enclosures filled with different fluids was studied by a numerical method. The enclosure was divided by a solid impermeable divider. One side of partition of enclosure was filled with air and the other side had water. The enclosure was heated from one vertical wall and cooled from the other while horizontal walls were adiabatic. The governing equations which were written in stream function–vorticity form were solved using a finite difference technique. Results were presented by streamlines, isotherms, mean and local Nusselt numbers for different thermal conductivity ratios of solid impermeable material (plywood or concrete), inclination angle (0° ≤ ? ≤ 360°) and Grashof numbers (10³ ≤ Gr ≤ 10⁶). The code was validated by earlier studies, which are available in the literature on conjugate natural convection heat transfer. Analytical solutions were obtained for low Grashof numbers. Obtained results showed that both heat transfer and flow strength strongly depended on thermal conductivity ratio of the solid material of partition, inclination angle and Grashof numbers. The heat transfer was lower in the air side of the enclosure than that of the water side.     

Natural convective flow in an inclined lid-driven enclosure with a heated thin plate in the middle

Natural convection heat transfer from a heated thin plate located in the middle of a lid-driven inclined square enclosure has been analyzed numerically. Left and right of the cavity are adiabatic, the two horizontal walls have constant temperature lower than the plate’s temperature. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using a fully higher-order compact (FHOC) finite difference scheme on the 9-point 2D stencil. Air was chosen as a working fluid (Pr = 0.71). Two cases are considered depending on the position of heated thin plate (Case I, horizontal position; Case II, vertical position). Governing parameters, which are effective on flow field and temperature distribution, are Rayleigh number values (Ra) ranging from 10³ to 10⁵ and inclination angles γ (0° ? γ < 360°). The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and Nusselt number (Nu). It is found that fluid flow and temperature fields strongly depend on Rayleigh numbers and inclination angles. Further, for the vertical located position of thin plate heat transfer becomes more enhanced with lower γ at various Rayleigh numbers.     

Natural convection on inclined QFN32 electronic package generating constant volumetric heat flux

Qualification and quantification of the natural convective phenomena are examined in the case of a Quad Flat Non-lead (QFN32). This active electronic package is inclined with respect to the horizontal plane by an angle varying between 0° and 90° corresponding to the horizontal and vertical position respectively. It generates during its operation a constant volumetric heat flux leading to Rayleigh numbers varying in the range 1.31x10⁷ ‐ 1.01x10⁸. The walls of the large air-filled cubic cavity containing this device are maintained isothermal. The temperature and velocity fields are presented for different combinations of the Rayleigh number and inclination angle. The convective heat transfer concerning the whole component exchange surface is determined for all the treated configurations. Correlations of Nusselt–Rayleigh type are proposed. They allow optimizing the thermal design of electronic assemblies used in various engineering domains.     

Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method

A thermal lattice Boltzmann method based on the BGK model has been used to simulate high Rayleigh number natural convection in a square cavity. The model uses the double populations approach to simulate hydrodynamic and thermal fields. The traditional lattice Boltzmann method on a uniform grid has unreasonably high grid requirements at higher Rayleigh numbers which renders the method impractical. In this work, the interpolation supplemented lattice Boltzmann method has been utilized. This is shown to be effective even at high Rayleigh numbers. Numerical results are presented for natural convection in a square cavity with insulated horizontal walls and isothermal vertical walls maintained at different temperatures. Very fine grids (wall y⁺ < 0.3) have been used for the higher Rayleigh number simulations. A universal structure is shown to exist in the mean velocity turbulent boundary layer profile for y⁺ < 10. This agrees extremely well with previously reported experimental data. The numerical results (for Rayleigh numbers up to 10¹⁰) are in very good agreement with the benchmark results available in the literature. The highlight of the calculations is that no turbulence model has been employed.     

Heat generation effects in natural convection inside a porous annulus

The interplay between internal heat generation and externally driven natural convection inside a porous medium annulus is studied in detail using numerical methods. The axisymmetric domain is bounded with adiabatic top and bottom walls and differentially heated side walls sustaining steady natural convection of a fluid with Prandtl number, Pr = 5, through a porous matrix of volumetric porosity, ? = 0.4. The generalized momentum equation with Brinkman–Darcy–Forchheimer terms and the local thermal non-equilibrium based two-energy equation model are solved to determine the flow and the temperature distribution. Beyond a critical heat generation value defined using an internal Rayleigh number, Ra_I,cr^?, the convection transits from unicellular to bicellular mode, as the annulus T_max becomes higher than the fixed hot-wall temperature. The Ra_I,cr^? increases proportionately when the permeability based external Rayleigh number Ra_E^? and the solid–fluid thermal conductivity ratio γ are independently increased. A correlation is proposed to predict the overall annulus Nu as a function of Ra_E^?, Ra_I^?, Da and γ. It predicts the results within ± 20% accuracy.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

Effects of the dimensions of upward- and downward-facing vertical cavities on natural convection

The mass transfer due to natural convection in open upward- and downward-facing vertical cylindrical cavities was measured experimentally for Rayleigh numbers (Ra_Lw) ranging from 2.57 × 10⁸ to 1.04 × 10¹⁰ for various diameters and heights. Mass transfer was measured using a sulfuric acid–copper sulfate electroplating system and the limiting current technique. The results of preliminary natural convection experiments using horizontal circular disks were in good agreement with predictions based on existing correlations for horizontal surfaces. The Sherwood numbers (Sh_Lw) for upward-facing cylindrical cavities were higher than those for downward-facing ones. Cavity dimension affected mass transfer rate. Total mass transfer rates measured in cavities were compared with ones calculated using horizontal and vertical correlations for the same areas to delineate flow interactions in the cavities. For both cavity orientations, diameter had a stronger effect for lower cavity heights. In upward-facing cavities, the total mass transfer rate was increased due to the secondary flow generated by the negative pressure formed by two ascending flows from the bottom plate and the vertical inner wall. In downward-facing cavities, flow interaction impaired the mass transfer rate. Empirical correlations for upward- and downward-facing vertical cylindrical cavities were derived based on the test results.     

Transient natural convection in 3D tilted enclosure heated from two opposite sides

In the present work, we investigate numerically the natural convection flow in 3D cubic enclosure tilted at an angle (γ) with respect to the vertical position. The enclosure is heated and cooled from the two opposite walls while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yield consistent performance over a wide range of parameters. Simulations have been carried out for Rayleigh numbers Ra ranging from 10³ to 1.3 × 10⁵, Prandtl number, Pr, (0.71 ≤ Pr ≤ 75) and inclination angle γ (0° ≤ γ ≤ 90°). Particular attention is focused on the three-dimensional steady effects that can arise in such configuration that seem to be unknown in the literature, even for relatively small values of the Rayleigh number. The 3D flow characteristics and thermal fields are analyzed in terms of streamlines, isotherms and Nusselt numbers. A periodic behavior of the 3D flow has been observed at Ra = 8.5 × 10⁴ with a fundamental frequency of 8.27. The Hopf bifurcation is localized. In addition, time-dependent solutions reveal that the flow characteristics depend on the inclination angle γ. The effects of Prandtl number on heat transfer and fluid flow is significant for Pr ≥ 6.     

Numerical modeling of the electrohydrodynamic effect to natural convection in vertical channels

The electrohydrodynamic effect to natural convection inside the vertical channels is numerically investigated by computational fluid dynamics technique. The range of parameters considered are 10⁴ = Ra = 10⁷, 7.5 = V₀ = 17.5 kV, and 2 = aspect ratio = 10. Flow and temperature distributions are affected with supplied voltage at the wire electrodes, and the heat transfer enhancement is significantly influenced at low Rayleigh number. The augmented volume flow rate of fluid is indicated in relation with the number of electrodes. Moreover, heat transfer enhancement also depended on the electrode arrangement while the number of electrodes is initially fixed. The relation between channel aspect ratio and number of electrodes that performs the maximum heat transfer is expressed incorporating with the optimum concerning parameters.