Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter

This paper presents the results of a study of conjugate turbulent natural convection inside a building attic in the shape of a rectangular enclosure bounded by realistic walls made from composite construction materials under winter day boundary conditions. The effects of cavity aspect ratio, Rayleigh number (Ra), depth of the external concrete beam, and external wall construction materials on the flow and heat transfer characteristics were the main focus of the investigation. The Shear stress transport k–ω turbulence model is implemented to calculate air-flow velocities and temperatures in a steady, turbulent, two-dimensional conjugate natural convection heat transfer inside an attic. The governing equations were solved by employing the line-by-line tri-diagonal matrix algorithm (TDMA) control volume method. For Ra ranging from 10⁷ to 10¹⁰, steady-state results of the streamline and temperature contours in addition to local and mean Nusselt numbers at all surfaces of the cavity were obtained. The results show that the values of Ra, attic aspect ratio and the composite wall materials have significant effect on the temperature and stream function contours within the enclosure, and the heat flux out of the room through the enclosure.     

Conjugate natural convection in the roof cavity of heavy construction building during summer

This paper presents the results of a study of conjugate natural convection inside a building attic in the shape of a rectangular enclosure bounded by realistic walls made from composite construction materials under summer day boundary conditions. The effects of cavity aspect ratio, Rayleigh number (Ra), and orientation of the external surfaces on the flow and heat transfer characteristics were the main focus of the investigation. The problem was formulated in terms of the vorticity-stream function procedure, and the governing equations for steady, laminar, two-dimensional conjugate natural convection heat transfer were solved by employing the Alternating Direction Implicit (ADI) control volume method along with under-relaxation factors for temperature, vorticity, and stream functions. For Ra ranging from 10³ to 10¹⁰, steady state results of the streamline and temperature contours in addition to local and mean Nusselt number at all surfaces of the cavity were obtained. The results show that the values of Ra and the aspect ratio have significant effect on the temperature and stream function contours within the enclosure. Another important finding of the study is that heat flux into the room increases with the increase of both the aspect ratio and Rayleigh number.     

Convective transport in rectangular cavities partially heated at the bottom and cooled at one side

Laminar natural convection heat transfer inside air-filled, rectangular enclosures partially heated from below and cooled at one side is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum, and energy transfer governing equations. Simulations are performed for a complete range of heater size, for Rayleigh numbers based on the height of the cavity ranging from 10~3to 10~6, and for height-to-width aspect ratios of the cavity spanning from 0.25 to 4. It is found that the heat transfer rate increases with increasing the heater size and the Rayleigh number, while it decreases with increasing the aspect ratio of the cavity. Dimensionless heat transfer correlations are also proposed.     

Laminar natural convection in inclined open shallow cavities

Laminar steady state natural convection in inclined shallow cavities has been numerically studied. The side facing the opening is heated by a constant heat flux, sides perpendicular to the heated side are insulated and the opening is in contact with a fluid at constant temperature and pressure. Equations of mass, momentum and energy are solved using constant properties and Boussinesq approximation and assuming an approximate boundary conditions at the opening. Isotherms and streamlines are produced, heat and mass transfer is calculated for Rayleigh numbers from 10³ to 10¹⁰, cavity aspect ratio A=H/L from 1 to 0.125. The results show that flow and heat transfer are governed by Rayleigh number, aspect ratio and the inclination. Heat transfer approaches asymptotic values at Rayleigh numbers independent of the aspect ratio. The asymptotic values are close to that for a flat plate with constant heat flux. The effect of elongation of open cavities is to delay this asymptotic behavior. It is also found that the inclination angle of the heated plate is an important parameter affecting volumetric flow rate and the heat transfer.     

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.     

A numerical study of mixed convection in a two-sided lid-driven tall cavity containing a heated triangular block for non-Newtonian power-law fluids

The study of hydrodynamics and thermal characteristics inside a lid-driven cavity has been one of the most captivating problems in computational fluid dynamics. In this numerical work, the mixed convection phenomenon inside a two-dimensional, tall lid-driven cavity with top and bottom lids moving in opposite directions, +x and –x, respectively, has been explored for non-Newtonian power-law fluids. The cavity contains a uniformly heated equilateral triangular obstacle at its geometric center.  Numerical experimentation is performed for a range of flow governing parameters, such as aspect ratio (0.25, 0.5, and 0.75), Prandtl number (1, 50, and 100) Richardson number (0.1, 1, and 10), power-law index (0.6–1.4) and Grashof number of 10⁴. The physical perceptions of the cavity are explained by using streamline and isotherm contours. The fluid movement is limited adjacent to the moving wall concerning the Richardson number at the lower Prandtl number. With a rise in the aspect ratio of the cavity, the flow-pattern becomes more dispersed inside the cavity. Heat transfer enhancement is observed at a lower aspect ratio equal to 0.25.     

Natural convection of nanofluids in enclosures with low aspect ratios

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO-water nanofluid heated from one side and cooled from the ceiling. The transport equations for the flow are solved numerically by the finite volume element method using the SIMPLER algorithm Based on numerical predictions. The effects of Rayleigh number and aspect ratio on flow pattern and energy transport are investigated for Rayleigh numbers ranging from 10⁴ to 10⁷ volume fraction of solid varied to 0%–4% and for five different aspect ratios of 0.08, 0.1, 0.125, 0.25 and 0.5. It is found that the effect of Rayleigh number on heat transfer is less significant when the enclosure is shallow (AR = 0.5) and the influence of aspect ratio is stronger when the enclosure is tall and the Rayleigh number is high.     

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.     

Double dispersion,natural convection in an open end cavity simulation via Lattice Boltzmann Method

Double dispersion in an open end cavities are simulated using Lattice Boltzmann Method (LBM). The flow is driven by the buoyancy effect due to the heated vertical wall and species concentration at the heated wall of the cavity (closed end). The paper is intended to address the physics of flow, heat and mass transfers in open ended cavities and close end slots. Prandtl number (Pr) is fixed to 0.71 (air) for the thermal Rayleigh number (Ra_T) of 10⁴, 10⁵ and 10⁶. The results are presented for moderate Lewis number of 2, 4 and 8 and for a range of buoyancy ratio, N, (species to thermal). The species concentration induced buoyancy force either aids or opposes the thermally driven flow, which is determined by the value of buoyancy ratio (positive or negative, respectively). Interesting flow patterns were predicted for opposing buoyancy forces.     

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.     

Conjugate heat transfer in open cavities with a discrete heater at its optimized position

In this article, we determined optimum position of a discrete heater by maximizing the conductance and then studied heat transfer and volume flow rate with the discrete heater at its optimum position in open cavities. Continuity, Navier–Stokes and energy equations are solved by finite difference-control volume numerical method. The relevant governing parameters were: the Rayleigh numbers from 10⁶ to 10¹², the Prandtl number, Pr = 0.7, the cavity aspect ratio, A = H/L from 0.5 to 2, the wall thickness l/L from 0.05 to 0.15, the heater size h/L from 0.15 to 0.6, and the conductivity ratio k_r from 1 to 50. We found that the global conductance is an increasing function of the Rayleigh number, the conductivity ratio, and a decreasing function of the wall thickness. Best thermal performance is obtained by positioning the discrete heater at off center and slightly closer to the bottom. The Nusselt number and the volume flow rate in and out the open cavity are an increasing function of the Rayleigh number and the wall thickness, and a decreasing function of the conductivity ratio. The Nusselt number is a decreasing function of the cavity aspect ratio and the volume flow rate is an increasing function of it.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Mixed convection from an open cavity in a horizontal channel

Heat transfer results for mixed convection from a bottom heated open cavity subjected to an external flow are reported in this study for a wide range of the governing parameters (i.e., 1 ≤ Re ≤ 2000, 0 ≤ Gr ≤ 10⁶) over cavities with various aspect ratios (A = 0.5, 1, 2 and 4). It has been found that the Reynolds number and Garshof number control the flow pattern and the occurrence of recirculating cells while the aspect ratio has a significant influence on the orientation of these cells. Heat transfer from the cavity base approaches that of natural convection at a low Reynolds number (i.e., the asymptotic natural convection regime) and approaches that of forced convection at a high Reynolds number (i.e., the asymptotic forced convection regime). In the mixed convection regime, the heat transfer rate is reduced and the flow may become unstable. A unique heat transfer correlation which covers all three convection regimes is also presented.     

Flow and heat transfer over shallow cavities

The flow over a shallow cavity heated with constant heat flux form the bottom side has been studied experimentally and numerically. In the experimental part, pressure coefficient and Nusselt number have been measured along the cavity floor. In the numerical simulation, the conservation equations of mass, momentum, and energy have been solved. The standard k–? turbulence model is used to account for the turbulent fluctuations. In both experimental and numerical part, the effect of changing cavity aspect ratio and Reynolds number has been studied. It is found that, a single elongated eddy has been formed for aspect ratio lower than 7. As the aspect ratio increases the flow impinges with the cavity floor creating two eddies, one beside the upstream cavity side and the second beside the downstream cavity side. Local Nusselt number along the cavity floor is affected mainly by the flow structure inside the cavity and the average Nusselt number has increased with increasing the aspect ratio up to 10 and with increasing Reynolds number. A correlation for the average Nusselt number, as a function of Reynolds number and cavity aspect ratio, is developed.     

Natural convection on an open square cavity containing diagonally placed heaters and adiabatic square block and filled with hybrid nanofluid of nanodiamond - cobalt oxide/water

A finite difference based two dimensional simulations on laminar natural convection inside the open square cavity containing diagonal heaters and a central adiabatic square block is presented by vorticity – stream function approach. The enclosure is filled with hybrid nanofluid of Nanodiamond - Cobalt Oxide/Water. The top and bottom walls are considered as adiabatic and the vertical walls have diagonal heaters. The inlet port is placed on the left end of the top wall and the outlet is placed at the bottom of the right wall. The variables considered are Rayleigh number (10⁴ to 10⁶) and volumetric fraction of Nanodiamond - Cobalt Oxide (0 to 6%) particles. The results of fluid flow with single phase model are elucidated with streamlines, Isotherms and Average Nusselt number. The strength of the primary vortex depreciated with the increasing percentage of nano composites for all the Rayleigh numbers. Intensity of heat transfer is high in the right wall than the left wall.     

2D natural convection flows in tilted cavities: Porous media and homogeneous fluids

Natural convection flows are studied numerically for porous media and homogeneous fluids inside a rectangular cavity with inclination. These thermal fluid flows are considered under the respective two-dimensional unsteady Boussinesq approximation in stream function and vorticity variables. The study depends on the Rayleigh number, angle of inclination, and the aspect ratio of the cavity. At the validation stage our results are in good agreement with those reported by other authors. Results suppose to be new are presented either for angles of inclination not reported before or for high Rayleigh numbers with large aspect ratios. In rectangular porous cavities with Rayleigh number 10² multiple cells appear for some angles. In homogeneous fluids, for Rayleigh numbers of the order of 10⁵–10⁶ in large enough vertical cavities at most secondary cells appear for some angles and the flow becomes more complex and looks like to be oscillatory.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Energy and entropy analysis in a square cavity with protruding body: effects of protruding body aspect ratio

In the present study, the simulation of mixed convection in a square cavity with protruding body having different aspect ratios is carried out. The governing flow and energy equations are solved numerically using a control volume approach. Air is used as fluid in the cavity while steel is considered as protruding body. To investigate the heat transfer characteristics due to different aspect ratios of the protruding body, Stanton number (St) variation with the aspect ratio is considered. The entropy analysis is carried out to determine the irreversibility generated in the cavity for different aspect ratios. The heat transfer to irreversibility ratio is determined for each aspect ratio. It is found that the aspect ratio influences the heat transfer characteristics and the irreversibility generated in the cavity, in which case, the heat transfer increases at high aspect ratio while the irreversibility reduces. Moreover, heat transfer to irreversibility ratio improves considerably at an aspect ratio of 3. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom

Laminar mixed convective heat transfer in two-dimensional shallow rectangular driven cavities of aspect ratio 10 is studied numerically. The top moving lid of the cavity is at a higher temperature than the bottom wall. Computations are performed for Rayleigh numbers ranging from 10⁵ to 10⁷ keeping the Reynolds number fixed at 408.21, thus encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. The fluid Prandtl number is taken as 6 representing water. The effects of inclination of the cavity on the flow and thermal fields are investigated for inclination angles ranging from 0° to 30°. Interesting behaviours of the flow and thermal fields with increasing inclination are observed. The streamline and isotherm plots and the variation of the local and average Nusselt numbers at the hot and cold walls are presented. The average Nusselt number is found to increase with cavity inclination. The rate of increase of the average Nusselt number with cavity inclination is mild for dominating forced convection case while it is much steeper in dominating natural convection case.