Natural convection in inclined two dimensional rectangular cavities

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated. The channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. The field equations for a Newtonian Boussinesq fluid are solved numerically for three cavity height based Rayleigh numbers, Ra = 10⁴, 10⁵ and 10⁶, and several aspect ratios. The calculations are in excellent agreement with previously published benchmark results. The effect of the inclination of the cavity to the horizontal with the angle varying from 0° to 180° and the effect of the startup conditions on the flow pattern, temperature distribution and the heat transfer rates have been investigated. Flow admits different configurations at different angles as the angle of inclination is increased depending on the initial conditions. Regardless of the initial conditions Nusselt number Nu exhibits discontinuities triggered by gradual transition from multiple cell to a single cell configuration. The critical angle of inclination at which the discontinuity occurs is strongly influenced by the assumed startup field. The hysteresis effect previously reported is not always present when the calculations are reversed from 90° to 0°. A comprehensive study of the flow structure, the Nu variation with varying angle of inclination, the effect of the initial conditions and the hysteresis effect are presented.     

Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non-participating fluid

This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 10⁴ ? Ra ? 3 × 10⁵, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.     

Turbulent flow past a transverse cavity with inclined side walls. 2. Heat transfer

Convective heat transfer in a transverse cavity with a small aspect ratio, angle of wall inclination ϕ = 30–90°, and heated bottom, frontal, and rear walls of the cavity is studied experimentally. Temperature distributions are measured in longitudinal and transverse sections on three walls; temperature fields are measured over the entire heated surface. Local and mean heat-transfer coefficients are calculated. The highest intensification of heat transfer is found to occur on the rear wall for low values of ϕ Reconstruction of the one-cell structure to the two-cell structure of the primary vortex in the cavity leads to a drastic decrease in heat transfer over the cavity span from the end faces toward the center in the case with ϕ = 60 and 70°. A certain increase in the mean heat-transfer coefficient averaged over the entire heated surface is noted for ϕ = 60°. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 23–29, July–August, 2007.     

Experimental determination of the boundaries of the region of existence of anomalous convection flow in an tilted cube

This paper presents an experimentally study of the bifurcation of steady-state air convection in a cubic cavity heated from below under controlled deviations from equilibrium heating conditions due to a slow quasisteady-state tilt of the cavity at a predetermined angle α. It is found that in the supercritical range of Rayleigh numbers Ra at a tilt of the cavity not exceeding 7°, the existence of two stable steady-state convection regimes (normal and anomalous) with circulation in opposite directions is possible. A study is made of the transformations of the temperature distribution in the middle (with respect to the planes in which heat exchangers are located) plane during transition from the anomalous flow regime to the normal regime by instantaneous rotation of the entire mass of air in the cavity around the vertical axis by an angle of 90 to 135°. It is shown that this rotation occurs when the tilt of the cavity exceeds a critical value α _cr(Ra), which was determined experimentally for Rayleigh numbers 0 < Ra < 25Racr, where Racr is the critical Rayleigh number for stability of mechanical equilibrium for heating from below.     

Double-diffusive natural convection in inclined porous cavities with various aspect ratios and temperature-dependent heat source or sink

Laminar double-diffusive natural convective flow of a binary fluid mixture in inclined square and rectangular cavities filled with a uniform porous medium in the presence of temperature-difference dependent heat generation (source) or absorption (sink) is considered. Transverse gradients of heat and mass are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function-vorticity formulation. A numerical solution based on the finite-difference methodology is obtained for relatively high Lewis numbers. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, heat generation or absorption coefficient and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature and concentration at mid-section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers are presented for various parametric conditions and discussed.     

Ice-water convection in an inclined rectangular cavity filled with a porous medium

This paper reports on the results of a numerical study on the equilibrium state of the convection of water in the presence of ice in an inclined rectangular cavity filled with a porous medium. One side of the cavity is maintained at a temperature higher than the fusion temperature while the opposite side is cooled to a temperature lower than the fusion temperature. The two remaining sides are insulated. Results are analysed in terms of the density inversion parameter, the tilt angle, and the cooling temperature. It appears that the phenomenon of density inversion plays an important role in the equilibrium of an ice-water system when the heating temperature is below 20°. In a vertical cavity, the density inversion causes the formation of two counterrotating vortices leading to a water volume which is wider at the bottom than at the top. When the cavity is inclined, there exist two branches of solutions which exhibit the bottom heating and the side heating characteristics, respectively (the Bénard and side heating branches). Due to the inversion of density, the solution on the Bénard branch may fail to converge to a steady state at small tilt angles and exhibits an oscillating behavior. On the side heating branch, a maximum heat transfer rate is obtained at a tilt angle of about 70° but the water volume was found to depend very weakly on the inclination of the cavity. Under the effect of subcooling, the interplay between conduction in the solid phase and convection in the liquid leads to an equilibrium ice-water interface which is most distorted at some intermediate cooling temperature.     

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures

Computational and experimental studies of the fluid motion and heat transfer characteristics of an incompressible fluid contained in a non-rectangular inclined enclosure are described in this paper. The enclosure has two 45° inclined side walls one of which was heated and the other cooled. The remaining two sides of the enclosure are parallel and insulated. The enclosure was rotated about the long axis in steps of 30° through 360°. Experiments were performed to study the effects of Rayleigh number, aspect ratios and orientation of the enclosure. The computational method uses a mesh transformation technique coupled with the introduction of ‘false transient’ parameters for the steady state solution of the problem. The experimental method uses smoke for flow visualization studies. With aspect ratios of 3 and 6, the results indicate that the heat transfer and fluid motion within the enclosure is a strong function of both the Rayleigh number and the cavity orientation angle. A minimum and a maximum mean Nusselt number occurred as the angle of inclination was increased from 0 to 360°. A transition in the mode of circulation occurred at the angle corresponding to the minimum or maximum rate of heat transfer. Stream lines and isotherms are presented for the most representative cases     

Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid

This paper discusses the results of a study related to natural convection cooling of a heat source located on the bottom wall of an inclined isosceles triangular enclosure filled with a Cu water-nanofluid. The right and left walls of the enclosure are both maintained cold at constant equal temperatures, while the remaining parts of the bottom wall are insulated. The study has been carried out for a Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁶, for a heat source length in the range 0.2 ≤ ε ≤0.8, for a solid volume fraction in the range 0 ≤ ?≤0.06 and for an inclination angle in the range 0° ≤ δ≤45°. Results are presented in the form of streamline contours, isotherms, maximum temperature at the heat source surface and average Nusselt number. It is noticed that the addition of Cu nanoparticles enhances the heat transfer rate and therefore cooling effectiveness for all values of Rayleigh number, especially at low values of Ra. The effect of the inclination angle becomes more noticeable as one increases the value of Ra. For high Rayleigh numbers, a critical value for the inclination angle of δ = 15° is found for which the heat source maximum temperature is highest.     

Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number

Finite element predictions of two-dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half-divider in water for Rayleigh number up to 10¹¹ and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.     

Natural convection in an inclined rectangular porous cavity with uniform heat flux from the side

The problem of natural convection in an inclined rectangular porous layer enclosure is studied numerically. The enclosure is heated from one side and cooled from the other by a constant heat flux while the two other walls are insulated. The effect of aspect ratio, inclination angle and Rayleigh number on heat transfer is studied. It is found that the enclosure orientation has a considerable effect on the heat transfer. The negative orientation sharply inhibits the convection and consequently the heat transfer and a positive orientation maximizes the energy transfer. The maximum temperature within the porous medium can be considerably higher than that induced by pure conduction when the cavity is negatively oriented. The peak of the average Nusselt number depends on the Rayleigh number and the aspect ratio. The heat transfer between the two thermally active boundaries is sensitive to the effect of aspect ratio. For an enclosure at high or low aspect ratio, the convection is considerably decreased and the heat transfer depends mainly on conduction.     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Cooling of an electronic board situated in various configurations inside an enclosure: lattice Boltzmann method

Natural convection heat transfer in a square cavity induced by heated electronic board (as a thin plate at constant temperature) is investigated using the lattice Boltzmann method. Lattice Boltzmann simulation of natural convective heat transfer in a cavity in the presence of internal straight obstacle has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The present work is an extension to our previous paper (see Nazari and Ramzani in Modares. Mech. Eng. 11(2):119–133, 2011) in which the effects of position and dimensions of obstacle on the flow pattern and heat transfer rate are completely studied. A suitable forcing term is represented in the Boltzmann equation. With the representation, the Navier–Stokes equation can be derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Top and bottom of the cavity are adiabatic; the two vertical walls of the cavity have constant temperatures lower than the plate’s temperature. The study is performed for different values of Grashof number ranging from 10³ to 10⁵ for different aspect ratios and position of heated plate. The effect of the position and aspect ratio of heated plate on heat transfer are discussed and the position of the obstacle in which the maximum rate of heat transfer is investigated in both vertical and horizontal situation. The obtained results of the lattice Boltzmann method are validated with those presented in the literature.     

Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×10⁶ and 1.43×10⁶. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.     

Performance characteristics of HFC-134a and HFC-410A refrigeration system using a short-tube orifice as an expansion device

In the present article, the effect of heat source temperature, heat sink temperature, short-tube orifice diameter and short-tube orifice length on the performance characteristics of HFC-140A and HFC-134a refrigeration system using a short-tube orifice as expansion device, i.e., mass flow rate, cooling capacity, compressor pressure ratio, power consumption, and second law efficiency are experimentally studied. The short-tube orifices diameters ranging from 0.849 to 1.085 mm with length ranging from 10 to 20 mm are used in this examination. The test run are done at heat source temperature ranging between 16.5 and 18.5°C, and heat sink temperature ranging between 30 and 35°C. The results show that the tendency of second law efficiency is increased as the short-tube orifice diameter and heat source temperature are enhanced, but it is decreased by increasing the short-tube orifice length and heat sink temperature. Under the similar conditions, the mass flow rate, cooling capacity, and compressor power consumption obtained from HFC-410A are higher than those obtained from HFC-134a.     

Effects of walls temperature variation on double diffusive natural convection of Al2O3–water nanofluid in an enclosure

The effect of wall temperature variations on double diffusive natural convection of Al₂O₃–water nanofluid in a differentially heated square enclosure with constant temperature hot and cold vertical walls is studied numerically. Transport mechanisms of nanoparticles including Brownian diffusion and thermophoresis that cause heterogeneity are considered in non-homogeneous model. The hot and cold wall temperatures are varied, but the temperature difference between them is always maintained 5 °C. The thermophysical properties such as thermal conductivity, viscosity and density and thermophoresis diffusion and Brownian motion coefficients are considered variable with temperature and volume fraction of nanoparticles. The governing equations are discretized using the control volume method. The results show that nanoparticle transport mechanisms affect buoyancy force and cause formation of small vortexes near the top and bottom walls of the cavity and reduce the heat transfer. By increasing the temperature of the walls the effect of transport mechanisms decreases and due to enhanced convection the heat transfer rate increases.     

Turbulent free convection in a vertical converging channel

This paper presents the results of experimental and numerical investigations of the problem of turbulent natural convection in a converging-plate vertical channel. The channel has two isothermally heated inclined walls and two adiabatic vertical side walls. The parameters involved in this study are the channel geometry represented by the channel width at exit, the inclination of the heated walls and the temperature difference between the heated walls and the ambient. The investigation covered modified Rayleigh numbers up to 10⁸ in the computational study and up to 9.3 × 10⁶ in the experimental work. The experimental measurements focused on the velocity field and were carried out using a PIV system and included measurements of the mean velocity profiles as well as the root-mean-square velocity and shear stress profiles. The experiments were conducted for an inclination angle of 30°, a gap width of 10 mm and two temperature differences (∆T=25.4°C and 49.8°C). The velocity profiles in the lower part of the channel indicated the presence of two distinct layers. The first layer is adjacent to the heated plate and driven by buoyancy forces while the second layer extends from the point of maximum velocity to the channel center plane and driven mainly by shear forces. The velocity profile at the upper portion of the channel has shown the merging of the two boundary layers growing over the two heated walls. The measured values of the Reynolds shear stress and root mean square of the horizontal and vertical velocity fluctuation components have reached their maximum near the wall while having smaller values in the core region. The computational results have shown that the average Nusselt number increases approximately linearly with the increase of the modified Rayleigh number when plotted on log–log scale. The variation of the local Nusselt number indicated infinite values at the channel inlet (leading edge effect) and high values at the channel exit (trailing edge effect). For a fixed value of the top channel opening, the increase of the inclination angle tended to reduce flow velocity at the inlet section while changing the flow structure near the heated plates in such a way to create boundary-layer type flow. The maximum value of the average Nusselt number occurs when θ = 0 and decreases with the increase of the inclination angle. On the other hand, the increase of the channel width at exit for the same inclination angle caused a monotonic increase in the flow velocity at the channel inlet.     

Effects of surface radiation on natural convection in a rayleigh-benard square enclosure: steady and unsteady conditions

Coupled laminar natural convection with radiation in air-filled square enclosure heated from below and cooled from above is studied numerically for a wide variety of radiative boundary conditions at the sidewalls. A numerical model based on the finite difference method was used for the solution of mass, momentum and energy equations. The surface-to-surface method was used to calculate the radiative heat transfer. Simulations were performed for two values of the emissivities of the active and insulated walls (ɛ₁=0.05 or 0.85, ɛ₂=0.05 or 0.85) and Rayleigh numbers ranging from 10³ to 2.3×10⁶ . The influence of those parameters on the flow and temperature patterns and heat transfer rates are analyzed and discussed for different steady-state solutions. The existing ranges of these solutions are reported for the four different cases considered. It is founded that, for a fixed Ra, the global heat transfer across the enclosure depends only on the magnitude of the emissivity of the active walls. The oscillatory behavior, characterizing the unsteady-state solutions during the transitions from bicellular flows to the unicellular flow are observed and discussed.     

Double-diffusive natural convection in a porous enclosure partially heated from below and differentially salted

This paper reports numerical results of two-dimensional double-diffusive natural convection in a square porous cavity partially heated from below while its upper surface is cooled at a constant temperature. The vertical walls of the porous matrix are subjected to a horizontal concentration gradient. The parameters governing the problem are the thermal Rayleigh number (Ra=100 and 200), the Lewis number (Le=0.1, 1 and 10), the buoyancy ratio (−10N10) and the relative position of the heating element with respect to the vertical centerline of the cavity (δ=0 and 0.5). The effect of the governing parameters on fluid characteristics is analyzed. The multiplicity of solutions is explored and the existence of asymmetric bicellular flow is proved when the heated element is shifted towards a vertical boundary (δ=0.5). The solutal buoyancy forces induced by horizontal concentration gradient lead to the elimination of the multiplicity of solutions obtained in pure thermal convection when N reaches some threshold value which depends on Le and Ra.     

Natural convection in an inclined enclosure containing internal energy sources and cooled from below

Natural convection in an inclined enclosure from below and containing internally heated fluid has been investigated using a finite difference calculation procedure. Results have been obtained for Rayleigh number values up to 10⁶ and for inclination angles of 30 and 60°. For internal Rayleigh numbers that are much larger than the external Rayleigh number, the flow rises in the interior and moves down both the hot and cold walls. On the other hand, if the external Rayleigh number has a larger magnitude, the flow moves upwards along the hot surface and downwards along the cold surface. For the latter situation, the inner core is multicellular in nature at large external Rayleigh numbers. The average heat flux ratio along the cold surface (convective heat flux/corresponding conduction heat flux) increases with increasing external Rayleigh number and decreasing internal ratio is non-monotonic in nature. The heat flux ratio along both surfaces is observed to be strongly dependent on the inclination angle at high external Rayleigh numbers. A maximum in the local heat flux along the cold surface is obtained in the vicinity of x/L = 1 where hot fluid, either from the interior or directly from the opposite hot wall, meets the surface. Along the hot wall, a maximum in the heat flux ra flo