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.     

Free convective mass transfer at down-facing horizontal surfaces with free or collared edges

Free convective mass transfer at down-facing horizontal surfaces was experimentally studied using the electrochemical technique with emphasis on the influence of the edge condition. It was found that the mass transfer rate is significantly lower for collared surfaces which was explained in terms of the different fluid flow conditions at the disc edge. The previous literature was critically reviewed and reported correlations were compared with those found for the present case, which, for discs with free edges, was found to be Sh_d = 2.08 Ra_d^0.178 for Ra_d in the range 7 × 10³ to 1 × 10¹¹.     

The effect of a surfactant monolayer on oxygen transfer across an air/water interface during mixed convection

A set of laboratory experiments are presented that reveal the effect of a surfactant monolayer on the transport of oxygen across an air/water interface during mixed convection conditions. The experiments were conducted in a wind/water tunnel where forced convection was imposed via the air flow, and natural convection by heating the water bulk above the air temperature, resulting in mixed convection conditions. The data acquired during these experiments were used to develop a parameterization between the Sherwood number for oxygen transport Sh and the Reynolds Re and Rayleigh Ra numbers. This parameterization was obtained for the case of a clean water surface and for a water surface covered with a surfactant monolayer. The data reveal that, at a given Ra and Re, the presence of a surfactant monolayer reduces Sh by approximately one order of magnitude. The elasticity of the air/water interface which results from the presence of a surfactant is used to explain these results. The data also show that Sh was not sensitive to Re. For both the clean and surfactant cases, Sh increases with Ra.     

Numerical investigation of bubble coalescence characteristics under nucleate boiling condition by a lattice-Boltzmann model

A numerical study was performed to investigate the characteristics of bubble growth, detachment and coalescence on vertical, horizontal, and inclined downward-facing surfaces. The FlowLab code, which is based on a lattice-Boltzmann model of two-phase flows, was employed. Macroscopic properties, such as surface tension (σ) and contact angle (β), were implemented through the fluid–fluid (G_σ) and fluid–solid (G_t) interaction potentials. The model predicted a linear relationship between the macroscopic properties (σ,β) and microscopic parameters (G_σ,G_t). The simulation results on bubble departure diameter appear to have the same parametric dependence as the empirical correlation. Hydrodynamic aspects of bubble coalescence are investigated by simulating the growth and detachment behavior of multiple bubbles generated on horizontal, vertical, and inclined downward-facing surfaces. For the case of horizontal surface, three distinct regimes of bubble coalescence were represented in the lattice-Boltzmann simulation: lateral coalescence of bubbles situated on the surface; vertical coalescence of bubbles detached in a sequence from a site; and lateral coalescence of bubbles, detached from the surface. Multiple coalescence was predicted on the vertical surface as the bubble detached from a lower elevation merges with the bubble forming on a higher site. The bubble behavior on the inclined downward-facing surface was represented quite similar to that in the nucleate boiling regime on a downward-facing surface.     

Conjugate heat transfer in inclined open shallow cavities

Conjugate heat transfer in inclined open shallow cavities has been numerically studied. A thick wall facing the opening is heated by a constant heat flux, sides perpendicular to the heated wall are insulated and the opening is in contact with a fluid at constant temperature and pressure. Conjugate heat transfer by conduction and natural convection is studied by numerically solving equations of mass, momentum and energy. The governing parameters were: Rayleigh numbers, Ra from 10⁶ to 10¹², conductivity ratio, k_r from 1 to 60, cavity aspect ratio, A=H/L from 1 to 0.125, dimensionless wall thickness, ?/L from 0.05 to 0.20 and the inclination angle, ? from 0° to 45° from the horizontal. Isotherms and streamlines are produced, heat and mass transfer is calculated. It is found that volume flow rate, is an increasing function of Ra, A, ?/L, ?, and a decreasing function of k_r. Heat transfer, Nu is an increasing function of Ra, ?/L, and a decreasing function of k_r. A mixed pattern is found with respect to A and ?. In the former, Nu is an increasing function of the aspect ratio up to a critical Rayleigh number, above which the relationship changes and it becomes a decreasing function of A. In the latter case, Nu is a decreasing function at low Raleigh numbers and an increasing one at high Rayleigh numbers.     

Developing laminar mixed convection with heat and mass transfer in horizontal and vertical tubes

The effects of the solutal and thermal Grashof numbers on the flow, temperature and concentration fields in tubes with uniform heat flux and concentration at the fluid-solid interface have been investigated numerically using a three-dimensional axially parabolic model. Results show a complex development of the flow field which is strongly influenced by the values of the two Grashof numbers and by the tube inclination. For vertical tubes the flow field is also influenced by the relative direction of the flow and the buoyancy forces. In general, very close to the tube inlet forced convection boundary layer development dominates. Further downstream, the effects of solutal buoyancy predominate while those of thermal origin determine the flow field far downstream and, in particular, the fully developed conditions. The axial evolution of the wall shear stress τ_z, the Nusselt number Nu_z and the Sherwood number Sh_z in both horizontal and vertical tubes are presented for different combinations of the two Grashof numbers. For horizontal tubes and vertical tubes with upward flow these three variables are greater than the corresponding ones for forced convection. The opposite is true for downward flow in vertical tubes.     

Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate

Natural convection heat transfer and fluid flow characteristics in horizontal and vertical narrow enclosures with heated rectangular finned base plate have been experimentally investigated at a wide range of Rayleigh number (Ra) for different fin spacings and fin lengths. Quantitative comparisons of finned surface effectiveness (ε) and heat transfer rate between horizontal and vertical enclosures have been reported. In comparison with enclosure of a bare base plate, insertion of heat conducting fins always enhances heat transfer rate. Optimization of fin-array geometry has been addressed. The results gave an optimum fin spacing at which Nusselt number (Nu_H) and finned surface effectiveness (ε) are maximum. It has been found that: (1) increasing fin length increases Nu_H and ε; (2) increasing Ra increasesNu_H for any fin-array geometries and (3) for any fin-array geometry and at Ra > 10,000, increasing Ra decreases ε while for fin-array geometries of large fin spacing and at Ra < 10,000, increasing Ra increases ε. Useful design guidelines have been suggested. Correlations of Nu_H have been developed for horizontal and vertical enclosures. Correlations predictions have been compared with previous data and good agreement was found.     

Numerical investigation of several physical and geometric parameters in the natural convection into trapezoidal cavities

Natural convection in trapezoidal cavities, especially those with two internal baffles in conjunction with an insulated floor, inclined top surface, and isothermal left-heated and isothermal right-cooled vertical walls, has been investigated numerically using the Element based Finite Volume Method (EbFVM). In numerical simulations, the effect of three inclination angles of the upper surface as well as the effect of the Rayleigh number (Ra), the Prandtl number (Pr), and the baffle’s height (H_b) on the stream functions, temperature profiles, and local and average Nusselt numbers has been investigated. A parametric study was performed for a wide range of Ra numbers (10³ ? Ra ? 10⁶) H_b heights (H_b = H¹/3, 2H¹/3, and H¹), Pr numbers (Pr = 0.7, 10 and 130), and top angle (θ) ranges from 10 to 20. A correlation for the average Nusselt number in terms of Pr and Ra numbers, and the inclination of the upper surface of the cavity is proposed for each baffle height investigated.     

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.     

Experimental assessment of the effects of body force, surface tension force, and inertia on flow boiling CHF

The interfacial instabilities important to the modeling of critical heat flux (CHF) in reduced-gravity systems are sensitive to even minute body forces, especially for small coolant velocities. Understanding these effects is of paramount importance to both the reliability and safety of two-phase thermal management loops proposed for future space and planetary-based thermal systems. Unfortunately, reduced gravity systems cannot be accurately simulated in 1g ground-based experiments. However, ground-based experiments can help isolate the effects of the various forces (body force, surface tension force and inertia) which influence flow boiling CHF. In this project, the effects of the component of body force perpendicular to a heated wall were examined by conducting 1g flow boiling experiments at different orientations. Boiling experiments were performed using FC-72 in vertical and inclined upflow and downflow, as well as horizontal flow, and with the heated surface facing upward or downward relative to gravity. CHF was very sensitive to orientation for flow velocities below 0.2 m/s and near-saturated flow; CHF values for downflow and downward-facing heated surface were much smaller than for upflow and upward-facing surface orientations. Increasing velocity and subcooling dampened the effects of flow orientation on CHF. For saturated flow, the vapor layer characteristics fell into six different regimes: wavy vapor layer, pool-boiling, stratification, vapor stagnation, vapor counterflow, and vapor concurrent flow. The wavy vapor layer regime encompassed all subcooled and high-velocity saturated conditions at all orientations, as well as low-velocity upflow orientations. Prior CHF correlations and models were compared, and shown to predict the CHF data with varying degrees of success.     

Flow visualization of natural convection in a tall,air-filled vertical cavity

Natural convection of air in a tall vertical cavity was studied using a smoke patterns and interferometry. Experiments covered Rayleigh numbers of 4850 < Ra < 54,800 and aspect ratio A ≈ 40. Secondary cells were noted at Ra as low as 6228. The flow was stable at Ra < 10⁴. As Ra exceeded 10⁴ the flow became irregular, the core flow became increasingly unsteady and 3-D motion became evident. Interferometry showed that most of the temperature drop exists in boundary layers near the walls. The core is well mixed and of relatively uniform temperature with little or no vertical stratification.     

Experimental study on heat and fluid flow in LNG tank heated from the bottom and the sidewalls

Heat and fluid flow in a layer heated from the bottom and the sidewalls simulating an underground LNG tank is experimentally studied under high Rayleigh number (7.5×10¹⁰<Ra<1.5×10¹³) conditions by electrochemical mass transfer technique. The experiment yielded the following results. When sidewalls are heated, the heat transfer along the bottom surface is reduced. Heat transfer along sidewalls is independent of bottom heating, and is modeled by an equation for laminar natural convection flow even for Ra>10⁹. Convective flow pattern in the tank is visualized by the Schlieren technique. The results, combined with local mass transfer measurement, show that Sh of the bottom surface is reduced in the area where impinging downward flow exists. It is caused by the suppression of thermal plume formation by the downward flow. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 417–430, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20031     

Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers

The critical Rayleigh number Ra_C at the onset of natural convection was studied by linear stability analysis for high porosity anisotropic horizontal porous layers of uniformly arraying vertical thin circular wires stretched across a hot and a cold surface. Navier–Stokes equations including flow resistance by the wires were solved since Darcy’s law cannot be applied due to high porosity. Ratio of permeability in the horizontal direction to the vertical direction is constant to be 0.5 but ratio of effective thermal diffusivity ξ is changed dependent on wire materials. The critical Rayleigh number Ra_C for the case of ξ = 1 obtained by the analysis agreed well with the experiment.     

Computation of turbulent free convection in left and right tilted porous enclosures using a macroscopic k–ε model

Comparisons of computations for turbulent natural convection within clockwise and counter-clockwise inclined cavities, filled with a fluid saturated porous medium, are presented. The finite volume method in a generalized coordinate system is applied. Oblique walls are maintained at constant but different temperatures, whereas horizontal surfaces are kept insulated. Flow and heat transfer characteristics are investigated for Rayleigh number up to 10⁴ and inclination angles up to 45°, in both directions of rotation. Turbulent is handled using a macroscopic two-equation model with a wall function. In this work, the turbulence model is first switched off and the laminar branch of the solution is obtained. Subsequently, the turbulence model is included and the solution merges to the laminar branch for a reducing value of Ra_m. Present computations are compared with published results and the influence of the inclination angle on Ra_cr is analyzed, for both the left and right rotating directions. For Ra_m greater than around 10⁴, both laminar and turbulent flow solutions deviate, possibly indicating that a critical value for Ra_m was reached. Both left and right rotation of the hot wall reduce Nu, but rotating the hot wall on the counter-clockwise direction decreases Nu at a faster rate than when bending the cavity to the right.     

Heat transfer by free convection from the inside surface of the vertical and inclined elliptic tube

Free convection from the inside surface of vertical and inclined elliptic tubes of axis ratio (a:b) 2:1 with a uniformly heated surface (constant heat flux) is investigated experimentally. The effects of orientation angle (α) and inclination angle (ϕ) on the heat transfer coefficient were studied. The orientation angle (α) is varied from 0° (when the major axis is horizontal) to 90° (when the major axis is vertical) with steps of 15°. The inclination angle (ϕ) is measured from the horizontal and varied from 15° to 75° with steps of 15°. The vertical position is considered as a special case of the inclined case when ϕ = 90. The experiments covered a range of Rayleigh number, Ra from 2.6 × 10⁶ to 3.6 × 10⁷. The local and average Nusselt numbers are estimated for different orientation angles and inclination angles at different Rayleigh numbers. The results obtained showed that the local Nu increased with the increase of axial distance from the lower end of the elliptic tube until a maximum value near the upper end, and then, it gradually decreased. The average Nu increases with the increase of α or ϕ at the same Ra. The results obtained are correlated by dimensionless groups and with the available data of the inclined and vertical elliptic tubes.     

Nucleate Boiling Enhancements on Porous Graphite and Microporous and Macro–Finned Copper Surfaces

Enhancements in nucleate boiling heat removal with dielectric liquids, by increasing either the bubbles nucleation sites density and/or the wetted surface area, are desirable for immersion cooling of high-power computer chips. This article presents the results of recent investigations of nucleate boiling enhancement of FC-72, HFE-7100, and PF-5060 dielectric liquids on porous graphite, copper microporous surfaces, and copper surfaces with square corner pins, 3 mm × 3 mm in cross-section and 2, 3, and 5 mm tall. All surfaces have a footprint measuring 10 × 10 mm. These investigations examined the effects of liquid subcooling up to 30 K and surface inclination, from upward-facing to downward-facing, on nucleate boiling heat transfer coefficient and critical heat flux. Natural convection of dielectric liquids for cooling chips while in the stand-by mode, at a surface average heat flux <20 kW/m², is also investigated for the different surfaces.     

Momentum and heat transfer in a turbulent cylinder wake behind a streamwise oscillating cylinder

The work aims to understand the effect of an oscillating circular cylinder on momentum and heat transport in the turbulent wake of a downstream identical cylinder, which is slightly heated. The oscillating amplitude, A, was 0.79d (d is the cylinder diameter) and the frequency was 0.17f_s for L/d = 2.5 and 0.24f_s for L/d = 4, where L and f_s are the cylinder centre-to-centre spacing and the frequency of vortex shedding from the downstream cylinder, respectively, at A = 0. The velocity and temperature fields were measured using a three-wire probe at 10d behind the stationary cylinder and a Reynolds number of 5920 based on d and the free-stream velocity. It is found that the upstream cylinder oscillation modifies the frequency of vortex shedding from the stationary cylinder, which is locked on with one harmonic of the oscillating frequency. This harmonic frequency is nearest to and below the natural vortex-shedding frequency. Furthermore, the wake response to the oscillation depends on L/d in terms of the cross-stream distributions of mean velocity, Reynolds stresses, temperature variance and heat fluxes; the turbulent Prandtl number decreases at L/d = 4 but increases at L/d = 2.5. The observations are linked to whether the flow regime experiences a change under the upstream cylinder oscillation.     

MHD natural convection in a laterally and volumetrically heated square cavity

A numerical study is presented of unsteady two-dimensional natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. The flow is characterized by the external Rayleigh number, Ra_E, determined from the temperature difference of the side walls, the internal Rayleigh number, Ra_I, determined from the volumetric heat rate, and the Hartmann number, Ha, determined from the strength of the imposed magnetic field. Starting from given values of Ra_E and Ha, for which the flow has a steady unicellular pattern, and gradually increasing the ratio S = Ra_I/Ra_E, oscillatory convective flow may occur. The initial steady unicellular flow for S = 0 may undergo transition to steady or unsteady multicellular flow up to a threshold value, Ra_I,cr, of the internal Rayleigh number depending on Ha. Oscillatory multicellular flow fields were observed for S values up to 100 for the range 10⁵-10⁶ of Ra_E studied. The increase of the ratio S results usually in a transition from steady to unsteady flow but there have also been cases where the increase of S results in an inverse transition from unsteady to steady flow. Moreover, the usual damping effect of increasing Hartmann number is not found to be straightforward connected with the resulting flow patterns in the present flow configuration.     

Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity

Turbulent double-diffusive natural convection is of fundamental interest and practical importance. In the present work we investigate systematically the effects of thermal Rayleigh number (Ra), ratio of buoyancy forces (N) and aspect ratio (A) on entropy generation of turbulent double-diffusive natural convection in a rectangle cavity. Several conclusions are obtained: (1) The total entropy generation number (S_total) increases with Ra, and the relative total entropy generation rates are nearly insensitive to Ra when Ra ≤ 10⁹; (2) Since N > 1, S_total increases quickly and linearly with N and the relative total entropy generation rate due to diffusive irreversibility becomes the dominant irreversibility; and (3) S_total increases nearly linearly with A. The relative total entropy generation rate due to diffusive and thermal irreversibilities both are monotonic decreasing functions against A while that due to viscous irreversibility is a monotonic increasing function with A. More important, through the present work we observe a new phenomenon named as “spatial self-copy” in such convectional flow. The “spatial self-copy” phenomenon implies that large-scale regular patterns may emerge through small-scale irregular and stochastic distributions. But it is still an open question required further investigation to reveal the physical meanings hidden behind it.