Natural convection heat transfer in the open space between two horizontal circular planes with different temperatures

A vertical cylinder maintained at room temperature is located right above a horizontal circular heated plane to constitute a narrow air space between the plane and the cylinder bottom surface. Natural convection heat transfer in the space is experimentally investigated. Average heat transfer coefficients of the heated plane are presented with the variation of space distance and Rayleigh number, and are compared with the predictions of the correlation equations which have been proposed for the space between two infinite parallel plates. Visualized flow patterns above the heated plane are also shown. The relation between the flow pattern and the heat transfer coefficient is discussed to clarify the mechanism of heat transfer in the narrow space. As a result, a heat transfer correlation is proposed, which is applicable over a wide range of space distances. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 521–531, 2001     

Improvement of the basic correlating equations and transition criteria of natural convection heat transfer

In this paper, improvements in the basic physical laws of natural convection heat transfer were implemented in two major respects by incorporating recent research findings in this field. A preferred transition criterion was adopted in this paper to correlate all of the experimental data. Since transition correlations are primarily flow stability problems, the Grashof number, instead of the Rayleigh number, was found to be the preferred criterion. Furthermore, in the case of natural convection heat transfer from a horizontal cylinder, a series of experimental data in the high‐Rayleigh‐number regions recently became available. These data made it possible to establish new reliable correlations and also to test the validity of previous correlations. It is concluded that the previous correlation for a horizontal cylinder in high‐Rayleigh‐number regions was based on unreliable experimental results. The transition correlation for a horizontal cylinder occurred at much higher values of Rayleigh number than the previous recommendation. In the case of natural convection heat transfer from a vertical plate, more accurate property values for air under pressurized conditions are now available. This made it possible to replot the reliable data of Saunders. From this result and the experimental result of Warner and Arpaci, a new set of basic correlations in natural convection heat transfer for laminar, transitional, and turbulent regimes are recommended. These recommendations reflect a better understanding of the basic physical laws in the field of heat convection. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 293–300, 2001     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Natural convection heat transfer of water in a horizontal gap with downward-facing circular heated surface

An experimental study of natural convection heat transfer from a downward-facing horizontal circular heated surface in a water gap has been carried out. The results were correlated in different forms of Nusselt number vs Rayleigh number according to different independent variables. The effects of different characteristic length and temperature were discussed and the gap size is the preferred characteristic length, the average fluid temperature between bulk temperature and the saturated temperature is the preferred film temperature. For the estimation of the natural convection heat transfer under the present conditions, empirical correlations in which Nusselt number is expressed as a function of Rayleigh number, or Rayleigh and Prandtl numbers both, may be used. However, the best accuracy is provided by an empirical correlation which expresses the Nusselt number as a function of the Rayleigh and Prandtl numbers, as well as the gap width-to-heated surface diameter ratio, the dimensionless temperature. Artificial neural networks have been trained successfully for analyzing the influences of the gap width-to-heated surface diameter ratio and the wall temperature difference between the temperature of wall and ambient fluid on natural convection heat transfer based on the experimental data in the present study. The results show that the Nusselt number will increase by increasing the gap ratio and decrease by increasing the wall temperature difference.     

Natural convection heat transfer of water in a horizontal circular gap

An experimental study on the natural convection heat transfer on a horizontal downward facing heated surface in a water gap was carried out under atmospheric pressure conditions. A total of 700 experimental data points were correlated using Rayleigh versus Nusselt number in various forms, based on different independent variables. The effects of different characteristic lengths and film temperatures were discussed. The results show that the buoyancy force acts as a resistance force for natural convection heat transfer on a downward facing horizontal heated surface in a confined space. For the estimation of the natural convection heat transfer under the present conditions, empirical correlations in which Nusselt number is expressed as a function of the Rayleigh number, or both Rayleigh and Prandtl numbers, may be used. When it is accurately predicted, the Nusselt number is expressed as a function of the Rayleigh and Prandtl numbers, as well as the gap width-to-heated surface diameter ratio; and uses the temperature difference between the heated surface and the ambient fluid in the definition of Rayleigh number. The characteristic length is the gap size and the film temperature is the average fluid temperature.     

Free convection suppression using honeycomb cellular materials

It is well-known that an undisturbed layer of air forms an effective insulating barrier against heat transfer because of its low thermal conductivity. In confined air spaces any initiation of free convection will inevitably lead to an increase in the rate of heat transfer across the gap for a fixed temperature difference. To delay the onset of convection for horizontal layers of fluid it has been shown theoretically and experimentally that the introduction of cell walls will effectively raise the critical Rayleigh number by providing more shear surfaces within the fluid. This paper reports on some of the earlier work dealing with the horizontal cell (this being vertical cellular constraining walls within a horizontal fluid layer) and extends the theory to cover the case of the inclined cell and the vertical cell. The photographic results of flow visualization studies are also presented as it is felt that an inspection of the flow patterns leads to a fuller understanding of the problem. Whereas the concept of the critical Rayleigh number is quite valid for the horizontal layer of fluid heated from below, it is shown to be inadequate for the inclined fluid layer as would be found in an inclined solar absorber of the flat plate type. Instead, the solutions of the equations show that convection must be initiated for any temperature gradient to be established between the absorber plate and the glass cover plate. Although the honeycomb may be effective in suppressing convection in the horizontal case, the effect of such constraints on the fluid in the inclined case is negligible as far as suppression of natural convection is concerned.     

Fluid flow and heat transfer in the transition process of natural convection over an inclined plate

The present study deals with fluid flow and heat transfer in the transition process of natural convection over an inclined plate. In order to examine the mechanism of the transition process, experiments on the flow and heat transfer were performed for various plate inclination angles in the range of 20 to 75°. The wall temperature and fluid flow fields were visualized using a liquid crystal sheet and fluorescent paint, respectively. The visualization confirmed that separation of a boundary layer flow took place, and the onset point of streaks appeared over the plate wall when the modified Rayleigh number exceeded a characteristic value for each inclination angle. The local Nusselt number in the transition range was proportional to the one‐third power of the local modified Rayleigh number. By introducing a nondimensional parameter, a new correlation between visualizations of the flow and temperature fields and heat transfer was proposed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 648–659, 2001     

Assessment of thermal characteristics of square wavy plates

In this paper, the thermal characteristics and air flow behavior over heated square plate of wavy configurations are assessed. Two cases of heated wavy configurations were considered, one having an elliptical and other with the sinusoidal cross‐sectional shape to augment heat transfer rate over the plate. To explore the impact of wavy configurations of plate on convective heat transfer, the Rayleigh numbers in the range of 10⁴ to 10¹³ were considered. The steady‐state two‐dimensional momentum and energy equations were solved using a validated numerical model. The numerical results in terms of Nusselt numbers, Rayleigh numbers, aspect ratio (AR), and flow/temperature distribution over the plate are presented. The variations in the heat transfer coefficient and temperature contours with Rayleigh number and AR of waves were concentrated for both the elliptical and sinusoidal configurations of the plate. The results obtained indicate that the enhancement in heat transfer rate from the heated plate depends on the Rayleigh number, the AR of waves, plate configuration, and the Prandtl number.     

Fluid flow and heat transfer of natural convection over upward‐facing,horizontal, heated plate shrouded by a parallel insulated plate

The present paper describes experimental results on the fluid flow and heat transfer of natural convection between a horizontal, heated plate facing upward and an insulated cover plate. The experiments were carried out with water. The width of the test plates W and their gaps H were changed from W = 50 to 250 mm and H = 10 to 30 mm and ∞ (no cover plate). The visualization studies with dye and liquid crystal thermometry revealed that the roll cells whose axes are perpendicular to the flow direction appear and become dominant over the heated plate on decreasing the gap. These roll cells inhibit the heat transfer, and thus, the heat transfer coefficients become smaller than those without a cover plate. It was found that the flow and heat transfer in the region near the plate edges are unaffected by the cover plate. The conditions of the above reduced heat transfer were determined empirically. Moreover, nondimensional correlations for the local and the overall heat transfer coefficients of the heated plates are proposed based on the present heat transfer results. © 2000 Scripta Technica, Heat Trans Asian Res, 29(4): 333–346, 2000     

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.     

Effect of gap thickness on a rectangular-cell compound-honeycomb solar collector

Compound-honeycomb solar collectors employ a honeycomb to suppress natural convection and air gaps between the honeycomb and the absorber plate or the glazing to reduce conductive and radiative heat losses. Results of an experimental study on the effect of the thickness of these gaps on the total heat transfer across a compound honeycomb confined between two isothermal and low emissivity boundaries are presented. The honeycomb consists of rectangular cells with elevation aspect ratio 6.3 and plan aspect ratio 82 (15.8 mm thick, 206 mm wide and 2.5 mm deep), constructed from parallel glass strips. Plots of Nusselt number versus Rayleigh number are given for compound honeycombs with air gaps of thickness 1.6 mm, 3.3 mm, 6.4 mm and 9.6 mm above and below the honeycomb and for a compound-honeycomb layer with an air gap of thickness 6.4 mm below the honeycomb. Measurements are reported for tilt angles of 0°, 30° and 60° where the long dimension of the rectangular cells in the honeycomb is horizontal. As the air gaps' thickness increase, coupled conductive-radiative heat transfer is reduced, while the critical Rayleigh number is also reduced and convective heat transfer increases. However, even for relatively thick air gaps, the decrease in critical Rayleigh number is moderate, and the rectangular-cell compound honeycomb is found to be an effective convection suppressor. A compound honeycomb with air gaps above and below the honeycomb is shown to be superior in suppressing convection to a compound honeycomb of equal total thickness with only one air gap below the honeycomb.     

Natural Convection in a Square Enclosure with Two Horizontal Cylinders

This study investigates natural convection in a cooled square enclosure with two inner heated circular cylinders with the same diameter. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively. The immersed boundary method (IBM) to model the inner circular cylinders based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh numbers varying in the range of 10³ ≤ Ra ≤ 10⁵. The effect of the radius of inner circular cylinders in an enclosure on heat transfer and fluid flow at different Rayleigh numbers has been examined. As the Rayleigh number increases, the horizontal symmetry is broken and the asymmetry occurred from the smaller radius. As the radius decreases, the dependence of the convection on the Rayleigh number is considerable. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.     

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfer and volume flow rate than an unheated entry does. The presence of the unheated entry or unheated exit severely affects the convection process, especially at low Rayleigh number. A notable effect of an unheated exit on convection characteristics was found for the case of UHF at high Rayleigh number.     

An experimental investigation into forced, natural and combined forced and natural convective heat transfer from stationary isothermal circular disks

Experimental heat transfer data are presented and dimensionless correlations developed for forced, natural and combined assisting forced and natural convection for heated stationary isothermal circular disks over wide ranges of the Reynolds, Rayleigh and modified Reynolds numbers, respectively. Experiments with air were performed for a variety of disks ranging in diameter and thickness-to-diameter aspect ratio. The correlation for combined forced and natural convection was developed utilizing the concept of a modified Reynolds number which accounts for a buoyancy-induced velocity. Utilizing this concept, the experimental data and respective empirical correlations for all three convection modes can be collapsed and plotted on the same continuous curve.     

HEAT TRANSFER OF SOLID–LIQUID PHASE-CHANGE MATERIAL SUSPENSIONS IN CIRCULAR PIPES: EFFECTS OF WALL CONDUCTION

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.     

Lattice Boltzmann simulations of a radiatively participating fluid in Rayleigh–Benard convection

Thermal radiation is an integral part of the heat transfer process but it is often neglected due to the complexity involved in the analysis of radiative transfer. We use the lattice Boltzmann method as a common computational tool to solve all three modes of heat transfer: conduction, convection, and radiation. This tool is then used to analyze the effect of radiatively participating medium on Rayleigh–Benard convection. We find that increasing the effects of radiation (i) increases the critical Rayleigh number required for the onset of Rayleigh–Benard convection and (ii) affects the temperature and flow patterns of convection rolls significantly changing the net heat transfer between the hot and cold plates. Both these effects are due to the presence of radiation available as an additional mode of heat transfer. Thus, we establish that the unified lattice Boltzmann framework is an effective computational tool for heat transfer and propose to use this method for a large range of problems in science and engineering involving radiative heat transfer.     

Effects of Heating Location and Size on Natural Convection in Partially Heated Open-Ended Enclosure by Using Lattice Boltzmann Method

Natural convection heat transfer in an square enclosure, consisting of a partially heated west wall with east end open to ambient, is investigated numerically by using an in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10³–10⁶), heating location (bottom, middle, and top) on west wall, and dimensionless heating length (0.25–0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at the lowest Rayleigh number for bottom and middle heating, whereas at the highest Rayleigh number, all heating positions yield bifurcation and elongation of flow patterns with a secondary vortex near the lower side of open end. The middle and bottom heating locations show a linear increase in Nusselt number with heater size, whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in the case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of the average Nusselt number on flow governing parameters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

Local and average natural convection Nusselt numbers for a uniformly heated,shrouded or unshrouded horizontal plate

Experiments were performed to determine the local and average natural convection heat transfer characteristics for a uniformly heated, upward-facing horizontal plate shrouded by a parallel adiabatic surface situated above the plate. Three parameters were varied during the experiments, including the dimensionless height of the interplate gap (the no-shroud case serving as the upper limit), the dimensionless heating rate (the Rayleigh number), and the configuration of the surroundings (absence or presence of an obstruction and of supplemental insulation). Air was the heat transfer medium. The local Nusselt number was highest at the edge of the heated plate and decreased along the plate surface; at the center of the plate, the Nusselt number was about one-third of that at the edge. The local Nusselt number distributions, when normalized by the corresponding average Nusselt number, were found to be universal (i.e. independent of the parameters) for gap heights above a threshold value. Both the local and average Nusselt numbers were depressed at small gap heights but rebounded rapidly with increasing gap height. A critical gap height was found such that for values exceeding it, the average Nusselt number was independent of the presence or absence of the shroud.     

On the aspect ratio for which the heat transfer in differentially heated cavities is maximum

A numerical study of two dimensional natural convection of air in rectangular, differentially heated cavities was conducted. For three Rayleigh numbers the aspect ratio S was varied. It was found that heat transfer between the active walls has a maximum at each Rayleigh number, which is located at values of S between 1 and 2. The aspect ratio for which the maximum heat transfer occurs is determined by the process of transition from a shallow cavity regime to a slender cavity regime.