Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planes

Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier–Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485–502, 2001     

Fluid flow and heat transfer of natural convection over upward‐facing,horizontal heated circular disks

Natural convective flows induced over upward‐facing, circular disks were investigated experimentally. The test disks were heated with uniform temperatures and their diameters were varied from 20 to 500 mm. The test fluid was air and water at room temperature. The flow fields over heated disks were visualized with dye and smoke. The results showed that the ambient fluid first enters the outer edge of the disk and, then, separates three‐dimensionally from the surface at certain distance downstream of the edge when the Rayleigh numbers exceed certain critical values. The separated flow is gradually distorted and a fully turbulent state is accomplished in the central portion of the disk. It was found that the onset and the pitches of the separation points could be predicted with the Rayleigh numbers. The overall Nusselt numbers of the disks were also measured in a wide range of Rayleigh numbers from 2 × 10⁵ to 3 × 10¹⁰. The results showed almost identical Nusselt numbers between air and water. Based on these results, empirical equations for the overall Nusselt numbers were proposed. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 339– 351, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20215     

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.     

Natural convection heat transfer in a circular enclosure

Natural convection heat transfer in a circular enclosure, one half of which was heated and the other half of which was cooled, was investigated experimentally, focusing on the effect of the inclination angle. The experiments were carried out with water. Flow and temperature field were visualized by using the aluminum and liquid-crystal suspension method. The results show that with downward heating the heat transfer coefficient increased as the inclination angle of the boundary between the heating wall and the cooling wall approached the vertical. But with upward heating, the heat transfer coefficient showed minimal change, exhibiting a small peak value when the inclination angle was γ ˜ –45°. The heat transfer coefficient of a flat circular enclosure was estimated from the circular enclosure's heat transfer coefficient. These results can be explained by the obtained flow and temperature fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 152–163, 1999     

Natural convection heat transfer between horizontal concentric rectangular pipes

Natural convection heat transfer between concentric rectangular pipes was studied numerically. It has been found that rolls of even numbers form in the region on the top surface of the inner pipe. The number of rolls depends on both the Rayleigh number and the aspect ratio. An oblong circulation of flow forms in the region between the side surface of the inner pipe and the surface of the outer pipe. The aspect ratio does not have much effect on the average Nusselt number at the side surface of the inner pipe. The relation between the Nusselt and Rayleigh numbers at the top surface resembles that of the Rayleigh-Bénard convection obtained by Silveston (Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 68). The average Nusselt number at the bottom surface of the inner pipe decreases with increasing aspect ratio because the region where heat transfer is affected significantly by convection is limited. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(4): 271–283, 1998     

Natural convection heat transfer from a horizontal cylinder using holographic interferometry

The natural convection heat transfer from a horizontal cylinder with a uniform wall temperature in an infinite space was experimentally investigated. Infinite fringe interferograms of the cylinder heated from 295.15 to 355.15 K were recorded using the holographic interferometry technique. The temperature field around the cylinder was reconstructed based on phase difference recovery using a MATLAB code. The distributions of the local and average Nusselt numbers over the cylinder were then obtained. A correlation of the average Nusselt number was proposed for a Rayleigh number range of 2.7–6.0 × 10⁴. The experimental results are in good agreement with previous correlations, with a deviation of ±10%. The holographic interferometry technique was found to be satisfactory and reliable for heat transfer analyses.     

Natural-convection heat transfer to air from a horizontal array of cylinders with different surface temperatures

Heat transfer measurements were made on natural convection around horizontal in-line arrays of cylinders whose surface temperatures were different from each other. Through the experiments for a three-cylinder array, a correlation was obtained for the heat transfer coefficient of the array-center cylinder. By using the correlation with some assumptions, the heat-flux distributions could be estimated for an array of five cylinders which were heated to their respective temperatures. Consequently, it was found that both the correlation and the method proposed here were useful in the estimation of heat-flux distributions for a horizontal array of cylinders. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 116–121, 1997     

水平窄空间沸腾换热的数理模型研究

窄空间只有在间距小于汽泡脱离直径时，对沸腾传热强化才有比较显的效果。窄空间沸腾强化传热的机理在于较大的泡底微层加速了蒸发传热和窄空间中被加热的液体周期性地与池液进行容积交换。水平圆盘窄空间中的汽泡生长分为性质完全不同的自由生长期和抑制长大期；在一个周期内，加热面的总传热量等于壁面传导给窄空间液体的热量与通过合体泡底微层蒸发潜热之和。在对圆形水平窄空间的沸腾传热的现象和机理进行分析的基础上，提出了窄空间的沸腾换热过程的数理模型；进而对窄空间沸腾的本质规律在理论上进行了初步探索，并得到分析解。理论计算结果与实验数据比较表明，该分析解适合于中低壁面过热度的情形。由于问题的复杂性，该模型仍需不断完善。     

Turbulent heat transfer of natural convection between two vertical parallel plates

We measure heat transfer coefficients of natural convection between two vertical smooth parallel plates heated uniformly in the laminar, transition, and turbulent regions. The heat transfer characteristics are experimentally investigated with changing width, δ, between the vertical parallel plates, wall heat flux, q_w, overall watercourse length, L,of the vertical parallel plate and heating conditions. For natural convection between the vertical parallel plates, in the turbulent region of , the heat transfer is strongly suppressed owing to the effect of combined convection. On the contrary, the heat transfer in the laminar region is enhanced due to the tunnel effect. These tendencies become pronounced with decreasing δ and increasing L.The location of the heat transfer reduction shifts downstream with increasing q_w under a fixed δ. Furthermore, under smaller δ, we cannot clearly distinguish the transition process in accordance with both the heat transfer enhancement in the laminar region and the heat transfer reduction in the turbulent region. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 56–67, 2002     

An Experimental and Numerical Study of Natural Convection Heat Transfer in Horizontal Annuli between Eccentric Cylinders

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Film boiling heat transfer from a horizontal circular plate facing downward

The two‐dimensional, steady, pool film boiling heat transfer from a horizontal circular plate facing downward to a stagnant saturated liquid is studied theoretically. It is assumed that the vapor‐liquid interface is smooth and that radiation can be disregarded. The relevant governing equations for the vapor film are solved for saturated water at atmospheric pressure using an improved two‐equation boundary‐layer integral method. It is shown that the dimensionless temperature profile is affected by the wall superheat ΔT_sat and that the ratio of Nu to X^0.2 is an increasing function of ΔT_sat. Here, Nu represents the mean Nusselt number and X the film‐boiling Rayleigh number. In addition, it is revealed that the one‐equation boundary‐layer integral method developed by Nishio and colleagues is fairly accurate in predicting the film thickness, the representative radial velocity, and the mean Nusselt number. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 72–84, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10071     

Natural convection heat transfer from two horizontal cylinders using a large lateral shearing interferometer

Natural convection heat transfer from two horizontal cylinders in the air was investigated experimentally and numerically. Two cylinders were spaced at 1.3, 1.8, and 2.7 cylinder diameters horizontally. The experiments were carried out by large lateral shear interferometry (LSI) for various Rayleigh numbers in the range of 10³ to 10⁴. Large LSI is common path interferometry with the advantages of simple structure, strong antivibration, and fewer required optical components. It is not necessary for LSI to perform a complex algorithm to restore wavefront with a large shear amount. Simple and infinite fringe interferograms of the cylinders heated from ambient temperature 282.15 to 723.15 K were obtained. A numerical simulation was carried out with ANSYS-Fluent 18.0. The influence of two factors, the distance between the cylinders, and the Rayleigh number, on the heat transfer of two horizontal cylinders was examined. The average Nusselt number and local Nusselt number were determined from the experimental results and numerical results, respectively, and the two results were in good agreement. The rising direction for the plume flow pattern of each horizontal cylinder was no longer simply vertically upward but was inclined toward the central symmetry axis of the two cylinders. In addition, the heat transfer from a cylinder increased with the cylinder spacing at any Rayleigh number.     

Natural convection heat transfer from upward-facing plates in saline water

Saltwater or brackish water is used as a coolant in most industries. Therefore, understanding the heat transfer processes and hydrodynamics during the natural convection in saline water is crucial for enhancing the efficiency of a heat exchanger. This study elaborates on the natural convection heat transfer in saline water under atmospheric conditions. A DC power supply is used to regulate the power given to the heater in a liquid pool for thermal analysis. The pool liquid comprises solutions with varying salinity from 0%, 0.2%, 0.5%, and 2%. The effect of varying salinity on the heat transfer coefficient and the thermal aspects encountered during the desalination process is analyzed. The temperature distribution across the surface of the heater is monitored using an infrared camera. It is studied for the solution of different salinities. The heat transfer coefficient and Nusselt number are investigated during natural convection for normal water and salt solution of different concentrations. It is inferred from the study that in the regime of natural convection, there is no significant difference in the Nusselt number for normal water and saltwater for the lower value of temperature difference between the plate and pool. The heat transfer coefficient in 0.2% saline water is higher as compared to the other solutions.     

Natural convection heat transfer between concentric rectangular parallelepipeds

Natural convection heat transfer between concentric rectangular parallelpipeds was studied numerically for low Rayleigh numbers Ra(≦ 3500) with aspect ratios of the inner parallelepiped of 2.0, 4.0, 6.0, and 8.0. It has been found that the flow patterns for the higher Rayleigh numbers in the space over the inner parallelpiped are ring or rectangular rolls. The number of rolls increases with the aspect ratio. The flow pattern in the side space is an oblong circulation, which extends into the bottom space. The local Nusselt number distribution on the top surface of the inner parallelpiped has peaks at the stagnation points. The relation between the Nusselt and Rayleigh numbers on the top surface is similar to that of the Rayleigh–Bénard convection obtained by Silveston (Chandrasekhar S.Hydrodynamic and Hydromagnetic Stability, 1961, p 68, Oxford University Press), while on the side and bottom surfaces the Nusselt number increases proportionately with the power of the Rayleigh number. © 2001 Scripta Technica, Heat Trans Asian Res, 30(2): 152–163, 2001     

双绝热圆柱对水平三角腔内自然对流影响的数值研究

针对含双绝热圆柱的底部加热水平等腰三角腔内空气的稳态层流自然对流开展研究.通过有限容积法对控制方程进行了数值求解,其中瑞利数的变化范围为104 ～106,圆柱体的尺寸比则分别为0（无圆柱体）、1/8和1/4.基于计算结果对自然对流的流动与传热特性随瑞利数和尺寸比的变化规律进行了分析和讨论.结果表明,双绝热圆柱的存在较大程度上改变了三角腔内自然对流的流型和温度场分布,但对整体传热影响较小,仅略微提高了平均努赛尔数,强化传热的效果在尺寸比为1/8时较为明显.     

Flow and heat transfer of natural convection around an upward‐facing horizontal plate with a vertical plate at the edge

Natural convective flows around an upward‐facing horizontal heated plate with a vertical plate at the edge were investigated experimentally. Of particular concern were the influences of the vertical plate on the fluid flow and the heat transfer of the horizontal plate. The flow and temperature fields adjacent to the horizontal plate were visualized with dye and a liquid‐crystal thermometry. The results show that the vertical plate obstructs the flow from the top of the vertical plate, while the flow from the open edge of the horizontal plate covers the whole horizontal surface when the height of the vertical plate exceed H/W = 0.14 for adiabatic vertical plate and H/W = 0.1 for the heated vertical plate. The local heat‐transfer‐coefficients of the horizontal plate were also measured. It was found that the vertical adiabatic plates deteriorate the heat transfer, while the heated vertical plates enhance the heat transfer from the horizontal plates. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(8): 527–539, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20033     

Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080     

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.     

Heat transfer enhancement of free convection from a heated horizontal plate

A device was developed to enhance heat transfer from heated horizontal plates. The device consists of six straight gutters with slits at the center for the introduction of air. Heat transfer coefficients were measured for several device heights above the heated surface. A height of about 10 mm was found to give rise to the highest heat transfer coefficients. In this case heat transfer rates were 1.2 to 1.4 times larger than those for smooth plates. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 26 (1): 30–38, 1997     

Natural convection heat transfer in eccentric horizontal annuli between a heated outer tube and a cooled inner tube with different orientation: The case of an elliptical outer tube

This study conducts numerical analyses and experiments on natural convection heat transfer in eccentric horizontal annuli between a heated outer tube and a cooled inner tube with different orientations. The outer tube is an elliptical tube, and the inner tube is a cylindrical tube. Experiments are conducted with the outer tube oriented to the vertical side and horizontal side, respectively. The numerical analyses were performed by changing the oriented angle and eccentricity parameters. Results obtained for different conditions are presented as temperature profiles, flow patterns, local Nusselt numbers, and total heat transfer. It is found that the heat transfer enhancement effect or heat transfer obstruction effect for the total heat transfer is changed by eccentricity and oriented angle. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 624–635, 2001