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 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 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.     

Experimental study of natural convection heat transfer of air layers in vertical annuli under high rayleigh number conditions

In this paper experimental investigations of natural convection heat transfer of air layers in vertical annuli are presented. In these experiments, the surface of the inner cylinder is maintained at a constant heat flux condition and the outer cylinder is cooled in the atmosphere. In order to obtain the convective contribution, the overall heat transfer data are corrected for thermal radiation and axial conduction losses from the end plates in the annuli. Special emphasis, in these investigations, was placed on the high Rayleigh number region where no experimental data are available in the literature. Data were obtained for Rayleigh numbers greater than 10⁹. The radius ratios studied were 2.03 and 3.92, and the aspect ratios studied were 23.94 and 66.67. Heat transfer correlations for average Nusselt numbers were developed for different Rayleigh number regions. For the low Rayleigh number region the results of this paper agree with the correlations reported in the literature. Much needed data and correlations for the high Rayleigh number region are obtained for the first time. These results improve the predictive ability for the heat transfer characteristics in the high Rayleigh number region. ©1999 Scripta Technica, Heat Trans Asian Res, 28(1): 50–57, 1999     

NATURAL CONVECTION OVER A ROTATING CYLINDRICAL HEAT SOURCE IN A RECTANGULAR ENCLOSURE

A numerical study of laminar two-dimensional natural convection heat transfer from a uniformly heated horizontal cylinder rotating about its center, and placed in an isothermal rectangular enclosure, is performed using a spectral element method. The physical aspects of the flow and its thermal behavior are studied for a wide range of pure natural convection to mixed convection at low and high rotational speeds of the cylinder. The computer program has been validated against experimental correlations available on pure natural convection of heated bodies in enclosures. The rotation of the cylinder has been found to enhance the heat transfer. At low ratios of Rayleigh number to the square of the rotational Reynolds number, Ra / Re_ω ², the maximum temperature on the cylinder surface is decreased by as much as 25–35% from similar cases with fixed cylinders. At moderate values of Ra/ Re_ω ², the thermal plume rising above the cylinder is shifted in the rotation direction and the angular shift decreases as Ra / Re_ω increases. The rotation produces more uniform temperature and shear stress distributions around the cylinder surface. At high Rayleigh numbers the increase in rotation reduces the cylinder mean Nusselt number by 2–10% as compared with the fixed cylinder.     

Experimental Study of Air Pressure Effects on Natural Convection From a Horizontal Cylinder

The topic of this research is the importance of convection heat transfer coefficient and the effect that ambient pressure has on it. Toward this end, an experimental study was performed to investigate the effects of air pressure on natural convection heat transfer from a horizontal cylinder. Pressure was varied from 1 to 220 kPa and the convection coefficient was obtained in the temperature range from 50 to 100°C. Various diagrams and tables were obtained to show the dependence of natural convection on pressure. A correlation was derived to describe the heat transfer coefficient and Nusselt number as a function of pressure and Knudsen number or Rayleigh and Knudsen number. The rate of heat transfer by radiation was also compared with convection at different temperatures and pressures.     

Experimental Study of Free Convection Heat Transfer from Horizontal Isothermal Cylinders Arranged in Vertical and Inclined Arrays

Laminar free convection heat transfer from vertical and inclined arrays of horizontal isothermal cylinders in air were investigated experimentally. Experiments were carried out using a Mach-Zehnder interferometer. For the vertical array, the cylinder spacing (center to center) varied from 2 to 5 cylinder diameter. The same range of vertical spacing also was used for the inclined array. The horizontal spacing varied from 0 to 2 cylinder diameter in the inclined array. The Rayleigh number based on the cylinder diameter varied between 10³ and 3× 10³. The effect of vertical and horizontal cylinder spacing and Rayleigh number on the heat transfer from each individual cylinder and the whole array were investigated. It is found that the free convection heat transfer from any individual cylinder in the array depends on its position relative to the others. Heat transfer correlations have been developed for any individual cylinder in the vertical and inclined arrays and for the arrays. Also the experiment was carried out on a single cylinder for a comparison with the results from other research.     

Natural convection from a confined horizontal cylinder: the optimum distance between the confining walls

The laminar natural convection from an isothermal horizontal cylinder confined between vertical walls, at low Rayleigh numbers, is investigated by theoretical, experimental and numerical methods. The height of the walls is kept constant, however, their distance is changed to study its effect on the rate of the heat transfer. Results are incorporated into a single equation which gives the Nusselt number as a function of the ratio of the wall distance to cylinder diameter, t/D, and the Rayleigh number. There is an optimum distance between the walls for which heat transfer is maximum.     

Application of artificial neural networks for prediction of natural convection from a heated horizontal cylinder

A generalized neural network analysis for natural convection heat transfer from a horizontal cylinder is developed in this paper. Cylinder diameter, cylinder surface temperature and ambient temperature are selected as the input parameters, while the Nusselt number as the output. A three-layer network is used for predicting the Nusselt number. The number of the neurons in the hidden layer was determined by a trial and error process together with cross-validation of the experimental data evaluating the performance of the network and standard sensitivity analysis. The trained network gives the best values over the correlations with less than 2.5% mean relative error. The experimental data of the average Nusselt number over the horizontal cylinders having different diameters of 4.8 mm–9.45 mm are from Atay?lmaz and Teke [1]. The results from the trained network were compared with the proposed correlation for the average Nusselt number over the cylinder and it is shown that the results are in satisfactory agreement. The Nusselt numbers obtained from the experimental study were seen to be consistent by ± 20% with the well known correlations for natural convection heat transfer from horizontal cylinder developed by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4]. Moreover it is seen that that results from the trained network show absolute agreement with the experimental data in ± 5% deviation band better than the correlations given by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4].     

Experimental and numerical study of the natural convection from a heated horizontal cylinder

Natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically. Experimental study had taken place in different environmental temperature in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The environmental and cylinder surface temperatures varied between 10 °C–40 °C and 20 °C–60 °C respectively. In the experimental study, two cylinders having different diameters of 4.8 mm–9.45 mm are used and constant heat flux was applied. On the basis of the experimental data, a correlation for the average Nusselt number over the cylinder is proposed in the range of 7.4 10¹ < Ra < 3.4 10³. The proposed correlation is compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is shown that the results are in satisfactory agreement. The problem is also investigated numerically. The experimental data and the numerical results fall in ± 20% band. The numerical results obtained in this study are also compared with the results of Merkin. The characteristics of trend lines are similar.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

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     

Combined forced and natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper reports the results of an experimental study of heat transfer by combined forced and natural convection from a horizontal cylinder embedded in a porous medium composed of randomly packed glass spheres saturated with water. The direction of the flow of water was horizontal and normal to the longitudinal axis of the cylinder. The diameter of the cylinder, D, was 11.45mm and the equivalent diameter of the glass spheres was 3.072mm. It is shown that the condition Gr_k/Re²_D ⩽ 0.5 represents a conservative criterion for segregating heat transfer data that are predominantly governed by forced convection from those in which natural convection effects are significant. A correlation hypothesis for convection heat transfer which is based upon four assumptions, primary among which is that the flow can be (conceptually) regarded as being composed of ‘coarse’ and ‘fine’ components, is presented. This hypothesis is shown to provide a basis for successfully correlating a set of experimental heat transfer data that extends from the Darcy regime into the turbulent regime and spans the intervening Forchheimer and transition regimes. It is suggested that the correlation procedure adopted here may yield useful results if applied to other geometries such as, for example, forced convection heat transfer in ducts packed with porous media.     

Natural convection heat transfer of the low prandtl number fluid with solidified layer formation

Experimental and analytical studies have been performed on natural convection heat transfer in the low Prandtl number fluid of the molten metal with a rapid solidified layer formation. The experimental results on the relationship between the Nusselt number and Rayleigh number were compared with the existing correlations. The temperature distribution and the heat transfer rate have been evaluated using the numerical model. The experimental study has shown that a solidified layer formation leads to a decrease of natural convection heat transfer rate in the metal pool, due to the solidified layer's action as a conducting thermal barrier. The experimental results are more similar to Globe and Dropkin's correlation than any others. Even though the Rayleigh number rapidly decreases due to an increase of the solidified layer thickness, the Nusselt number does not rapidly decrease because of the aspect ratio effect. The numerical results on the temperature profile and the heat transfer rate in the metal pool region match well with the experimental data.     

Heat transfer from small objects in microgravity: Experiments and analysis

Heat transfer over a sub-millimeter spheroidal solid is of interest in many engineering processes. One important mechanism of heat transfer in the above processes is natural convection which leads to heat transfer rates many times larger than that of pure conduction. Despite the huge literature devoted to natural convection heat transfer rates over spheres (and to a smaller extent over spheroids) there is not a generally accepted correlation especially for small Rayleigh numbers. Existing correlations for external geometries predict a progressively increasing contribution of natural convection to heat transfer with respect to gravity (starting from zero gravity). To test the validity of these correlations, experiments are performed for the estimation of heat transfer rates at low gravity. Heat pulses are given to a miniature thermistor with a nearly spheroidal shape immersed in a liquid and its thermal response is registered during heating in parabolic flights. The contribution of natural convection to heat transfer is undoubtedly estimated from runs in which acceleration varies from 0 to 1.8 g. Surprisingly enough, the experiments showed that the Rayleigh number must take a minimum value before non-negligible effect of natural convection on heat transfer appears (existence of a threshold Rayleigh number). In the absence of natural convection (below Ra_thr) the experimental thermal response curves can be successfully described by approximating solutions of the transient heat conduction equation for the spheroidal geometry of the thermistor. Apparently, additional research is needed regarding the natural convection around sub-millimeter objects for small Rayleigh numbers.     

Transient natural convection and heat transfer during the storage of granular media

Transient heat transfer in an originally isothermal cylinder filled with a porous medium after sudden change of wall temperature is studied experimentally and computationally. Lab-scale experiments with water as the interstitial fluid are used in order to imitate the conditions prevailing in large, air-filled industrial silos. The proposed model assumes isotropy of the porous medium, local thermal equilibrium between the phases, Darcy flow and applicability of the Boussinesq approximation. Its predictions are in satisfactory agreement with the experimental results. Simulations reveal the role of dimensionless parameters like the modified porous media Rayleigh number and the cylinder aspect ratio. A criterion for neglecting the influence of natural convection on heat transfer is established.     

Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material

Natural convection heat transfer enhancement from a horizontal cylinder with a textile coating is studied experimentally and numerically. The coating layer may be used for two purposes. According to the thickness of the coating it may be used as an insulating material or for surface augmentation. In the experimental study, two cylinders having different diameters of 4.8 mm and 9.45 mm are used. The bare cylinders having a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 and 12.8 mm respectively after coating and constant heat flux was applied to all bare and wrapped cylinders. Experimental study was carried out at different ambient temperatures in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The ambient and cylinder surface temperatures (T_∞ and T_w) varied between 10 °C – 40 °C and 20 °C – 60 °C respectively. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was observed. On the basis of the experimental data average Nusselt numbers were calculated and compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is seen that the results are in good agreement. The problem is also investigated numerically. Experimental and the numerical results fall in ± 30% band.     

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     

Natural cooling of horizontal cylinder using Artificial Neural Network (ANN)

Artificial Neural Network (ANN) is used to determine natural convection heat transfer and fluid flow around a cooled horizontal circular cylinder having constant surface temperature. Governing equations of natural convection were solved using finite volume technique by writing a FORTRAN code to generate the database for ANN scheme and Rayleigh number is changed from Ra = 10⁶ to 10⁸. Results obtained from numerical solutions were used for training and testing the ANN approach. A comparison was performed among the soft programming (ANN), experimental observation and Computational Fluid Dynamic (CFD) code. It is observed that ANN soft programming code can be used more efficiently to determine cold plume and thermal field generated around a cold cylinder. Based on the results a new correlation is developed for natural convection of cooled horizontal cylinders.     

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