Cylindrical heat sources are used to model the fuel pins in the reactor core of a nuclear power plant and also in the spent fuel storage. This research was aimed at studying convection through slender cylinders arranged in a square array, placed inside a ventilated enclosure. Four cylindrical heat sources were manufactured, each having L/D ratio of 6.1. These heat sources were placed inside an enclosure which had one inlet and three outlets. At first, optimum configuration of outlets for heat transfer was found by keeping the inlet speed of air and heat flux constant. This optimum outlet configuration was then used to study the effect of changing heat flux on heat transfer. Speed of air was kept constant at 0.7m/s throughout this study. The heat flux was changed, ranging from 79.83W/m² to 513.59W/m² and Rayleigh number changed accordingly from 2.093×10⁹ to 8.575×10⁹. It was observed that by increasing Rayleigh number, Nusselt number decreased along with the heat transfer.

1.     Introduction

Convective heat transfer is one of the important areas of research in heat transfer. Efficient heat transfer from heat sources has been an important topic of research over the past few years. Cylindrical heat sources are widely used in many industries such as building, solar and nuclear industry. In nuclear industry, fuel pins inside reactor core and spent fuel storage can be modeled as cylindrical heat sources with convective fluid flowing around them. Due to such vast applications and importance, researchers around the world have studied heat transfer through cylindrical heat sources both experimentally and computationally to solve issues related to temperature control.

There are many configurations in which convective heat transfer through cylindrical heat sources can be studied. The medium through which the heat is transferred, could be finite or infinite, the heat sources could be single or multiple, and could be ranged in a  horizontal, vertical or inclined orientation, the convective fluid could be air, water or any other suitable fluid, the type of convection could be free, forced or mixed convection and the enclosure could be ventilated or non-ventilated. All these different types of configurations have been studied previously. Popiel [1] reviewed heat transfer through slender cylinders in which he used the data put forth by Cebeci [2] and differentiated between heat transfer through thick and slender cylinders. This is important since thick cylinders can be approximated as flat plates and thin cylinders cannot. Griffiths and Davis [3] studied convection in 1922, where they studied vertical cylinders in isothermal condition. They did experiments on various cylinders, keeping their diameters constant and varying the length of the cylinders and determined the average Nusselt numbers. Later on, Morgan [4] used that data to find two correlations, which are valid over their respective ranges of dimensionless number. Fujii et al. [5] did experiments on isothermal vertical cylinders, using three different fluids i.e. water (Pr = 5), mobiltherm oil (Pr = 100) and spindle oil (Pr = 100). Separate correlations were then developed for the local Nusselt numbers for each of the fluids used. Jarral and Campo [6] carried out an experimental study, using isoflux boundary condition and determined local Nusselt numbers in terms of Rayleigh number for air. They did their experimentation using cylinders with three different slenderness ratios. Ali Riaz et al. [7] performed experiments on vertical cylinders and horizontal cylinders to find the heat transfer coefficients. The Nusselt number was observed to decrease from the bottom of the cylinder, towards the top, up to a certain point after which it started to increase. The reason behind this is that thermal boundary layer thickness increases from bottom to top of the cylinder. In the horizontal configuration, however, the local Nusselt number was least at the outlet and maximum at the inlet. Arshad et al. [8] performed experiments with natural convection at high Rayleigh numbers using nine cylinders in a 3×3 array placed vertically and enclosed inside an enclosure. It was observed that surface temperatures increased up to a specific point and then decreased, this is attributed to mixing, which results in increase in heat transfer. K. Hata et al. [9] studied heat transfer through natural convection in laminar region, using vertical rods placed in a 7×7 array placed in liquid sodium. The effect of pitch-to-diameter (P/D) ratio, array size, bundle geometry and Rayleigh number on heat transfer, was observed by calculating Nusselt number under different conditions. Yuji Isahai and Naozo Hattori [10] worked on a numerical study of heat transfer through natural convection in a heated rod bundle, that was placed vertically in an equilateral triangle configuration inside an enclosure. They used a total of 19 cylinders in their study in a hexagonal formation, with the center cylinder dedicated for instrumentation. Five different P/D ratios were studied which varied between minimum of 1.1 to maximum of 7.0. Abdul Jabbar Khalifa and Zaid Ali [11] studied heat transfer through natural convection in single and in multiple cylinders. For multiple cylinder configuration, they used nine cylinders in a 3 x 3 array, out of which only three cylinders were heated. A square array configuration was used for cylinders having a P/D ratio of 2. The fluid used for heat transfer was water. Heat flux was varied and its effect was studied. K. Tehseen et al. [12] performed a numerical study, using ANSYS, to find the effects of different orientations of core on heat transfer along bare circular tubes and tube bundles. They found that the heat transfer was directly proportional to the heated length and inversely proportional to the inside diameter of the tube.

Convection heat transfer is affected by geometry parameters of enclosure such as position and area of vents. There has been limited research considering such parameters and, therefore, this found the motivation behind the present experimental study. In this present work, cylindrical heat sources were used, which can be used to model fuel pins inside a nuclear reactor or spent fuel inside spent fuel storage. Heat transfer through a 2×2 array of heat sources in square configurations was studied. Heat transfer between heat sources and air was tabulated and compared in different arrangements of the outlets present on the enclosure. The results were then plotted showing the relation between Nusselt number and modified Rayleigh number.

2.     Mathematical Modeling

The equations used for the present system were:

                                                           (2.1)

                                              (2.2)

Due to small thickness of aluminum tube, all the heat from the heat source is conducted to the outer surface.

                      (2.3)

                                 (2.4)

Where, h_avg is the average heat transfer coefficient.

And    

For calculating the local heat transfer coefficients, the following formula was used.

                                      (2.5)

Heat losses through radiation can be calculated by:

                                    (2.6)

ε is 0.04 for Aluminum and σ is 5.67×10^-8 W/m² K⁴. Due to small emissivity of Aluminum and a very low value of σ, radiation can be neglected and it can be assumed that all the heat transfer from the outer surface of heat sources is via convection.

The formulae for Nusselt number and modified Rayleigh number are:

                                                                                                               (2.7)

                                                                                                         (2.8)

3.     Experimental Setup

Four identical sources each having a diameter of 50.8 mm and a slenderness ratio of 6.1 were manufactured. Each of these heat sources had a rated power of 1000W. Outer surface of heat sources was made of Aluminum. Each of the heat sources was equipped with four K-type thermocouples, the positions shown in figure 1. In figure 1(b), the stars show the thermocouple facing the flow channel and the triangles represent the thermocouples on the opposite side of the flow channel.

The heat sources were placed inside a wooden enclosure of dimensions 20”x20”x20”. There were three outlets of same size (4”x2”) in the enclosure, one at the top and one each on right top and left top of the enclosure. For the measurement of the ambient temperature, a thermocouple was installed near inner boundary of the wooden enclosure. To convert the data provided by the thermocouples into temperatures, PANGU data acquisition system was used. All these components of the experimental setup are shown in figure 2.

In this research work, data acquisition system was used which had a calibration uncertainty of 1^oC and data scatter was observed to be 5.1^oC. Total uncertainty in measurement of temperature was calculated to be 4.8%. Uncertainty in voltage was 1% with a full scale reading of 600V and in current, the uncertainty was 1.5% with a full scale reading of 10 A. Anemometer that was used for the measurement of velocity of air had an uncertainty of 0.03m/s. Also, different dimensions that were measured e.g., diameter of the aluminum pipes, length of aluminum pipes and size of inlet and outlet vents had an uncertainty of about 2mm. Each experiment was repeated thrice so that the results are reported with precision and accuracy. Mean values were shown in the graphs and error bars were displayed, representing standard deviation in the results.

4.     Results and Discussions

In the experimentation phase, the outlet configuration was first optimized to give best heat transfer and then the further experimentation was carried out using different heat fluxes.

4.1.   Optimization of Outlets Configuration

Five cases were studied, each case differing from the other on the basis of locations of the outlets’ opening.

In the natural convection case, top outlet was opened and inlet at the bottom was opened, but the fan was remained switched off. Air flowed freely and naturally from the bottom and exited through the top outlet. In other four cases, bottom inlet was opened with the fan operating at a constant speed of 0.7m/s. The corresponding outlets were opened for each case and temperatures were measured which were then used to find the values of heat transfer coefficients for each case.

In figure 3, the near outlet refers to the outlet which is closest to that particular cylinder and far outlet is the outlet which is at a distance from that cylinder. For example, for cylinders 1 and 2, near outlet is the left outlet and far outlet is the right outlet as shown in figure 1.

It is evident from the plots above, that for any given cylinder, the heat transfer is the least in case of natural convection and improved for forced convection as more outlets were then opened. Heat transfer is maximum when all the three outlets were opened. This gave an optimum configuration of outlets with respect to heat transfer.

4.2.   Effect of Heat Flux on Heat Transfer

A total of five different heat fluxes were used to study their effect on heat transfer. Heat fluxes were changed from 79.83 W/m² to 513.59 W/m². The data was also translated in the form of dimensionless numbers. Due to change in heat fluxes, modified Rayleigh number, Ra^* changed from a minimum value of 2.093×10⁹ at heat flux of 79.83 W/m² to a maximum value of 8.575×10⁹ at heat flux of 513.59 W/m².  The results for these five cases are shown in figure 4.

It is clear form the plotted points that the heat transfer dropped as the flux and modified Rayliegh number was increased. Nusselt number did not change much as the modified Rayleigh number increased from 2.09×10⁹ to 5.79×10⁹. Beyond that point, with increase in the modified Rayleigh number, there is a certain decrease in the values of Nusselt number. The reason behind this behaviour is attributed to the fact that the outlets were not large enough to allow heat transfer away from the cylinders and the temperatures were seen to go higher as the heat flux and modified Rayleigh number of the heaters was increased.

5.     Conclusions

Heat sources were manufactured and arranged in a square array inside a ventilated enclosure with one inlet and three outlets at three different walls of the enclosure. Experiments were carried out for five different outlet configurations at constant heat flux and constant speed of air form the inlet to determine the optimum configuration of the outlets for heat transfer. After that, experiments were carried out for five different heat fluxes ranging from 79.83 W/m² to 513.59 W/m² and the results were plotted in the form of dimensionless numbers.

The results of the experiments can be summarized as following:

• Heat transfer improved by almost 25% in the cases with forced convection i.e., when the fan was switched on and all three outlets were opened as compared to the natural convection case when the fan was off.
• Heat transfer from the cylinders seemed to remain almost constant with increase in heat flux and the modified Rayleigh number up to a certain range and then decreased as the modified Rayleigh number was increased further.
• The reason could be attributed to the fact that the size of the outlets was small (4” x 2”) as compared to the size of the enclosure (20”x20”x20”).

6.     References