Numerical Study of the Tube Effect on Natural Convection in an Inter-Plate Channel

Abstract

The article presents a numerical study of the effect the diameter of a central tube in the slit-shaped channel between the finned radiator plates has on the heat flux transferred under natural convection conditions. The numerical solution is compared with the calculation carried out according to the Elenbaas formula and with the experimental relationship obtained by Karami et al. It is shown that if there is a tube in the radiator interfin channel, the heat flux transferred under natural convection conditions decreases; the larger the tube diameter, the more significant the heat flux decrease is. This is because of a decrease in the total heat transfer area when there are small relative distances between the fins and a decrease in the air velocity if there is an obstacle. A correction to the Elenbaas formula is proposed for calculating the dimensionless heat transfer coefficient in the slit channel between the radiator vertical plates with a central tube at a constant fin temperature, and the correction application domain is determined. The correction has the form of a power dependence that includes the ratio of heat transfer surface areas with and without the tube, and also such parameters as the tube diameter and fin height, and air density at the temperature of fins and environment. It has been determined that with small tube diameters and distances between the fins, for describing the heat flux in a correct way, it is sufficient to use the formula that takes into account the change in the total heat transfer area. The heat flux values obtained from the calculations carried out according to the proposed relationship differ from the results of calculations carried out using the relationship of Karami et al. by no more than 5.5% in the range of central tube diameter to fin height ratios of 0‒0.4 and the interfin distance to fin height ratios of 0.03‒0.12.