The influence of geometrical parameters on the natural convection heat transfer in a pipe with transverse square-shaped fins

Abstract

The natural convection heat transfer in a single pipe transversely finned with square-shaped plates is considered. A mathematical model for determining the heat flux transferred by this heat transfer device is constructed, which takes into account the actual temperature distribution pattern over the fin height. The analytical solution obtained by Sparrow and Lin was used to determine the effectiveness of square fins. For determining the transferred heat flux, the heat-transfer coefficient variation pattern over the fin height proposed by V.F. Yudin was taken into account. The transferred heat flux to the device weight ratio was adopted as the objective function to determine the thermal device performance efficiency. It has been found that the objective function has a maximum if both the fins and the carrying pipe are considered as the heat transfer surface. If heat transfer from only the surface of fins is considered, the objective function dependence on the fin size has a monotonic pattern and its maximum is not observed. The effect the fin pitch and the square fin height have on the transferred heat flux and on the specific heat flux per unit mass is clarified. It is shown that the maximum heat flux is observed at the fin pitch equal to 5 mm, which does not depend on the fin height at the given fin thickness (5 = 0.6 mm) and the specified design conditions. The maximal transferred specific heat flux per unit mass is observed at a distance of 6--8 mm, which remains unchanged in further changing the fin pitch. The fin plate size at which the specific heat flux per unit mass reaches its maximum is determined. It is shown that this size does not depend on the fin pitch. The obtained results can be used for further optimization of the geometric parameters of space heating convectors, air cooling devices, and other devices used for space heating or heat removal purposes.