An Approximate Model for Slug Flow Heat Transfer in Channels of Arbitrary Cross Section

In this paper, a novel approximate solution to determine the Nusselt number for thermally developed, slug (low-prandtl), laminar, single phase flow in channels of arbitrary cross section is presented. Using the Saint-Venant principle in torsion of beams, it is shown that the thermally developed Nusselt number for low-prandtl flow is only a function of the geometrical parameters of the channel cross section, i.e., area, perimeter and non-dimensional polar moment of inertia. The new proposed model is compared with the existing numerical results for elliptic, rectangular, regular polygonal, flat plate, isosceles triangular, equilateral triangular and circular sector channels. The model predicts the Nusselt number for the above mentioned channels within the about 10% or better with the exception of the circular sector in very small aspect ratios. The new model is expected to be accurate for other singly connected channels and can be used to determine the fully developed turbulent Nusselt number for liquid metal flows. Finally, the proposed model is used to determine the slug flow Nusselt number for unavailable geometries in the literature such as rhombic, circular segment, annular sector channel as well as rectangular channel with semicircular ends.