Development of heat transfer correlations for multi-row helically coiled tube heat exchangers used in surface water heat pump systems

For a type of multi-row helically coiled tube (MHCT) heat exchanger used in surface water heat pump systems, a series of numerical simulations for outside mixed and forced convections and experiments for natural convection are carried out with a conjugate thermal condition. The effects of geometric parameters of vertical spacing (Δy), horizontal spacing (Δx), tube length (L), and number of rows (K) on the outside Nusselt number (Nu_o) are detailed for 11 heat exchangers in different configurations. The results show that an increase in Δy or a decrease in K can increase Nu_o both in the forced and natural convections, whereas, there is a slight change in Nu_o as K > 2 or Δy−d_o≥d_o. Furthermore, Nu_o is insensitive to changes in Δx and L. The correlations for natural and forced convections are first developed by considering the effects of these geometric parameters. Then, the correlation for mixed convection is modeled using a function of the natural and forced convections. A dimensionless parameter, Gr/Re^1/r, is proposed to divide the convection region and can be used to select the corresponding correlation for the design of the MHCT heat exchanger in different surface-water bodies.