Natural convection and radiative heat transfer from constant surface area vertical helical coils: Effect of pitch and diameter

A numerical investigation of natural convection and surface radiation heat transfer from a vertically oriented isothermal helical coil has been presented in this work. Computations are carried out in the laminar flow regime to study the effects of Rayleigh number (10⁴≤ Ra ≤10⁸), surface emissivity (0 ≤ ε ≤1), and geometrical parameters of the helical coil like coil-diameter (8 ≤ D/d ≤ 24), and pitch (3 ≤ p/d ≤ 7.5) on the heat transfer characteristics. Temperature-dependent fluid properties are implemented to obtain accurate results at higher temperature ranges. The primary objective of this work is to compare heat transfer results and identify the optimum shape of the helical coil with the same surface area but different pitch and diameters. At a high Ra of 10⁸, when D/d rises from 8 to 24, the mass flow rate inducted through the helical coil augments about 2.25 times at p/d = 3 to nearly 3 times at p/d = 7.5 of the initial mass flow rate. As a result, the relative strength of convection heat loss upsurges with an increase in D/d and p/d. For a higher emissivity of the coil surface (ε = 0.9) and a lower Ra of 10⁴, heat transfer by convection contributes only about 13% of the total heat transfer. In contrast, the contribution of radiative heat transfer is only about 7% for a lower emissivity of the coil surface (ε = 0.1) and a higher Ra of 10⁸. Finally, a correlation for the average Nusselt number is developed based on the entire range of pertinent parameters considered in the present study.