Influence of free convection on heat transfer during laminar flow in tubes with twisted tapes

Abstract

Experiments were carried out with a viscous oil flowing through a horizontal tube containing a twisted tape to understand and quantify heat transfer in the presence of free convection. Data were obtained with the constant wall heat flux boundary conditions for two tube diameters (31.7 mm and 22.8 mm) and for twist ratios varying from about 4 to 8. The Reynolds number (Re_b) was varied from 35 to 1756, the Prandtl number (Pr _b) from 73 to 404, the Rayleigh number (Ra_b) from 0.186 × 10⁶ to 33.57 × 10⁶, and the modified Rayleigh number (Ra_b⁺) from 5.59 × 10⁶ to 1.96 × 10⁹. The data points are classified into three zones: zone 1, where the secondary flow due to swirl is dominant; zone 2, which is a transition zone; and zone 3, where the secondary flow due to free convection is dominant. Data in zone 1 are found to agree well with the correlation of Hong and Bergles, while data in zone 3 are correlated against the Rayleigh number and the modified Rayleigh number in the forms Nu_b=C Ra_b ^m and Nu_b=C₁(Ra_b⁺)^m₁. In developing these correlations it is shown that the extent of transition zone 2 is small. Hence the simple generalized method recommended for all zones is to calculate the Nusselt number using the Hong and Bergles correlation and either one of the free convection correlations and then use the higher of the two values of Nusselt number obtained.