The heat transfer characteristics in coiled tubes are determined by the peculiarities of the axial velocity distribution and of secondary flow (see Coiled Tube, Flow and Pressure Drop In.)
The mean heat transfer coefficient for laminar flow in coiled tubes is given by the equation:
where , , D is the tube diameter, Dcoil is the coil diameter, and a is the mean heat transfer around the tube perimeter.
The Nusselt Number in turbulent flow of water and superheated vapor (Re > Rec) in coiled tube is
where Nu0 is the Nusselt number in straight pipe which for Pr = 0.7 − 2 may be determined from the equation
The multiplier F(D/Dcoil) can be approximated as:
For turbulent flow in coiled tubes, the heat transfer coefficient distribution around the tube perimeter is essentially nonuniform. The nonuniformity is caused by the nonhomogeneity of the flow velocity and temperature distributions which can cause heat transfer from the inner to the outer generatrix. It is necessary to consider this when determining the heat transfer coefficient from surface temperature measurements. The Nusselt number distribution along the coiled tube perimeter for a vertical axis coil with Dcoil/D = 16 and for water flow (Re = 2 × 104) is presented in Figure 1. This shows that the heat transfer coefficient in the vicinity of the outer generatrix is approximately constant. Upon approaching the inner generatrix, the heat transfer coefficient decreases. The ratio of heat transfer coefficient for the outer and inner generatrices is approximately equal to 4. The heat transfer coefficient in the vicinity of the inner generatrix of a coiled tube coincides nearly with value α for a straight tube. The Nusselt number for straight tube is shown by Line 2 in Figure 1. The mean Nusselt number for a coiled tube is greater and the heat transfer coefficient increases with a decrease in the ratio Dcoil/D.
Figure 1. Variation in average heat transfer coefficient from the outer generatrix (x = 0°) to the inner generatrix (x = 180°) for water flow in a coiled tube (dotted line (2) shows value for the straight tube).
The heat transfer coefficient αLG for forced convective boiling of water in a coil for p = (0.1 − 0.2) MPa, m = (80 − 3000) kg/ (m2s), W/m2, Dcoil/D = 7 − 50 can be calculated from the equation
where ; αb is the heat transfer coefficient for pool boiling of water at the same pressure and wall temperature and α0 is given by
is the mean velocity of vapor-water mixture, hLG is the latent heat of evaporation and x is the quality. Wall temperature fluctuations appear when burnout in coiled tube takes place, and they are essentially greater in the vicinity of the inner generatrix. The maximum intensity of wall temperature pulsations in a coiled tube is lower than in a straight tube. The length of the transition region where the burnout occurs develops quickly after burnout is first detected.
Schlichting, M. (1973) Grenzchicht-Theorie. Verlag G. Brawn. Karlsruhe.
Heat Exchange Design Hand Book. v. 1,2. Hemisphere Publishing Corporation, 1983.