**3.1.2 Influence of coil pitch (H)**

In this analysis, a helical coil with a pipe of inner diameter (*2r*) 20 mm and pitch circle diameter (*PCD*) of 300 mm was considered. Analyses were carried out by changing the coil pitch. Coil with pitch of (i) zero, (ii) 15 mm, (iii) 30 mm, (iv) 45 mm and (v) 60 mm were analysed.

When the coil pitch is zero, local Nusselt numbers at the top and bottom points on the periphery of a cross section are almost the same. As the coil pitch is increased, the difference between them also increases. This difference is caused by torsion experienced by the fluid. As the pitch increases, the torsional effect also increases. However, variation of local *Nu* for the coils with pitch of 45 and 60 mm are identical. Average values of Nusselt number in the fully developed region is given in table 1.


Table 1. Average values of Nusselt number.

It is found that the *Nuavg* increases marginally with increase in pitch and almost insensitive to its further changes at higher pitches. The percentage increase, when the pitch is changed from 0 mm to 15 mm is about 1% and this value changes to 0.2% when the pitch is changed from 45 mm to 60 mm. For any engineering application, the tube pitch has to be higher than pipe diameter and in that range the changes in *Nuavg* due to changes in pitch are negligible.

Helically Coiled Heat Exchangers 325

0.71 0.4 0.11 *Nu Re Pr* 0.116

The applicable ranges of parameters for the equation 8 are: (i) 14000 < Re < 70000;

Fig. 8 gives a comparison of the Nusselt numbers predicted by eqn. (8) with Roger & Mayhew (1964) and Mori&Nakayama (1967b). It is found that present correlation is fairly in agreement with Nusselt number predicted by the experimental correlations. The earlier correlations are found to be under predicting the Nusselt number. This is attributable to the approximations used by the authors in data reduction and conservative nature of their

This boundary condition is applicable to heat flux controlled surfaces such as electrically heated pipes, nuclear fuel elements etc. In these analyses, hot water at 330 K at a specified velocity of 0.8 ms-1 is entering the helical pipe at the top, where an inlet velocity boundary condition is specified. The fluid is made to cool down as it flows along the tube by

Influence of parameters such as *PCD*, coil pitch and pipe diameter has been studied in this case also. They are found to be behaving in a manner similar to those described in section 3.1 and are not repeated here. Hence in this case also a correlation of the form given by eqn. (7) will be applicable. In order to cover a wider range of parameters, analysis of eight

Multiple regression analysis of the data obtained from the above 20 runs was performed to

(ii) 3000 < De < 22000; (iii) 3.0 < Pr < 5.0; and (iv) 0.05 < δ < 0.2.

Fig. 8. Comparison of Nusselt number for the constant Tw B.C.

**3.2 Constant wall heat flux boundary condition** 

get a best fit of eqn. (7). The correlation resulted is,

specifying a wall heat flux of -150 kW m-2.

additional cases were also done.

approach.

. (8)

Hence the effect of coil pitch on overall heat transfer for design purposes need not be considered for most of the practical applications with helical coils. However, it has implications in heat transfer in the developing region (ref. Fig. 7). The maximum difference in Nusselt number between the top and bottom locations is given in table 2. This clearly shows the extent of oscillatory behaviour. Another observation is the shift of the symmetry plane of temperature and velocity profiles with the change in coil pitch.


Table 2. Difference in values of Nusselt number.
