Heat Transfer of Tubular Surfaces with Low Fins during Condensation

I. P. Chashchin, N. N. Norkin

(Presented by Prof. A. G. Stromberg, Doctor of Chemical Sciences)

In many branches of the chemical industry, as well as in thermal-power and refrigeration installations, various heat-exchange apparatuses are widely used, among which condensers occupy an important place. In the present work, a finned heat exchanger was tested as a condenser; an experimental determination of the heat-transfer coefficient $\alpha$ was carried out, and an attempt was made to generalize the data obtained by the methods of similarity theory.

The process of heat transfer during condensation is determined primarily by the physical properties of the liquid formed on the heat-exchange surface. The combination of physical properties in a number of organic substances is such that the heat-transfer coefficients during condensation have low values.

If the heat-transfer coefficients on the two sides of a heat-transfer surface differ significantly from one another, then the total resistance to heat transfer can be reduced by increasing that surface of the wall whose heat-transfer coefficient has the smaller value. This is what accounts for the use of finned surfaces during condensation.

In carrying out the present work, acetone was chosen as the working substance.

Three sets were tested: one—smooth tubes, and two—finned tubes with a constant fin height and different pitch. Some experimental data on heat exchange between a medium and a finned surface are available in the literature [1, 2]. A paper has been published on the study of vapor condensation on horizontal finned tubes [3]. There are no published works on the study of vapor condensation on finned vertical tubes. A vertical tubular heat exchanger with intensification of heat transfer in the intertube space was tested, namely, a tubular apparatus with rolled fins. Spiral transverse fins were obtained by rolling smooth tubes. In this case the surface of the tubes is increased by a factor of 2–2.5 without the use of welding or soldering. Saturated acetone vapor was supplied to the upper part of the intertube space of the apparatus, while cooling water was supplied through the tubes from bottom to top.

The temperature of acetone and water vapors at the inlet and outlet of the condenser was determined by thermocouples, and also by check mercury thermometers with a scale division of \(0.1^\circ\mathrm{C}\). The surface temperature of each tube was measured by thermocouples with a scale division of \(1.5^\circ\mathrm{C}\). The flow rate of water

Fig. 1.

Diagram labels:

• \(t_k = 56.5^\circ\mathrm{C}\)
• I set (smooth tubes), \(d = 23\ \mathrm{mm}\)
• II set (finned tubes), \(d = 20\ \mathrm{mm}\), \(h = 1.5\ \mathrm{mm}\), \(s = 4\ \mathrm{mm}\)
• III set (finned tubes), \(d = 20\ \mathrm{mm}\), \(h = 1.5\ \mathrm{mm}\), \(s = 2\ \mathrm{mm}\)
• type of heat-transfer surface

and condensate was measured by the weighing method. The 19 tubes of the condenser were arranged in a staggered pattern. The condenser shell was insulated. For visual observation of acetone vapor condensation on finned and smooth tubes, a special cha—

Diagram labels:

• Installation diagram
• air inlet

Fig. 2.

1. Shell-and-tube heat exchanger with finned tubes.
2. Vessel with organic liquid.
3. Thermometer.
4. Switch.
5. Mirror galvanometer.

The following three sets were tested:

Some experimental data obtained during testing of the condenser

chamber. In it, by means of a telescopic magnifier (40-fold magnification), film condensation of acetone vapors was observed.

The results of the experiments carried out to determine the heat-transfer coefficients during vapor condensation on different types of surfaces are presented in graph 1. The graph shows points corresponding to only one temperature of the condensing vapor.

In work [3] a formula is presented for determining the heat-transfer coefficient during condensation on horizontal single finned tubes

\[ \alpha = 0.72 \cdot C \cdot \sqrt[4]{\frac{r \cdot \lambda^{3} \cdot \gamma^{2}}{\mu \cdot \Delta t \cdot d_{0}}}\ \mathrm{kcal}/\mathrm{m}^{2}\ \mathrm{hour}\,^{\circ}\mathrm{C}\ldots \]

This is the Nusselt formula, derived for film condensation on smooth horizontal single tubes, with the introduction into it of an additional coefficient \(C\) for finned surfaces. The coefficient \(C\) indicates how many times the heat removal from a finned horizontal tube is greater than the heat removal from a smooth tube of the same kind, whose outside diameter is equal to the base diameter of the finned tube, at identical vapor-condensation temperatures.

The coefficient \(C\) for each tube has a constant value determined by its configuration, dimensions, and fin material. The author of work [3] proposed a formula for determining the coefficient \(C\). The formula does not take into account the effect of the lead angle of the helical line for tubes with rolled fins; nor does the formula take into account the effect of the thermal conductivity of the fin material on the ratio of the temperature heads on the fin and on the main surface of the tube.

In generalizing the results of the work, we made an attempt to use, for determining the heat-transfer coefficient, the Nusselt formula derived for film condensation on smooth vertical tubes,

\[ \alpha = 1.15 \cdot \sqrt[4]{\frac{r \cdot \lambda^{3} \cdot \gamma^{2} \cdot 3600}{\mu \cdot \Delta f \cdot H}} \ \text{kcal}/\text{m}^{2}\,\text{h}\,^{\circ}\text{C}. \]

We introduce into it an additional coefficient \(C\) for finned surfaces:

\[ \alpha = 1.15 \cdot C \cdot \sqrt[4]{\frac{r \cdot \lambda^{3} \cdot \gamma^{2} \cdot 3600}{\mu \cdot \Delta f \cdot H}} \ \text{kcal}/\text{m}^{2}\,\text{h}\,^{\circ}\text{C}. \]

Using Newton’s equation, this formula can be reduced to another form, sometimes more convenient for calculations, since the quantities \(\Delta f\) and \(H\) are eliminated from it. \(Q = Y \cdot r = \alpha \cdot \Delta f \cdot F;\ F = n \cdot \pi \cdot d \cdot H\), whence

\[ H \cdot \Delta f = \frac{Y \cdot r}{\alpha \cdot \pi \cdot d \cdot n}. \]

Substituting this value, we obtain

\[ \alpha = 27 \cdot C \cdot \sqrt[3]{\frac{\lambda^{3} \cdot \gamma^{2} \cdot n \cdot d}{\mu \cdot Y}} \ \text{kcal}/\text{m}^{2}\,\text{h}\,^{\circ}\text{C}. \]

As a result of determining the heat-transfer coefficient from the formula given above, it turned out that there are discrepancies with the experimental data.

Conclusions

1. The condensation of acetone vapor is of the film type.

2. Finned tubes produced by rolling should be used in heat-exchange apparatuses in order to increase the heating surface without increasing the dimensions or the number of apparatuses.

3. The outer surface of the tube after rolling increased by a factor of 1.5–2. The experimental data showed that after rolling the thermal resistances on the vapor side and on the cooling-water side became almost identical. A comparison of the amounts of heat removed in the course of 1 hour from 1 running meter of tube showed that, under identical conditions, 1.7–2 times more heat is removed from a rolled tube than from a smooth tube.

4. The formula for determining the heat-transfer coefficient during condensation on vertical finned tubes requires refinement with respect to the coefficient \(C\).

5. Determination of the most advantageous dimensions—the tube diameter, the spacing between fins, and the fin height—taking into account the weight of the apparatus and the cost of its manufacture, will be the subject of further investigations.

REFERENCES

1. M. A. Mikheev. Fundamentals of Heat Transfer. Gosenergoizdat, Moscow—Leningrad, pp. 130–136, 197, 1956.

2. V. M. Antuf’ev and G. S. Beletskii. Heat Transfer and Aerodynamic Resistances of Surfaces in Cross Flow. Mashgiz, Moscow—Leningrad, 1948.

3. E. E. Slepyan. Separation Processes, Condensation, and the Creation of Vacuum in Refrigerating Installations. Mashgiz, p. 75, 1953.