In this article we will discuss about the convective coefficient for film condensation on various tube arrangements. They are: 1. Convective Coefficient for Film Condensation on Vertical Tubes 2. Convective Coefficient for Film Condensation on Single Horizontal Tube 3. Convective Coefficient for Film Condensation on Banks of Horizontal Tubes 4. Convective Coefficient for Film Condensation inside Tubes.
1. Convective Coefficient for Film Condensation on Vertical Tubes:
When the tube diameter is large compared to the film thickness, the convective coefficient for condensation on vertical tubes are calculated by the Nusselt correlation for film condensation on a vertical flat surface. Thus,
2. Convective Coefficient for Film Condensation on Single Horizontal Tube:
The average coefficient for film condensation of a pure saturated vapour on the outside of a single horizontal tube is determined from the correlation-
Where, D is the outside diameter of the tube.
It is interesting to note the relative effectiveness of horizontal and vertical tubes as condensing surfaces-
When h͞h = h͞v, solution of the above relation yields l/D = 2.86. Thus for a cylindrical tube with a length-to-diameter ratio of 2.86, equal amount of heat transfer occurs from both horizontal and vertical orientations. As the ratio l/D increases, the greater heat transfer and so high condensation rate is possible with a horizontal tube. For most steam condensers, the ratio l/D for a tube is in the range 50 to 100 or even more.
3. Convective Coefficient for Film Condensation on Banks of Horizontal Tubes:
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For a vertical tier of n-horizontal tubes, the average convection coefficient for film condensation is-
Where, the equivalent tube diameter De of the tube bank is the sum of outside-tube diameter in a vertical column of the tube bank pattern.
For n-tubes in a vertical column of the tube bank pattern, De = nD where D is the diameter of a single tube in the bank.
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A reduction in the film coefficient with increasing n may be attributed to an increase in the average film thickness for each successive tube due to accumulation of drip from the upper tubes. Obviously it is advantageous to stagger the tubes as the accumulation of drip from the upper rows is at least partially offset by the splashing effects, i.e., by the agitation caused by the drip as it falls from one tube to another.
4. Convective Coefficient for Film Condensation inside Tubes:
Condensation of vapour occurs on the inside surface of cylindrical tubes used in condensers of refrigeration and air-conditioning systems and in many of the chemical and petrochemical industries. The flowing vapour, however, strongly influences the character and thickness of the condensate film and that affects the heat transfer. The magnitude of this effect is dependent upon the horizontal or vertical disposition of the tubes and also upon the upward or downward flow direction.
Following empirical correlations have been suggested to work-out the heat transfer when steam condenses on the inside surface of tubes-
Where, I is the cooled length, A is the surface area based on inside diameter of the tube and V is the entrance velocity.
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Example 1:
A condensation experiment for steam on plate type vertical condenser has been setup for a particular fluid with a given temperature difference.
The same setup was subsequently used with another fluid with thermo-physical properties given as:
If temperature difference is reduced to 80 percent, make calculations for the percentage change in the convection coefficient.
Solution:
The average heat transfer coefficient for vapour condensation on a vertical plate is given by –
Example 2:
(a) A plate condenser was designed to be kept vertical. How would the condensation coefficient be effected if due to site constraints, it has to be kept at 60° to the horizontal?
(b) A plate condenser of dimensions I × b has been designed to be kept with side I in the vertical position. However due to oversight during erection and installation, it was fixed with side b vertical. How would this affect the heat transfer? Assume laminar conditions and same thermo-physical properties in both cases and take b = 1/2.
(c) Determine the length of a 25 cm outer diameter tube if the condensate formed on the surface of the tube is to be same whether it is kept vertical or horizontal.
Solution:
(a) For a vertical flat plate
For inclined flat surfaces, the gravity acceleration g is replaced by g sin 9 where 9 is the inclination angle with the horizontal. Then-
Evidently:
hinc = hver (sin ϴ)0.25 = hver (sin 60)0.25 = 0.9647
This implies 3.53% reduction in condensation coefficient –
Comments:
The condensation coefficient and accordingly heat flow increases when the shorter side is kept vertical. For better condensation, the condensers should be installed with shorter side vertical.
(c) For laminar film condensation on a vertical tube-
For equal amount of condensation, the heat transfer rate and accordingly condensation coefficient should be same for the horizontal and vertical orientations. In that case-
