Correlations for Condensing Heat Transfer

These notes summarize the correlations recommended for use in this class for condensing heat transfer. All of these are for condensation of single component vapors.

Choice of a correlation depend on whether you are looking at horizontal or vertical tubes, and whether condensation is on the inside or outside.

Preliminaries

The condensate loading on a tube is the mass flow of condensate per unit length that must be traversed by the draining fluid. The length dimension is perpendicular to the direction the condensate flows; the perimeter for vertical tubes, the length for horizontal tubes.

Condensate Loading
The loading may be subscripted with a b when evaluated at the bottom of a vertical tube. This cana be used to calculate a Reynolds number
Condensate Reynolds Number
Flow is considered laminar if this Reynolds number is less than 1800.

The driving force for condensation is the temperature difference between the cold wall surface and the bulk temperature of the saturated vapor

Driving Force
The viscosity and most other properties used in the condensing correlations are evaluated at the film temperature, a weighted mean of the cold surface (wall) temperature and the (hot) vapor saturation temperature (MSH Eq. 13.11)
Film Temperature

Wall Temperatures

As we've seen before, it is often necessary to calculate the wall temperature by an iterative approach. The summarized procedure is:

  1. Assume a film temperature, Tf
  2. Evaluate the fluid properties (viscosity, density, etc.) at this temperature
  3. Use the properties to calculate a condensing heat transfer coefficient (using the correlations to be presented)
  4. Calculate the wall temperature. The relationship will typically be something like
    Wall Temperature
    although other arrangements may be more appropriate
  5. Use the wall temperature to calculate a film temperature
  6. Compare the calculated film temperature to that from the initial step. If not equal, reevaluate the properties and repeat.

Laminar Flow Outside Vertical Tubes

If condensation is occurring on the outside surface of vertical tubes, with a condensate loading such that the condensate Reynolds Number is less than 1800, the recommended correlation is (MSH eq. 13.10):

Laminar, Outside Vertical
Since the vapor density is usually much smaller than that of the condensate film, some authors neglect it and use the film density squared in the denominator.

The expression is written in terms of the condensate Reynolds number, and can be rearranged to calculate the heat transfer coefficient directly (MSH Eq 13.12, F 13.140, L 9.30)

Laminar, Outside Vertical
(The rearrangement algebra is shown as a supplement to this document.)

The presence of ripples (slight turbulence) improves heat transfer, so some authors advocate increasing the value of the coefficient by about 20%. This can easily be done by changing the leading number (0.943*1.2=1.13).

This form is still not convenient for all cases, since the length of the tubes is sometimes unknown. Another rearrangement yields

Laminar, Outside Vertical
which may also be compensated for rippling (0.925*1.2=1.11).

The key to all the rearrangements is the system energy balance. For condensation on the outside of a tube:

Laminar, Outside Energy Balance
This can be rearranged and substituted into the correlations as needed to obtain alternate forms.

Turbulent Flow Outside Vertical Tubes

When the condensate Reynolds Number is greater than 1800, the recommended correlation is (MSH5 Eq. 13.17, not in MSH6):

Turbulent, Outside Vertical

Laminar Flow Outside Horizontal Tubes

When vapor condenses on the surface of horizontal tubes, the flow is almost always laminar. The flow path is too short for turbulence to develop. Again, there are two forms of the same relationship (MSH5 13.13-14, MSH6 13.14-15, F 13.147)

Laminar, Outside Horizontal
The 6th Edition of MSH changes the constant in the second form from 0.725 to 0.729. The rippling condition (add 20%) is suggested for condensate Reynolds Numbers greater than 40.

Condenser tubes are typically arranged in banks, so that the condensate which falls off one tube will typically fall onto a tube below. The bottome tubes in a stack thus have thicker liquid films and consequently poorer heat transfer. The correlation is adjusted by a factor for the number of tubes, becoming for the Nth tube in the stack (MSH 13.16, F 13.148)

Laminar, Outside Horizontal, Stacked
Splashing of the falling fluid further reduces heat transfer, so some authors recommend a different adjustment
Laminar, Outside Horizontal, Stacked

Condensation Inside Tubes

Condensate falls from tubes under the influence of gravity or by vapor shear. Outside of tubes, there is usually enough vapor space to keep velocities low enough that vapor shear is not important; however, inside tubes the velocities are higher and more likely to effect the heat transfer coefficient. Thus, for condensation inside tubes it is often necessary to calculate a second value of the heat transfer coefficient (assuming vapor shear). The larger of the two values is then used.

When vapor shear is controlling, the heat transfer coefficient can be determined from

Vapor Shear

Inside Vertical Tubes

For condensation inside vertical tubes, use the gravity controlled "outside vertical" or the shear controlled value of the heat transfer coefficient, whichever is larger.

Inside Horizontal Tubes

As condensation occurs inside a horizontal tube, some liquid pools in the bottom. This reduces the flow area and changes heat transfer. To account for this, the gravity driven condensation equation becomes

Inside Horizontal
As with vertical tubes, the designer should use the larger of the gravity or vapor shear controlled forms.

Rearrangement Proofs

The rearranged energy balance is substituted into the base form and rearranged.

Rearrange1
The energy balance can be used to make another substitution, which rearranges to become the third desired form
Rearrange1

References:

  1. Bell, K.J., Process Heat Transfer Notes, Oklahoma State University, 1982, Chapter IX.
  2. Foust, A.S. et al., Principles of Unit Operations, 2nd Edition, John Wiley, 1980, pp. 291-94.
  3. Levenspiel, O., Engineering Flow and Heat Exchange, Revised Edition, Plenum Press, 1998, pp. 179-80.
  4. McCabe, W.L., J.C. Smith, and P. Harriott, Unit Operations of Chemical Engineering (5th Edition), McGraw-Hill, 1993, pp. 374-85.
  5. McCabe, W.L., J.C. Smith, and P. Harriott, Unit Operations of Chemical Engineering (6th Edition), McGraw-Hill, 2001, pp. 379-84.

R.M. Price
Original: 12/16/99
Modified: 1/3/2000, 2/14/2000, 2/14/2002, 2/18/2003

Copyright 1999, 2000, 2002, 2003 by R.M. Price -- All Rights Reserved