Heat Transfer in Boiling & Condensation - 4 | Heat Transfer - Mechanical Engineering PDF Download

Illustration 6.1

Saturated steam at 70.14 kPa is condensing on a vertical tube 0.5 m long having an outer diameter of 2.5 cm and a surface temperature of 80^oC. Calculate the average heat-transfer coefficient.

Solution 6.1

It is a problem of condensation on a vertical plate, thus eq.6.10b can be used, 

where, different liquid and steam properties are evaluate at average film temperature,

Using steam table, the temperature of the steam corresponding to 70.14kPa pressure is 90^oC. The average film temperature will then be the average of 80 ^oC and 90 ^oC and it comes out to be 85 ^oC,

Using given data the different properties can be found using steam table and other relevant tables given in the standard literature. The data is tabulates below at 85^oC,

On putting the above values in the above equation,

h_av = 1205.2 W/m² °C

6.5 Condensation for horizontal tube

6.5.1 Condensation outside horizontal tube or bank of tube
This type of condensation is very common especially for the shell and tube heat exchanger. In case of condensation outside the vertical array of horizontal tubes the condensate flows as a film along the cylindrical surface or it may drop down. In case of another tube below, the condensate film flows down from the bottom edge of the upper tube to the upper edge of the bottom tube. As it goes on to the lower tubes, the thickness of the condensate film increases. Some of the correlations are given below.

6.5.1.1 Condensation on a single horizontal tube

            (6.13)

6.5.1.2 Condensation on a vertical tube of N horizontal tubes

               (6.14)

6.5.1.3 Condensation inside a horizontal tube
Figure 6.5 shows the physical picture of the condensation inside a horizontal tube (like an open channel flow).

Fig. 6.5: Film condensation inside a horizontal tube

Case 1: The length is small or the rate of condensation is low.

This situation will have small thickness of the flowing condensate layer at the bottom of the tube and the following coefficient can be used,

               (6.15)

where,  and the vapour Reynolds number (Re_v) should be less than 35,000. The Re_v is calculated based on inlet condition of vapour and inside diameter of tube.

Case 2: The length is high or the rate of condensation is high.

In this the following relation can be used.

                  (6.16)

where,

(Condition: Re_l >5000, Re_v > 20,000)

where, G_l and G_v are the liquid and vapour mass velocities calculated on the basis of the cross-section  of the tube.

6.6 Correlations for packed and fluidized bed

6.6.1 Packed bed
The heat transfer correlation for gas flow through a packed bed is given as,

 (6.17)

Conditions to use eq.6.12 are,

where,

 is the Stanton number.

 is the particle Reynolds number

d_p = Diameter or the effective diameter of a particle

v₀ = Superficial fluid velocity. It is the velocity based on the cross-section of the bed).

∈ : Bed porosity or void fraction

∈ : 0.3 → 0.5

Theoretically :   ∈ = 0.69 for uniform shape

                           = 0.71 bed of cubes

                           = 0.79 bed of cylinder  

  Colburn factor

6.6.2 Fluidized bed

The heat transfer coefficient to or from particles in a fluidized bed can be estimated with the help of following correlation,

  (6.18 )

where, v₀ is the superficial velocity.