Condensation on

vertical surface

Convective Heat Transfer Seminar

Mostafa Ghadamyari

M. SC. Student

Spring 2014 - Tarbiat Modares university

Outline

Here, We will discuss about:

Condensation definition

Different types of condensation

Film Surface Condensation

Laminar film equation derivation

Laminar film heat transfer coefficient diagram

Turbulent Film heat transfer coefficient diagram

2/12

Condensation definition

A phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform.

A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another one by heat transfer.

Condensation is the change of the physical state of matter from gas phase into liquid phase, and is the reverse of vaporization

3/12

Modes of condensation

Condensation modes:

(a &b). Surface condensation

(a). Film

(b). Dropwise

(c) Homogeneous condensation

(d) Direct Contact condensation

We’ll focus on Film Surface condensation

4/12

Dropwise and Film Surface condensation

(a) Dropwise condensation occurs if the

surface is coated with a substance that inhibits wetting, Silicones, Teflon,

assortment of waxes and fatty acids

(b) Film condensation is generally

characteristic of clean, uncontaminated

surfaces

The condensate provides a resistance to

heat transfer between the vapor and the surface

It’s desirable but difficult to maintain

dropwise condensation, so calculations

are often based on Film condensation5/12

Film condensation

Film condensation has Three distinct regions:

1. Laminar region, near the top, the film is

relatively thin

2. Wavy region, The film becomes thick enough

to show the signs of transition

3. Turbulent region, Ripples appear irregular in

both space and time

Laminar Region complexities:

Flow of liquid interacts with layer of vapor

Tinterface= Saturation temperature of local P

Tw < Saturation temperature < Tvapor

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Laminar Film – Momentum Equation

Momentum equation for simplified laminar film:

Because of slenderness of the film:

Substituting:

Assuming negligible Inertia [Solved by Nusselt]:

2

2(1) l l l

v v dP vu v g

x y dy x

2

2(3) ( )l l l v

Sinking EffectFrictionInertia

v v vu v g

x y x

(2) / vdP dy g

2 21(4) ( , ) ( ) ( )

2l g

l

g x xv x y 7/12

Laminar Film – First thermodynamics law

The first law of thermodynamics:

Substituting conduction & (2):

Substituting (1)

Integrating from y=0

Local mass flow rate:

Vertical enthalpy inflow:

Assume linear temperature distribution:

3

0(1) (y) ( )

3l

l l v

l

gvdx

,0(2) [ ( )]l f P l satH v h c T T dx

''(3) 0 ( ) hg wH H dH d q dy

'

,

3[ ( )]

8(4) ( )

fg

fg P l sat ts

h

a wl

w h c T Tk

T T dy d

3

'

( )(5)

( )l l sat w

fg l v

k v T Tdy d

h g

1/4

'

4 (T T )(6) ( )

( )l l sat w

fg l v

k vy y

h g

1sat

sat w

T T x

T T8/12

Laminar flow – Results

Now we can calculate Heat transfer coefficients:

Similar results can be obtained by Scale Analysis (Similar to laminar boundary layer natural convection)

Rohsenow refined preceding analysis by discarding linear profile assumption and performing an integral analysis.

Rohsenow recommends:

Jacob number = relative measure of subcooling:

To summarize:

1/43 ''' ( )(1)

4 ( )

l fg l vly

sat w l sat w

k h gq kh

T T yv T T

4

(2)3

L y Lh h

1/43 ' ( )(3) 0.943

( T )

fg l vLL

l l l sat w

L h gh LNu

k k v T

',(4) 0.68 ( ) (1 0.68 )

fgfg p l sat w fgh h c T h JaT

, ( )

(5) P l sat w

fg

c T TJa

h

'

(6) ( ) ( )lsat w L

fg

kL T T Nu

h '(7) ( ) (1 0.68 )fgq L h Ja 9/12

Laminar Film - Diagram

In the preceding analysis were derived by Nusselt, based on negligible inertia assumption

The complete momentum equation used by Sparrow & Gregg in similarity solution.

Their solution for Nu falls below Nusselt’ssolution -> Effect of Inertia

Chen abandoned the assumption of zero shear at interface, retaining effect of inertia

His results for Nu are smaller than Sparrow & Gregg’s solution -> Effect of restraining drag of vapor

Better agreement with experimental data 10/12

Turbulent Film - Diagram

Reynolds number of liquid film:

Experimental observations:

Laminar: Re < 30

Wavy: 30 < Re < 1800

Turbulent: Re > 1800

Experiments revealed that heat transfer

rate in wavy and turbulent regions is

considerably larger than laminar section

Following relation developed by Chen for

wavy and turbulent region:

4(1) Re (y)y

l

2

1/3 0.44 6 0.8 1.3 1/2(2) ( ) (Re 5.82 10 Re Pr )L l

L L L

l

h

k g

11/12

Summary

Condensation is phase change from Gas to Liquid

There’re different types of condensation:

Surface (Film, Droplet), Homogeneous, Direct contact

Film surface condensation has three regions:

Laminar, Wavy, Turbulent

Laminar film condensation first solved by Nusselt by neglecting Inertia effect

Complete momentum equation used by Sparrow and Gregg in similarity solution

Chen Solution for laminar film contains vapor drag effect and inertia effect of liquid

Chen reviewed and developed a relation for Wavy and Turbulent regions

12/12

Thank you!

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