Lecture No.25

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Lecture No. 25Condensation and Boiling Heat Transfer

Condensation and boiling are convection processes associated with phase change of fluid. They are classified as convection because there is a fluid motion near a solid surface.

These processes occur at solid-fluid interfaces and latent heat transfer effects are involved, without a change in fluid temperature.

Heat transfer rates and coefficients are much higher than those encountered in other convection problems.

Example: Conventional home air conditioners, refrigerators and power plants.

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Condensation Heat Transfer

Condensation

Classification of condensation

a. Dropwise condensation

b. Filmwise condensation

Heat transfer rates in drop wise condensation are 10 times higher than those encountered in filmwise condensation

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Film Condensation on a vertical flat plate

Film condensation on a vertical flat plate (Nusselt) Note:

δ

TT

dy

dT ws

Tw Ts

A linear temperature profile exists between the condensing vapor and the surface.

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Assumptions:

1. The fluid properties are constant

2. No thermal resistance at the liquid-vapour interface.

3. No Momentum effects

4. No shear stress at the liquid-vapour interface.

5. A linear temperature profile exists between the condensing vapor

and the surface.

6. No Enthalpy change

δ

TT

dy

dT ws

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1.Forces acting on an element of thickness dx

Gravity force

Viscous force

Buoyancy force

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dxy)(δρg

The weight of the fluid element of thickness dx between y and per unit depth

The viscous shear force at y

Buoyancy force = dxy)(δgρv

vρ

= density of the Liquid u = velocity of the liquid film

= density of vapourm = viscosity of the fluid g = acceleration due to gravity.

Gravity force

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dxy)(δgρdxdy

duμdxy)(δρg v

dy

duμg)ρ(ρy)(δ v

Under steady-state conditions, a force balance on the element of the fluid gives

On simplification

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0yat0u

2v

y y2

1δy

μ

g)ρ(ρu

The boundary condition is

Integrating and using the boundary condition we obtain

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The mass flow rate of the condensate per unit depth of the film at any position x is given by

3μ

gδ)ρ(ρρdyy

2

1δy

μ

g)ρ(ρρm

3v2v

δ

0

As the liquid film flows from x to x + dx, the film thickness changes from to + d as a result of additional condensation.

Note:

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The change in condensate flow rate between x and x + dx is given by

dδμ

gδ)ρ(ρρdd

dx

dδ

3μ

gδ)ρρ(ρ

dδ

ddx

3μ

gδ)ρρ(ρ

dx

d 3v

3v

3v

This change in condensate flow rate is due to the energy transferred from the condensing vapor to the wall.

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That is, the heat transferred from the condensing vapor to the wall is equal to the increased mass flow rate times the latent heat of vaporization.

Therefore,

δ

TTkdxh

μ

dδgδ)ρ(ρρ wsfg

2v

fgh = latent heat of vaporization k = thermal conductivity of the condensate.

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0xat0δ

1/4

υfg

wsx )ρρ(ρgh

)T(Tk xμ 4δ

Integrating by using the boundary condition

we get

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δ

TTkdx)T(Tdxh ws

swx

xx δ

kh

The heat transfer across the condensate layer is by conduction. We can express the local heat transfer coefficient ‘h x ‘ as

or

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1/4

ws

3fgυ

x )T(Tμ x 4

kgh)ρ(ρρh

Heat transfer coefficient for film condensation decreases with increasing distance from the top as the film becomes thicker and thicker.

The thickness of the condensate film is similar to a boundary layer on a flat plate

An increase in the temperature difference (Ts - Tw) causes a decrease in heat transfer coefficient

Substituting the value of X

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The local Nusselt number ‘Nux ‘ is then given

by

1/4

ws

3fgυ

x )T(Tμ x 4

kh g)ρ(ρρ

k

X

k

hxNu

The local Nusselt number for film condensation decreases with increasing distance from the top as the film becomes thicker and thicker.

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xx0h

3

4dxh

1h

The average value of the heat transfer coefficient is obtained by integrating the local value ‘hx” over the plate and dividing by the length

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1/4

wsf

3ffgυ

)T(Tμ

kgh)ρ(ρρ0.943h

Where the subscript f denotes that the properties should be evaluated at

the film temperature ‘Tf ‘ given by

2

TTT ws

f

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Rohsenow:

performed a refined analysis of this problem and obtained results which are in better agreement with the experimental data if Pr > 0.5 and c(Ts - Tw)/hfg 1.0.

Similar results can also be obtained by replacing hfg by , where is defined as

= hfg + 0.68c(Ts-Tw)

c - is the specific heat of the condensate

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Film Condensation on Tubes and Spheres

The average heat transfer coefficient for laminar film condensation on the outside of a sphere or a horizontal tube can be evaluated from the relation

1/4

wsf

3ffgυ

)T(Tdμ

kgh)ρ(ρρAh

A = 0.815 for a sphereA = 0.725 for a tubed = diameter.

Where

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Film Condensation on Tube Banks.

1/4

wsf

3ffgυ

)T(TdNμ

kgh)ρ(ρρAh

A = 0.725 for a tubed = diameter.

W here

If condensation occurs on a horizontal tube bank with N tubes so arranged that the condensate from one tube flows directly onto the tube below, the average heat transfer coefficient for the system can be obtained by replacing d with N d

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Film Condensation on Inclined surfacese

If a plate or a cylinder is inclined at an angle with the horizontal, all the above equations be used by replacing g with its component parallel to the heat transfer surface. That is, by replacing g, with g sin .

Note:

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A fluid flowing over a surface undergoes a transition from laminar to turbulent flow. Therefore, the motion of the condensate becomes turbulent when its Reynolds number exceeds a critical value of about 1800.

If the plate on which condensation occurs is sufficiently large, or there is a sufficient amount of condensate flow, turbulence may appear in the condensate film. The Reynolds number of the condensate film is defined as

ff

Hf Pμ

m

Pμ

uρA 4

μf

uρ dRe

8001Pμ

uρA 4

μf

uρ dRe

f

Hc

Hd

m

ρAu

Where,

= hydraulic diameter

A = flow cross-sectional area

P = wetted perimeter

V = average velocity of flow

= mass flow of the condensate.

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Where

is the condensate flow rate for unit width of the plate

Film Reynolds number

The wetted perimeter P for a vertical tube is equal to d, and for a vertical plate of unit depth, P = 1. The Reynolds number is sometimes expressed in terms of the mass flow per unit width of plate as;

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fgws hm)TT(Ahq

The mass flow rate, , can be related to the heat transfer coefficient by

or

fg

ws

fg h

)TT(Ah

h

qm

and

ffg

ws

ff Pμh

)TA(Th4

Pμ

m4Re

ffg

wsf Ph

)TT(h4Re

For a plate of length L and width w, the flow cross-sectional area , A =Lw and the wettedPerimeter P=w, so for plate

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For laminar flow of condensate film, the experimental results are found to be in good agreement with the results predicted from these equations. However,

In practice, for turbulent flow it has been found that the theoretical results are approximately 20% lower than the experimental values if ripples develop in the film. In the light of this observation, McAdams suggests the following expression for predicting the average heat transfer coefficient for film condensation on plates, if the flow is turbulent:

4/1

ws

3fg

)TT(

kgh)(13.1h

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Film Condensation inside Horizontal Tubes

Condensation inside tubes is of considerable importance in refrigeration and air-conditioning systems where the refrigerant flows through the tubes.

The flow rate of condensable vapor through the tubes strongly influences the heat transfer coefficient, which in turn influences the rate of accumulation of liquid in the tubes.

For condensation of refrigerants at low vapor velocities inside horizontal tubes:

4/1

ws

3fg

)TT(d

kgh)(555.0h

This equation is valid for low vapor Reynolds number Rev which should be evaluated at the inlet conditions to the tube.

000,35Vd

Rev

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Condensation of Superheated Vapors

)TT(Ahq ws

sT

The equations developed earlier are strictly applicable to the condensation of saturated vapors. However, the same equations can also be used with reasonable accuracy for condensation of superheated vapors. The heat transfer rate from a superheated vapor to a wall at Tw is given by

- is the saturation temperature corresponding to the pressure of the super-heated vapor.

where

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Drop-wise Condensation

If the surface on which condensation takes place is coated with an agent such that the condensate does not wet the surface, the vapor condenses in drops rather than as a continuous film. In drop-wise. condensation, a large part of the surface is not covered by a liquid film which acts as an additional resistance for heat transfer. Therefore, in drop-wise condensation the heat transfer coefficients can be as high as 4 to 8 times that of film condensation.

Note:

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Effect of Superheated vapour and of Non-Condensable gases

Steam condensation in the presence of small amount of air

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Boiling Heat Transfer

Boiling:

When heat is added to a liquid from submerged solid surface which is at a temperature higher than saturation temperature of the liquid, The part of the liquid go through phase change. This change of phase is called boiling

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Classification of Boiling

1.Pool boiling

2.Flow boiling

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Pool boiling:

When there is no bulk motion of the fluid. Any motion is due to natural

convection currents or movement of vapour bubble formed due to

boiling.

Example: Boiling of liquid in a vessel placed on heater or

stove.

Flow boiling: The liquid is forced to move by an external agency like a pump

Example: Steam generators

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Pool boiling:

1. Saturated pool boiling 2. Sub-cooled pool boiling

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Regimes/ or Modes of Pool Boling

1. Convective boiling

2. Nucleate boiling

3. Film boiling

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Saturated pool boiling curve

Region or mode depending on (Tw

–Ts)

Different regimes of boiling heat transfer

The maximum heat flux is called critical heat flux and occurs at critical excess temperature.

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Region or mode depending on (Tw –Ts)

1. Natural convection region (Tw –Ts) 10 CHeat flux is proportional to (Tw - Ts) n = 1 to1.3

2. Nucleate boiling region (Tw –Ts) up to 20 or 30 CHeat flux is proportional to (Tw - Ts) n = 3

3. Film boiling region

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Using experimental data, Rohsehow, developed the correlation

33.0

fgsfn

fg

x

)(gh

qC

Prh

Tc

Nucleate Pool Boiling

c

q

where

= specific heat of saturated liquid

= heat flux for

nucleate boiling

= viscosity of

liquid

= surface tension of the

liquid to vapor interface

Csf = empirical constant

which depends on the nature of the

heating surface-fluid combination

n = 1.0 for water and

1.7 for other fluids

Pr = Prandtl number of the

saturated liquid.

Saturation temperature (oC)

20 40 60 80 100 150 200

Surface tension ( 103)

72.9 69.5 66.1 62.7 58.9 48.7 37.8

Vapor-liquid surface tension for water

It correlates the data for all types of nucleate boiling processes, including pool boiling of saturated liquids and , sub-cooled liquids and also for boiling of sub-cooled and saturated liquids flowing by natural or forced convection in tubes.

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Zuber, has developed the following expression for the Critical (peak) heat flux q” in nucleate boiling:

4/1fg

2/1 )](g[h24

q

This relation is in good agreement with experimental data. It can be observed from the above equation that the peak heat flux is larger for fluids with larger latent heats of vaporization.

Where - is the vapor-liquid surface tension.

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Flow Boiling

Flow boiling:Often referred to as forced convection boiling or as two-phase flow with heat transfer

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Thanks

Questions

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Question

A vertical plate of length 1m and width 0.50 m at 92C is exposed to saturated steam at 100 C. Calculate the average heat transfer coefficient and the mass of steam condensed in one second.

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Question

A tube of 2 m length and 25 mm OD is to be used to condense saturated steam at 100C while the tube surface is maintained at 92C. Estimate the average het transfer coefficient and the rate of condensation of steam if he tube is kept horizontal. The steam condenses on the outside of the tube.

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Question

It is desired to boil water at atmospheric pressure on a copper surface which is electrically heated. Estimate the het flux from the surface to the water, if the surface is maintained at 110 C. Also estimate the peak heat flux.

Lecture No.25

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