condensation-hmt.doc

8/9/2019 condensation-hmt.doc

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Q. 5.1. Define condensation?

Ans. When a vapour is in contact with the surface whose temperature t5 is lower than thesaturation temperature that corresponding to the vapour pressure then the gaseous or vapour

phase changes to liquid state with the liberation of heat from the vapour. This process is called

condensation and the heat flow during condensation process takes place from vapour to thesurface.

Q. 5.2. Differentiate between film condensation and. Drop wise condensation.

Ans. Film condensation : Occurs when a vapour relatively tree from un purifies isallowed to condensate on a clean surface. The liquid condensate wets the solid surface read out

and form a continuous film over the entire surface. The liquid flows down cooling surface under

the action of gravity and the layer continuously grows in thickness because of newly condensing

vapours. The film offers thermal resistance k at transfer between vapour and surface soconsequently coefficient of heat transfer kr film condensation is less.

Drop wise condensation: It occurs on highly polished surfaces or on surfaces contaminated with

impurities like fatty acids and organic compounds. The liquid condensate collects in droplets and

does not wet the solid cooling surface. The droplets generally develop in cracks and pits on thesurface, grow in sie, break away from the surface, knock off other droplets and eventually run

off the, surface without forming a film. !ince there is no barrier to heat flow, the dropwise

condensation gives coefficient of heat transfer five to ten times larger than the film condensation

and of the order of "5# kw$m%.

Q. 5.3. What are promoters?

Ans. &rop wise condensation may be provoked artificially by surface coatings that are eitherapplied to heat transfer surface or introduced into the vapour and these surface coatings called


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promoters inhibit wetting and promote drop wise condensation. 'ommon e(amples of promoters

are)!ilicon*s, Teflon*s, wa(es and fatty acids.

Q. 5.4. ro!e that a!era"e heat transfer coefficient is 4 # 3 times the local heat transfercoefficient at trailin" ed"e of plate d$rin" laminar film condensation on tl !ertical

plate#%ased on &$sselt theor' of laminar film condensation on !ertical plate pro!e that

a!era"e heat transfer coefficient ( 4 # 3 times local heat transfer coefficient at trailin" ed"e.

)tate ass$mptions made in the abo!e deri!ation.

Ans. Ass$mptions

+. iquid film is in good thermal contact with the cooling surface and therefore temperature atthe inside of the film is taken equal to the surface temperature

The condensate film is so thin that a linear temperature variation e(it between the plate surface

and vapour conditions.

%. -urther temperature at the outer surface of the film is taken equal to the saturation temperature

. The physical parameters like thermal conductivity /k* density /p* dynamic viscosity // of the

condensate film are independent of temperature.

0. The condensing vapour is entirely clean and free from gases.

5. 1adiation between vapour and liquid film is neglected.

2. 3oriontal component of velocity at any point in liquid film and the curvature of film is

neglected

". Inertia forces appearing in the condensate film are neglected.


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* +elocit' distrib$tion : 4n equation for the velocity distribution u as a function of distance y

from the wall surface can be set up by considering the equilibrium between the gravity andviscous forces on an elementary volume bd (, dy6 of the liquid film.

7ravitational force on the element 8 pg b d( dy6

9iscous shearing stress on the element face at y 8

change in shearing stress in distance dy 8

:quating the gravity force to the net shear focce.

;pon simplification,

Integrating twice


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The relevant boundary condition are

,hese conditions determine that

Therefore the velocity distribution through the film is prescribed by the following

parabolic relationship

The mean flow the velocity 9 of the liquid film at a distance ( from the top edgecan be determined from the e(pression.

* -ass flow rate

The downward flow of the liquid at any elevation ( i.e. over the layer of thickness 26 ismass flow rate ) mean flow velocity ( flow area ( density

The mass flow is thus a function of (< this is so because the film thickness 2 is

essentially dependent upon (.

4n increase in the mass flow rate of condensation during downward flow of condensate from (to x + dx can be worked out by differentiating equation I9 with

respect to x or d .


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• eat fl$/ : The heat rate into the film, d=, equal the rate of energy release due to

condensation at the surface. Thus,

where h f g is the latent heat of condensation. >usselt presumed that the heat released during condensation flows only by

conduction through the film.

'ombining equations 9I6 and 9II6, we get?

Integration yields an e(pression for the thickness of condensate layer

!ubstitution of the boundary condition 2 8 # at ( 8 # yields c 8 #

:vidently the film thickness increases as the fourth root of distance down the surfaces< the

increase is rather rapid at the upper end of tt vertical surface and slow there after.• -ilm heat transfer coefficient? >usselt had presumed that heat flow from the vapour to the

surface is by conduction through the liquid film, i.e.,

,he heat flow can also be e/pressed as

Where Ii is the local heat transfer coefficient. It follows from these e(periment that


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Thus at a definite point on the heat transfer surface, the film coefficient h is directly proportional

to thermal conductivity k and inversely proportional to thickness of film 2 at that point.

)$bstit$tin" the !al$e of film thic0ness from e$ation +

ocal heat transfer coefficient at the lower edge at plate, i.e., at ( 8 +

;ndoubtedly the rate of condensation heat transfer is higher at the upper end of the plate than atthe lower end.

@y integrating the local value of conductance equation A6 over the entire length l of the plate,

we get the average heat transfer coefficient<

where h+ is the local heat transfer coefficient at the lower edge of the plate.

Then it follows from equation IA6 that

where 2l6 is the film thickness at the lower end of the plate. Obviously the average


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heat transfer coefficient is 0$ times the local heat transfer coefficient at the trailing

edge of the plate.:quation AII6 is usually written in the form,

The >usselt solution derived above is an appro(imate one because of the assumptions admitted

in the statement of the problem. :(perimental results have shown that the >usselt equation is

conservative, it yields results which are appro(imately %#B lower than the measured values.

4ccordingly, use of a value of +.+ in place of the coefficient #.C0 has been recommended byDc. 4dams.

Q. 5.5. Write a short note on:

a ,$rb$lent film condensation6

b 7ondensation in ban0s of hori8ontal t$bes.

Ans. The character of condensate film range from laminar to highly turbulent. The liquid flows

in laminar film at upper end of plate and then becomes undulating in the middle section and

finally flows in a turbulent state.The parameter indicating the commencement of turbulent flow is the 1eynold >umber.

'onventionally, 1e

where deq is the equivalent diameter given

by<

-or vertical plate 4 8 bE and welted perimeter p of solid plate is simply the width /b* of the

plate.

)ince mass flow rate m) = pAV


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The transition from laminar to turbulent flow occurs at a critical 1eynold no of +F##. Whenturbulence sets in, the condensate film nv longer offers high thermal resistance and so it results in

increased convective coefficients. Girkbride suggested the following correlation for the averageheat transfer coefficient?

In the turbulent region, the average film coefficient increases with distance + because of theeddies which promote convection.

-or 1e H +F##

ii6 @anks of horiontal tubes? -or a vertical tier of nhoriontal tubes, the average convectioncoefficient for film condensation is


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where the equivalent tube diameter &, of the tube bank is the sum of outsidetube

diameter in a vertical column of the tube bank pattern.

-or ntubes in a vertical column of the tube bank pattern, &e 8 n& where I6 is the

diameter of a single tube in the bank.

4 reduction in the film coefficient with increasing n may be attributed to an irrease in the averagefilm thickness for each successive tube due to accumuIatioi of drip from the upper tubes.

Obviously it is advantageous to stagger the tubes -ig. 56 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 thedrip as it falls from o tube to another.

Q. 5.. Define boilin"? 9/plain briefl' different applications of boilin"


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Ans. @oiling is the convective heat transfer process that involves a phase change from liquid to

vapour state. @oiling is achieved when the temperature of the surface over which liquid flows is

maintained at a temperature above the saturation temperature of the liquid 4pplications of boiling process

+. Jroduction of steam in nuclear and steam power plants for generation and for industrial

processes and space heating.%. 4bsorption of heat in refrigeration and air conditioning system.

. &istillation and refining of liquids.

0. &ehydration and drying of foods and materials.

Q. 5.. 9/plain different t'pes of boilin".

Ans. &ifferent types of boiling are

1. ool %oilin": It occurs in steam boilers employing natural convection. Jool boiling is due to

natural convection and mi(ing induced by bubble growth and detachment.

2. Forced 7on!ection %oilin" : 'onvectional currents are set up by e(ternal means like pumps,fans etc. in forced convection. 3eat transfer rate is more in forced convection than free

convection and, bubble induced mi(ing also contribute, towards fluid motion.

3. )$bcooled or local %oilin"? The temperature of the liquid is below the saturation temperature

and boiling takes place only in the vicinity of heated surface. The bubbles travel a short distance

and then condenses in the bulk of liquid which is at a temperature less than the boiling point.

4. )$bcooled %oilin" : The temperature of the liquid e(ceeds the saturation temperature. The

vapour bubbles generated at solid surface is transported through the liquid by buoyancy effects

and eventually escape for liquidvapour interface and the actual evaporation process then sets in.

Q. 5.;. Describe the different boilin" re"imes in case of pool boilin"?

Ans. There are definite regimes of boiling corresponding to pool boiling?

1. 9!aporation process with no bubble formation Interface evaporation6 ? Interface boilingtakes place in thin layer of liquid adKoining the heated surface. The liquid in the vicinity of the

wall becomes superheated i.e., temperature of the liquid e(ceeds the saturation temperature at

given pressure. The superheated liquid rises to liquid vapour interface when evaporation takes place and heat transfer rate increases but gradually with growth in temperature e(cess.

2. &$cleate boilin": When the liquid is overheated with respect to the satiration temperature bubbles are formed at certain favourable spots like surface irregularities, dust particles called

nucleation or active sites. &epending on temperature e(cess, the nucleate boiling consists of the

following stages.

a6 @ubbles form and collapse on the surface itself.


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b6 @ubbles forms on heated surface but gets condensed in the liquid after detatching from the

surface.

c6 @ubbles form, break away from the heated surface and do not condense in the liquid surface.These bubbles rise to liquid surface and are directly e(pelled to vapour space and that helps rapid

evaporation.

The nucleation boiling is thus characterised by formation of bubbles at the nucleation sites andthe bubble agitation induces considerable fluid mi(ing and that promotes substantial increase in

heat flu( and the boiling heat transfer coefficient

3. Film boilin" : The bubble formation is very rapid leading to the formation of blanket over the

heating surface thereby preventing the incoming fresh liquid from taking their place. The bubbles

eventually coalesce to form a vapour film which covers the surface completely. Insulating effect

of the vapour film due to its low thermal conductivity6 overshadows the beneficial effect ofliquid agitation and consequently the heat flu( drops with growth in temperature e(cess. With in

the temperature range 5# L4t L +5#, conditions oscillate between nucleate and film boiling and

this phase is referred to as unstable film boiling or partial film boiling. :ventually the

temperature difference t )t6 becomes so large that radiant heat flu( becomes significant andheat flu( curve begins to rise upward with increasing temperature e(cess. That marks the region

of stable film boiling. The phenomena of stable film boiling is referred to as Meidenfrost effectN.

Q. 5.


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%. @ubble grows in sie and pushes the layer of superheated liquid away from the heated surface.

. Top of the bubble comes in contact with the cooler liquid which has the tendency to arrest the

bubble growth.0. @ubble grows to a sie where it looses more heat to cooler liquid than it gains by conduction

from the heated surface and so it begins to collapse.

5. 4s the bubble collapses, the cooler liquid gains velocity to fill in the bubble volume.2. @ubble suffers a total collapse and the inertia of cooler liquid bring it into contact with ++w

heating surface.

". :ventually the cooler liquid gets heated above the saturation temperature and another cycle of bubble form formation and collapse begins.

Q. 5.1=. What is %$rno$t point and critical heat fl$/?

Ans.

• The burnout point corresponds to the point of ma(imum heat flu( on the boiling curve

and the transition from nucleate to film boiling occurs at burnout point.

• The ma(imum heat flu( corresponding to burnout point is called critical heat flu( and the

corresponding temperature e(cess is termed as critical temperature difference.

• -or water evaporating at atmospheric pressure, the burnout occurs at a temperature

e(cess of slightly above 55 G and has the heat flu( of the order of +.5F ( +#2 W$m%.

• The boiling process remains in unstable state beyond the burnout point.

• With increase in temperature e(cess the heat That decreases and this process is continued

until a point is reached where boiling conditions gets stabilied and is in equilibrium, butat that point temperature e(cess is so high that surface temperature e(ceeds the

temperature limit of wall material and burnout structural damage and failure6 fo wall

occurs.


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Q. 5.11. Deri!e the e$ilibri$m relationship between the b$bble radi$s and amo$nt of

s$per heat.

Ans. 'onsider a spherical bubble with various forces acting on it.

et

8 vapour pressure inside the bubble

8 liquid pressure surrounding the bubble

8 Temperature of vapour corresponding to vapour pressure

8 Temperature of liquid surrounding the bubble

8 !aturation temperature of vapour inside the bubble

8 :ffective gas constant for vapour 8 atent heat of vaporisation.

+ario$s forces actin" on the spherical b$bble are:

ii6 The surface tension a of the vapour liquid interface acts on the interface length %rr and the

surface tension force equals %irru.

;nder equilibrium conditions, the pressure force is balanced by the surface tension

force. Thus

The vapour may be appro(imated as a perfect gas for which the 'layperon equation

is?


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'onsidering a noncondenseble gas inside the bubble e(erting a pressure Jgi then

:quation I6 then takes the form

This is the equilibrium relationship between the bubble radius and the amount of Water heat.

The bubble diameter &b at the time of detachment from the surface can be workedmat from the relation proposed by -rit?

where fi is the angle of contact and the empirical coastant 'd has the value #.#+0F

water bubbles.

9/ample 5.1. A condensation e/periment for steam on plate t'pe !ertical

-an denser has been set$p for a partic$lar fl$id with a "i!en temperat$re difftrent. ,he

same set$p was s$bse$entl' $sed with another fl$id with thmo>ph'sical properties "i!en

as:


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f temperat$re difference is red$ced to ;= percent6 ma0e calc$lations fo

percenta"e chan"e in the con!ection coefficient.

)ol$tion. The average heat transfer coefficient for vapour condensation on vertical plate is given

by

)$bstit$tin"

( h1 / 1.152

i.e., there is an increase of +5.%B in the convection coefficient.

9/ample 5.2. a A plate condenser was desi"ned to be 0ept !ertical. ow wo$ld the

condensatioe coefficient be effected if d$e to site constraints6 it has to be 0ept at == to thehori8ontal?

b A plate condenser of dimensions 1 / b has been desi"ned to be 0ept with side 1 in the

!ertical position. owe!er d$e to o!ersi"ht d$rin" erection and installation6 it was fi/ed

with side b !ertical. ow wo$ld this affect the heat transfer ? Ass$me laminar conditions

and same thermo>ph'sical properties in both cases and ta0e b ( 1#2.

c Determine the len"th of a 25 cm o$ter diameter t$be if the condensate formed on the

s$rface of the t$be is to be same whether it is 0ept !ertical hori8ontal.


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)ol$tion. a6 -or a vertical flat plate

-or inclined flat surfaces, the gravity acceleration g is replaced by g sin 2 where F

is the inclination angle with the horiontal. Then

This implies .5B reduction in condensation coefficient

b With side 1 !ertical:

With side b vertical.?

7omments : The condensation coefficient and accordingly heat flow increases when the shorter

side is kept vertical. -or better condensation, the condensers should be installed with shorter sidevertical.

c For laminar film6 condensation on a !ertical t$be

From e/pression 1 and ii6


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-or equal amount of condensation, the heat transfer rate and accordingly

condensation coefficient should be same for the horiontal and vertical orientations. In that case

8 %.F2 d 8 %.F2 ( %5 8 1.5 m Ans.

9/ample 5.3. a For condensin" conditions6 compare the condensation rate

when a .5 cm diameter and 1.25 m lon" pipe is 0ept 1 hori8ontall' and ii !erticall'.

Ass$me that other conditions remain same.

b For condensin" conditions6 compare the !al$es of con!ecti!e heat transfer coefficients

o!er a pipe of diameter with that of two pipes ha!in" the same total circ$mference when i

both pipes are hori8ontal and parallel and ii the pipes lie one o!er the other. Ass$me that

other conditions remain same.

)ol$tion. a -or vertical position

and for horiontal position

From identities 1 and ii

Obviously horiontal positioning provides 2+B more heat transfer. This may be

attributed to larger film thickness with increase in length. 4ccordingly condensers are generally

of horiontal type.b6 The average heat transfer coefficient for vapour condensation on a horiontal tube is given by


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7ase i : With same total circumference r& 8 % ( d and therefore d 8 &$ %. Whendiameter is reduced to half the value the convective coefficient becomes %6#.%5 8 +.+FC.

9/ample 5.4. A !ertical coolin" fin6 appro/imatin" a flat plate 4= cm in hei"ht is

e/posed to steam at atmospheric press$re. f s$rface of the fin is held at ;== 76 ma0e

calc$lations for the followin" parameters:

i Film thic0ness at the bottom ed"e of the fin6

ii !erall heat transfer coefficient6

iii eat transfer rate and the condensate mass flow rate.

Ass$me $nit width of the fin and chec0 the flow @e'nolds n$mber for the ass$mption of

laminar flow conditions.

b 9stimate the minim$m hei"ht of the plate necessar' for condensate to become $stt$rb$lent.

)ol$tion. -or saturated vapour at atmospheric pressure < the saturation temperature 8 +##P'

and the latent heat of vaporisation 8 %%5" ( Q$kg.

-or saturated water at the mean film temperature,

the relevant fluid properties are

1. ,he film thic0ness at a distance / from the top ed"e is6

4t the bottom edge of the fin ( 8 #.0 m,


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ii !erall heat transfer coefficient6

4pplying Dc 4dam*s correction for steam condensation on flat vertical plates,

iii eat transfer rate Q ( hA

8 +#F"C.% ( #.0 (l6 ( +## ) F#6 8 05FF.F W

!team condensation rate,

'hecking the film 1eynolds number, we get

Thus the assumption of laminar flow has been correct

b From the correlations

in the laminar regime

8 5"+.55cm 8 5."% m .

9/ample 5.5 )at$rated steam at atmospheric press$re condenses on the o$ter s$rface of a

!ertical t$be of lBn"th 1 m and o$ter diameter 5 mm. ,he t$be wall is maintained at a

$niform s$rface temperat$re of 4=C 7 b' the flow of coolin" water inside the t$be. 9stimate

the steam condensation rate and the heat transfer rate to the t$be. What water flow rate


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will res$lt in =.5C7 temperat$re difference of water between the o$tlet and inlet of pipe ?

Also calc$late the flow @e'nolds n$mber to chec0 the ass$mption of laminar flow

conditions.

)ol$tion. -or saturated vapour at atmospheric pressure,

-or saturated water at the mean film temperature

the relevant fluid properties are<

The film thickness at the bottom edge of the tube is,

Inserting heat transfer coefficient is,

( 2.354 / m ( =.2354 mm

The average heat transfer coefficient is,

4pplying Dc 4dam*s correction for steam condensing on vertical plates or

cylinders.

i. eat transfer6


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and the steam condensation rate is

'hecking the flow 1eynolds number, we get

4pparently the film flow is laminar in character.

ii6 The heat released during condensation is picked up by water flowhig the be. Therefore,

.. Flow rate of water

ans

9/ample 5.. A =.5 m s$are plate is e/posed to dr' sat$rated steam at =.=; bar. f s$rfaceof the plate is to be maintained at 1;.5C 76 ma0e calc$lation for the a film thic0ness6 local

heat transfer coefficient and mean flow !elocit' of condensate at 25 cm from the top of

plate6 b a!era"e heat transfer coefficient for the entire plate and c total steam

condensate rate and the total heat transfer rate to the plate.

What chan"e6 if an'6 wo$ld res$lt in the a!era"e heat transfer coefficient if the

plate is inclined at =C7 to the !ertical plane?

)ol$tion. -or saturated vapour at #.#F bar

-or saturated water at the mean film temperature % 8 #P' therelevant fluid properties are?

The film thickness at a distance ( from the top edge is,


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Inserting tt appo+iate values in consistent units,

aAt /(=.25m from the top ed"e

Dean condensate flow velocity,

b6 4t the bottom of the plate, ( 8 #.5 m

4verage heat transfer coefficient

Appl'in" -c Adams correction factor

8 +.% ( %##2F %0#F% kQ$ni.hrdeg

8 %0#F% ( #.5 (O.56 ( 0+.5 +F.56

8 +F0"+.5kQ$hr

!team condensation rate is


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3ence the film remains laminar in character

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