Etht grp 13 (140080125017,18,19,20)

Engineering Thermodynamics And Heat Transfer

Prepared By: 140080125017 Rohan Master140080125018 Ronak Modi140080125019 Parth Thakkar140080125020 Atri Patel

Guided by:Prof. Manish Mehta

Production Engineering Department

Topic

• Nusselt’s Theory of condensation- pool boiling, flow boiling

• Co-relations in boiling and condensation

Condensation

• Condensation occurs when the temperature of a vapor is reduced below its saturation temperature.

• Only condensation on solid surfaces is considered in this chapter.

• Two forms of condensation:– Film condensation,– Dropwise condensation.

Film condensation• The condensate wets the

surface and forms a liquid film.

• The surface is blanketed by a liquid film which serves as a resistance to heat transfer.

Dropwise condensation• The condensed vapor

forms droplets on the surface.

• The droplets slide down when they reach a certain size.

• No liquid film to resist heat transfer.

• As a result, heat transfer rates that are more than 10 times larger than with film condensation can be achieved.

Dropwise Condensation• One of the most effective mechanisms of heat

transfer, and extremely large heat transfer coefficients can be achieved.

• Small droplets grow as a result of continued condensation, coalesce into large droplets, and slide down when they reach a certain size.

• Large heat transfer coefficients enable designersto achieve a specified heat transfer rate with a smaller surface area.

Dropwise Condensation

• The challenge in dropwise condensation is not to achieve it, but rather, to sustain it for prolonged periods of time.

• Dropwise condensation has been studied experimentally for a number of surface–fluid combinations.

• Griffith (1983) recommends these simple correlations for dropwise condensation of steam on copper surfaces:

0 0

0

51,104 2044 22 100

255,310 100sat sat

sat

T C T Chdropwise

T C

General Considerations

General Considerations• Heat transfer to a surface occurs by condensation when the surface temperature is less than the saturation temperature of an adjoining vapor.

• Film Condensation Entire surface is covered by the condensate, which flows continuously from the surface and provides a resistance to heat transfer between the vapor and the surface.

Thermal resistance is reduced through use of short vertical surfaces and horizontal cylinders.

Characteristic of clean, uncontaminated surfaces.

• Dropwise Condensation

Surface is covered by drops ranging from a few micrometers to agglomerations visible to the naked eye.

General Considerations (cont).

Thermal resistance is greatly reduced due to absence of a continuous film.

Surface coatings may be applied to inhibit wetting and stimulate dropwise condensation.

Film Condensation: Vertical Plates

Film Condensation on a Vertical Plate• Distinguishing Features

Generally, the vapor is superheated and may be part of a mixture that includes noncondensibles.

,v satT T

A shear stress at the liquid/vapor interface induces a velocity gradient in the vapor, as well as the liquid.

• Nusselt Analysis for Laminar Flow

Assumptions: A pure vapor at .satT

Negligible shear stress at liquid/vapor interface.

0y

uy

Thickness and flow rate of condensate increase with increasing x

m

Vertical Plates (cont)

Negligible advection in the film. Hence, the steady-state x-momentum and energy equations for the film are

2

2

2

2

1

0

l l

pu Xy x

Ty

The boundary layer approximation, may be applied to the film.0/ ,p y Hence,

vp dp gx dx

Solutions to momentum and energy equations

Film thickness:

1 44

/

l l sat s

l l v fg

k T T xx

g h


Flow rate per unit width:

3

3l l v

l

gmb

Average Nusselt Number:

1 43

0 943/

.Ll l v fgL

l l l sat s

g h Lh LNuk k T T

1 0 68

Jakob number

.fg fg

p sat s

fg

h h Ja

c T TJa

h

Total heat transfer and condensation rates: L sat s

fg

q h A T T

qmh


• Effects of Turbulence: Transition may occur in the film and three flow regimes may be identified and delineated in terms of a Reynolds number defined as

44 4Re l m

l l l

umb


Wave-free laminar region Re 30 :

1 32-1/31 47 Re

//

.L l

l

h g

k

3

2

4Re

3l l v

l

g

Wavy laminar region 30 Re 1800 :

(10.37)

1 32

1.22Re

1.08 Re 5 2

//

.L l

l

h g

k

(10.38)

Turbulent region Re >1800 :

(10.39)

1 32

-0.5 0 75

Re8750 +58 Pr Re 253

/

.

/L l

l

h g

k


Calculation procedure:– Assume a particular flow regime and use the corresponding expression for (Eq. 10.37, 10.38 or 10.39) to determine Lh Re .

Re– If value of is consistent with assumption, proceed to determination of and .q m

– If value of is inconsistent with the assumption, recompute its value using a different expression for and proceed to determination of

Re

Lh and .q m

Film Condensation: Radial Systems

Film Condensation on Radial Systems

• A single tube or sphere:

1 43 /

l l l fgD

l sat s

g k hh C

T T D

Tube: C =0.729 Sphere: C=0.826

Film Condensation: Radial Systems (cont).

• A vertical tier of N tubes:

1 43

0 729

/

, . ll l fgD N

l sat s

g k hh

N T T D

Why does decrease with increasing N?,D Nh

How is heat transfer affected if the continuous sheets (c) breakdown and the condensate drips from tube to tube (d)?

What other effects influence heat transfer?

Film Condensation: Internal Flow

Film Condensation for a Vapor Flow in a Horizontal Tube• If vapor flow rate is small, condensate flow is circumferential and axial:

,iRe 35 000, , :m

i

u D

1 43

0 555/

. l l l fgD

l sat s

g k hh

T T D

0 375.fg fg sat sh h T T

• For larger vapor velocities, flow is principally in the axial direction and characterized by two-phase annular conditions.



• Steam condensation on copper surfaces:

dc

51100 2044 22 C< 100 C

255 500 100 C

,

,

dc sat sat

sat

h T T

h T

dc sat sq h A T T

Problem: Condensation on a Vertical Plate

Problem 10.48 a,b: Condensation and heat rates per unit width for saturatedsteam at 1 atm on one side of a vertical plate at 54˚C if (a) the plate height is 2.5m and (b) the height is halved.

KNOWN: Vertical plate 2.5 m high at a surface temperature Ts = 54C exposed to steam at atmospheric pressure.

FIND: (a) Condensation and heat transfer rates per unit width, (b) Condensation and heat rates if the height were halved.

ASSUMPTIONS: (1) Film condensation, (2) Negligible non-condensables in steam.

SCHEMATIC:

Problem: Condensation on a Vertical Plate (cont)

PROPERTIES: Table A-6, Water, vapor (1 atm): Tsat = 100C, v = 0.596 kgm3, hfg = 2257 kJkg; Table A-6, Water, liquid (Tf = (100 54)C2 = 350 K): 973.7 kgm3, k 0.668 WmK, 365 10-6 Nsm2 , p,c = 4195 JkgK, Pr = 2.29.

ANALYSIS: (a) The heat transfer and condensation rates are given by Eqs. 10.32 and 10.33, L sat s fgq h L T T m q h (1,2)

where, from Eq. 10.26, with Ja cp, (Tsat Ts)hfg , fg fg p, sat s fgh h 1 0.68 c T T h

fg 34195J kg K 100 54 KkJh 2257 1 0.68 2388kJ kg

kg 2257 10 J kg

.

Assuming turbulent flow conditions, Eq. 10.39 is the appropriate correlation,

1/32

0.5 0.75

hL g Re Re 1800k 8750 58Pr Re 253

(3)


Not knowing Re or Lh , another relation is required. Combining Eqs. 10.33 and 10.35,

fg fgL

sat sat

mh hRe bhA T T 4 A T T

. (4)

Substituting Eq. (4) for Lh into Eq. (3), with A bL,

fg1/30.5 0.75 2sat

Re bh Re k4 bL T T 8750 58Pr Re 253 g

. (5)

Using appropriate properties with L = 2.5 m, find

6 2 3365 10 N s m 2388 10 J kg4 2.5m 100 54 K

(6)

0.5 1/ 30.75 26 4 2 2

1 0.668W m K

8750 58 2.29 Re 253365 10 973.7 m s 9.8m s

Re 2979 .

Since Re 1800, the flow is turbulent, and using Eq. (4) or (3), find 2

Lh 5645W m K .


From the rate equations (1) and (2), the heat transfer and condensation rates are 2q 5645W m K 2.5m 100 54 K 649k W m <

3 3m 649 10 W m 2388 10 J kg 0.272kg s m . <

(b) If the height of the plate were halved, L = 1.25 m, and turbulent flow was still assumed to exist, the LHS of Eq. (5) may be reevaluated and the equation solved to obtain Re 1280 .

Since 1800 Re , the flow is not turbulent, but wavy-laminar. The procedure now follows that of Example 10.3. For L = 1.25 m with wavy-laminar flow, Eq. 10.38 is the appropriate correlation. The calculation yields Re 1372 2

Lh 5199 W m K q 299kW m m 0.125kg s m . <

COMMENT:

Note that the height was decreased by a factor of 2, while the rates decreased by a factor of 2.2. Would you have expected this result?

Classification of boiling Pool Boiling

• Boiling is called pool boiling in the absence of bulk fluid flow.

• Any motion of the fluid is due to natural convection currents and the motion of the bubbles under theinfluence of buoyancy.

Flow Boiling• Boiling is called flow

boiling in the presence of bulk fluid flow.

• In flow boiling, the fluid is forced to move in a heated pipe or over a surface by

external means such as a pump.

Pool BoilingBoiling takes different forms, depending on the Texcess=Ts-Tsat

Heat Transfer Correlations in Pool Boiling

• Boiling regimes differ considerably in their character different heat transfer relations need to be used for different boiling regimes.

• In the natural convection boiling regime heat transfer rates can be accurately determined using natural convection relations.

Film Boiling• The heat flux for film boiling on a horizontal

cylinder or sphere of diameter D is given by

• At high surface temperatures (typically above 300°C), heat transfer across the vapor film by radiation becomes significant and needs to be considered.

• The two mechanisms of heat transfer (radiation and convection) adversely affect each other, causing the total heat transfer to be less than their sum.

• Experimental studies confirm that the critical heat flux and heat flux in film boiling are proportional to g1/4.

143 0.4v v l v fg pv s sat

film film s satv s sat

gk h C T Tq C T T

D T T

Enhancement of Heat Transfer in Pool Boiling

• The rate of heat transfer in the nucleate boiling regime strongly depends on the number of active nucleation sites on the surface, and the rate of bubble formation at each site.

• Therefore, modification that enhances nucleation on the heating surface will also enhance heat transfer in nucleate boiling.

• Irregularities on the heating surface, including roughness and dirt, serve as additional nucleation sites during boiling.

• The effect of surface roughness is observed to decay with time.

Enhancement of Heat Transfer in Pool Boiling

• Surfaces that provide enhanced heat transfer in nucleate boiling permanently are being manufactured and are available in the market.

• Heat transfer can be enhanced by a factor of up to 10 during nucleate boiling, and the critical heat flux by a factor of 3.

Thermoexcel-E

Flow Boiling• In flow boiling, the fluid is forced to move by an

external source such as a pump as it undergoes a phase-change process.

• The boiling in this case exhibits the combined effects of convection and pool boiling.

• Flow boiling is classified as either external and internal flow boiling.

• External flow ─ the higher the velocity, the higher the nucleate boiling heat flux and the criticalheat flux.

Flow Boiling ─ Internal Flow• The two-phase flow in a

tube exhibits different flow boiling regimes, depending on the relative amounts of the liquid and the vapor phases.

• Typical flow regimes:– Liquid single-phase flow,– Bubbly flow,– Slug flow,– Annular flow,– Mist flow,– Vapor single-phase flow.

A

xial

pos

ition

in th

e tu

be

Flow Boiling ─ Internal Flow• Liquid single-phase flow

– In the inlet region the liquid is subcooled and heat transfer to the liquid is by forced convection (assuming no subcooled boiling).

• Bubbly flow– Individual bubbles– Low mass qualities

• Slug flow– Bubbles coalesce into slugs of vapor.– Moderate mass qualities

• Annular flow– Core of the flow consists of vapor only, and liquid adjacent to the walls. – Very high heat transfer coefficients

• Mist flow– a sharp decrease in the heat transfer coefficient

• Vapor single-phase flow– The liquid phase is completely evaporated and vapor is superheated.

Film Condensation on a Vertical Plate

• liquid film starts forming at the top of the plate and flows downward under the influence of gravity.

• increases in the flow direction x• Heat in the amount hfg is released

during condensation and is transferred through the film to the plate surface.

• Ts must be below the saturation temperature for condensation.

• The temperature of the condensate is Tsat at the interface and decreases gradually to Ts at the wall.

Vertical Plate ─ Flow Regimes • The dimensionless parameter

controlling the transition between regimes is the Reynolds number defined as:

• Three prime flow regimes:– Re<30 ─ Laminar (wave-free),– 30<Re<1800 ─ Wavy-laminar,– Re>1800 ─ Turbulent.

• The Reynolds number increases in the flow direction.

hydraulic diameter

4Re

hD

l lx

l

V

Heat Transfer Correlations for Film Condensation ─ Vertical wall

Assumptions:1. Both the plate and the vapor are

maintained at constant temperatures of Ts and Tsat, respectively, and the temperature across the liquid film varies linearly.

2. Heat transfer across the liquid film is by pure conduction.

3. The velocity of the vapor is low (or zero) so that it exerts no drag on the condensate (no viscous shear on the liquid–vapor interface).

4. The flow of the condensate is laminar (Re<30) and the properties of the liquid are constant.

5. The acceleration of the condensate layer is negligible.

Height L and width b