HW # 6 /Tutorial # 6

WRF Chapter 20; WWWR Chapters 21 & 22

ID Chapters 10 & 11

• Tutorial # 6

• WRF#20.6; WWWR #21.13, 21.14; WRF#20.7; WWWR# 21.19. 22.3,

• 22.15.• Hint: 21.13: You may neglect the

temperature drop across the tube wall. Suggested initial guess: Tw = 58oC, Ti(out) = 36oC.

• To be discussed during the week 2 - 6 March, 2020.

• By either volunteer or class list.

• Homework # 6 (Self-practice)

• WWWR # 21.17 Correction:

“If eight tubes of the size designated in Problem WRF 20.7.”

• ID # 10.54

Boiling and Condensation

Boiling

Two basic types of boiling:

• Pool boiling

– Occurs on heated surface submerged in a liquid pool

which is not agitated

• Flow boiling

– Occurs in flowing stream

– Boiling surface may be a portion of flow passage

– Flow of liquid and vapor important type of 2 phase

flow

Regimes of Boiling

Regime 1:

• Wire surface temperature is only a few degrees

higher than the surrounding saturated liquid

• Natural convection currents circulate the

superheated liquid

• Evaporation occurs at the free liquid surface as the

superheated liquid reaches that position

Regime 2:

• Increase in wire temperature is accompanied by

the formation of vapor bubbles on the wire surface

• These bubbles form at certain surface sites, where

vapor bubble nuclei are present, break off and

condense before reaching the free liquid surface

At a higher surface temperature, as in regime III, larger and more

numerous bubbles form, break away from the wire surface, rise,

and reach the free surface. Regimes II & III are associated with

nucleate boiling.

Regime IV:

• Beyond the peak of the curve the transition boiling

regime is entered.

• A vapor film forms around the wire, and portions

of this film break off and rise, briefly exposing a

portion of the wire surface

• This film collapse and reformation and this

unstable nature of the film is characteristic of the

transition regime.

• When present, the vapor film provides a

considerable resistance to heat transfer, thus the

heat flux decreases.

Correlations of Boiling Heat-

Transfer Data

( )L Vb

gD

Nub = Cfc Rebm PrL

n Refer to Appendix 6 for Detailed Derivation.

surface tension

As confirmed by Cengel 2007

Condensation

• Occurs when a vapor contacts a surface

which is at a temperature below the

saturation temperature of the vapor.

• When the liquid condensate forms on the

surface, it will flow under the influence of

gravity.

• Film Condensation

•Normally the liquid wets the surface, spreads out and forms a

film.

• Dropwise Condensation

•If the surface is not wetted by the liquid, then droplets form and

run down the surface, coalescing as they contact other

condensate droplets.

Example 1

Film Condensation:

Turbulent-Flow Analysis

• It is logical to expect the flow of the condensate

film to become turbulent for relatively long

surfaces or for high condensation rates.

• The criterion for turbulent flow is a Reynolds

number for the condensate film.

• In terms of an equivalent diameter, the

applicable Reynolds number is

Re = 4A Lu

P mf

41 ; 1; 4

44Re

L avg L avg

f f

AA P

P

v vA

P

m m

44Re

L avgc

f f

V

m m

44Re

L avgc

f f

V

m m

Dropwise Condensation

Dropwise Condensation

• Associated with higher heat-transfer

coefficients than filmwise condensation

phenomenon.

• Attractive phenomenon for applications

where extremely large heat-transfer rates

are desired.

Heat Transfer Equipment

• Single-pass heat exchanger – fluid flows through

only once.

• Parallel or Co-current flow – fluids flow in the

same direction.

• Countercurrent flow or Counterflow - fluids flow

in opposite directions.

• Crossflow – two fluids flow at right angles to one

another.

Double pipe heat exchanger (A) and

crossflow heat exchanger (B)

A B

Shell-and-tube Arrangement

• E.g. Tube-side fluid makes two passes, shell-side fluid

makes one pass.

• Good mixing of the shell-side fluid makes one pass.

Log-Mean Temperature Difference

• Temperature profiles for single-pass double-pipe heat

exchanger

Counterflow analysis

• Temperature vs. contact area

Log-Mean Temperature Difference (continued)

• First-law-of-thermodynamics

• Energy transfer between the two fluids

. .

p c p H

c H

q mC T mC T

. .

p c c c p H H H

c H

dq mC dT C dT mC dT C dT

( )

( )

H C

H C H C

dq UdA T T

T T T d T dT dT

Log-Mean Temperature Difference (continued)

Log-Mean Temperature Difference (continued)

q = U*T*dA

CH* (TH2-TH1) = q

Log-Mean Temperature Difference (continued)

Example #1

Example #1 (continued)

Shell-and-Tube Heat Exchanger (1)

Shell-and-Tube Heat Exchanger (2)

Shell-and-Tube Heat Exchanger (3)

Shell-and-Tube Heat Exchanger (4)

Cross Flow Heat Exchanger (1)

Cross Flow Heat Exchanger (2)

Cross Flow Heat Exchanger (3)

Example # 2

350

375

280 375

280 311.1

350 375

S, H, Water 280 -> 311.1

T, C, Oil 375-> 350