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,

HW # 6 /Tutorial # 6WRF 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 29 Feb. - 4 March, 2016.

• 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 L

P f

41 ; 1; 4

44Re L avg L avg

f f

AA PP

v vAP

44Re L avgc

f f

V

44Re L avgc

f f

V

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 Hc H

q mC T mC T

. .

p c c c p H H Hc H

dq mC dT C dT mC dT C dT

( )( )

H C

H C H C

dq UdA T TT T T d T dT dT

Log-Mean Temperature Difference (continued)

Log-Mean Temperature Difference (continued)

q = U*T*dACH* (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