ce311 fall 2016 final exam name: instructions...ce311 fall 2016 final exam name: _____ 1/16...

CE311 Fall 2016 Final Exam Name: __________________________________

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Instructions

1. Please solve the problems using the specified SI or IP system of units. 2. Please show all of your calculations to get full credit and pay attention to assumptions.

3. Neatly mark points and outline processes on the ASHRAE SI or IP psychrometric chart. � 4. Final solutions should be clearly summarized and marked/boxed. � 5. Neatly sketch all illustrations. 6. Use only the attached equation sheet. 7. Please attach additional pages of your work, clearly marking each problem.

Problem 1 (25/100pts)

Outdoor air enters an air handling unit (AHU) at 5� and 35% relative humidity at a steady volumetric flow rate of 25m3/min, and it leaves at 25� and 55% relative humidity. The outdoor air is first heated to 22� with a heating coil and then humidified through the injection of hot steam. Assuming the entire process takes place at a pressure of 1 atm, determine: (a) Draw a schematic of an AHU for this process. Label each point and the components (5pts)

(b) Neatly sketch the process on a psychrometric chart and label all points (5pts)

(c) The rate of heat supply in the heating section. (7.5pts)


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(d) The mass flow rate of steam required in the humidifying section. (7.5pts)


3/16


Recirculation air from a room having dry-bulb and wet-bulb temperatures of 33� and 29�, respectively, enters an AHU at a steady state and mixes with outdoor air entering with dry-bulb and wet-bulb temperatures of 16� and 12�, respectively. The volumetric flow rate of the outdoor air stream is three times that of the recirculation stream. A single mixed stream exits prior to conditioning and supply back to the room. The pressure is constant throughout at 1 atm. You can neglect kinetic and potential energy effects. (a) Draw a schematic of an AHU for this process. Label each point and the components (5pts)

(b) Neatly sketch the process on a psychrometric chart and label all points (5pts)

(c) The relative humidity of the mixed air stream (7.5pts)


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(d) The temperature, in �(7.5pts)


5/16


You are asked to evaluate the total thermal resistance and heat gain of a wall enclosure, considering the effects of natural and forced convection, radiation, and conduction. Consider the wall enclosure with the dimensions and associated material and air properties shown below. You can treat the surrounding indoor wall surfaces and sky as blackbodies. Airflow along the indoor wall surface is buoyancy-driven, whereas airflow across the outer surface is wind-driven. You can apply Nusselt number correlations for flat horizontal surfaces for the vertical outer wall.

Determine the following: (a) Indoor surface: Rayleigh number and Nusselt number (5pts)


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(b) Indoor surface: Natural convection and radiation heat transfer coefficients (5pts)

(c) Outdoor surface: Reynolds number and Nusselt number (5pts)

(d) Outdoor surface: Forced convection and radiation heat transfer coefficients (5pts)


7/16

(e) Draw a thermal resistance network for the entire system (2.5pts) (f) Compute the equivalent (parallel) resistances for the inner and outer wall surfaces (5pts)


8/16

(g) Compute total thermal resistance of the wall surface (5pts) (h) Compute heat flow rate (W) from outside to inside (2.5pts)


9/16

Problem 4 (15/100pts) – volatile organic compound (VOC) emissions from vinyl flooring

Toluene is being emitted from vinyl flooring in a living room. A small mixing fan is used in the room. You are asked to determine the emission rate (or net mass transport rate, Jmass) of toluene from the vinyl flooring to the room air.

!" = 100'(/*+ ," = 1*/- ." = 18�

(a) Compute the: Reynolds number, Schmidt number, and Sherwood number (5pts) (b) Determine the average mass transfer coefficient (2pts)

[toluene]

Pg@22�=3.76kPa

D=0.087cm2/s

(tolueneinair@22�)

Mtoluene=92.14g/mol


10/16

(c) Calculate the surface concentration of toluene (5pts) (d) Calculate the emission rate (or net mass transport rate, Jmass) of toluene (3pts)


11/16

Tina

Rectangle

Tina

Rectangle


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01 =212

01:*456789:;<42

21: 2=*>6847*456-47:4*?4262;(9-< *45

2: ;4;952=*>6847*456-47*<@;=86 *45

A1 =*1

21

ABCDE1C = 28.97

AJEKLCMENOC = 18.02

P = 8.314

P1 =PA1

A1:*456:=598S6<(ℎ;47(9-<((/*45)

*1:*9--47(9-<(()

ABCDE1C = *456:=598S6<(ℎ;47W809<8(g/mol)

AJEKLCMENOC = *456:=598S6<(ℎ;47S9;68(g/mol)

P: =2<\68-95(9-:42-;92;(]^/]*45 − `)

P1 = (9-:42-;92;47(9-<

idealgasequationofstate:

PV = nP.

T: temperature

V: volume

P: pressure

ω =*M

*E

ω = 0.622sMsE

φ =sMsu

φ =vs

(0.622 + v)su

s1 = 01s

ω: humidityratio (e.g.kgwv/kgda)

*M:massofwatervapor

*E:massofdryair

sM: partialpressureofwatervapor

sE: partialpressureofdryair

φ: relativehumidity (-)

su: saturationvaporpressure

s1: partialpressureofspeciesi

P:totalmixturepressure

h = ℎE + vℎM h:moistairmixtureenthalpy(kJ/kgdryair)

ℎE: 62;ℎ95?047W809<8(kJ/kgdryair)

ℎM: 62;ℎ95?047S9;68\9?48(kJ/kgwatervapor)

conservationofmass:

*E =1

*EL

*M +1

*J1

= *M +L

*JL

e:exiti: inlet

*E:*9--754S89;647W809<8(](W809<8/*<2)

*M:*9--754S89;647S9;68\9?48(](S9;68\9?48/*<2)


13/16

*J:*9--754S89;6475<�=<WS9;68(](5<�=<WS9;68/*<2)

conservationofenergy:

Ä −Å = *LℎL −L

*ÇℎÇ1

� =ÄÉ

�: ℎ69;75=@(Å/*Ñ)

Ä: ℎ69;754S89;6(Å)A: areaperpendiculartodirectionofheatflow(*Ñ)

Fourier’sLaw

ÄÜOáB = −]ÉW.W@

k: ;ℎ68*95:42W=:;<\<;0(Å/*℃48Å/*`)

T: temperature(℃orK)

W.W@

: ;6*?689;=86(89W<62;<2@ − W<86:;<42(℃/*48`/*)

α =]!ãN

α: thermaldiffusivity(*Ñ/s)

ρ: density(kg/*+)ãN: -?6:<7<:ℎ69;:9?9:<;0(^/](℃48^/](`)

ν ='!

ν: kinematicviscosity(*Ñ/s)

': W029*<:\<-:4-<;0(*Ñ/s)

Re =,èν

Re: Reynoldsnumber

V: characteristicvelocity(m/s)

L: characteristiclengthscale(m)

τ = µW=dy

τ: shearstress(N/*Ñ)W=dy: \654:<;0(89W<62;

R =Δ.

Ä

R: thermalresistance(℃/Å48`/Å)

Δ.: ;6*?689;=86W<776862:6(℃orK)

Newton’sLawofcooling:

Ä = ℎÉñ(.ñ − .")

Éñ: -=879:69869(*Ñ)

ℎ: :42\6:;<42:4677<:<62;(Å/*Ñ℃48Å/*Ñ`)

.ñ: -=879:6;6*?689;=86(℃orK)

.": >=5]75=<W487866 − -;869*;6*?689;=86(℃orK)

Pr =να

Pr: Prandtlnumber

Nu =ℎè]ó

Nu:Nusseltnumber local

ℎ: 54:95:42\6:;<42:4677<:<62;(Å/*Ñ℃48Å/*Ñ`)

è: :ℎ989:;68<-;<:562(;ℎ-:956(*)]ó: 75=<W;ℎ68*95:42W=:;<\<;0(Å/*℃48Å/*`)


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ò= =ℎè]ó

ò=: 9\689(6ò=--65;2=*>68

ℎ: 9\689(6:42\6:;<42:4677<:<62;

P6ÜC = 5 ∗ 10õ P6ÜC: :8<;<:95P60245W-2=*>68748-*44;ℎ759;?59;6

(748:6W:42\6:;<42)

ℎ =1Éñ

ℎW@W0úù

ℎ =1è

ℎW@û

ü

ℎ: 54:95:42\6:;<42:4677<:<62;(Å/*Ñ℃48Å/*Ñ`)

ℎ: 9\689(6:42\6:;<42:4677<:<62;è: 562(;ℎ47?59;6(*)

.ó =12(.ñ + .")

.ó: 7<5*;6*?689;=86(℃orK)

β =−1!(°s°.)

β = 1/.748<W695(9-

β: coefficientofexpansion(1/K)

ρ: density(kg/*+)

T: temperature(℃orK)

¢8û =(£(.ñ − .")è+

§Ñ

¢8û: ¢89-ℎ472=*>68

g = 9.81(m/-+), gravitationalacceleration

.ñ: -=879:6;6*?689;=86(℃orK)

.": >=5]75=<W;6*?689;=86(℃orK)

è: :ℎ989:;68<-;<:562(;ℎ(*)

ν: kinematicviscosity(*Ñ/s)

Ra = Gr ∗ Pr

P9 =(£(.ñ − .")è+

§ß

Ra: Rayleighnumber

P9ÜC~10© ∶ :8<;<:95P92=*>6874829;=895:42\6:;<42

Nusseltnumbercorrelationsforforcedconvection:LocalNuandhforlaminarflowoverflatplate

ò=´ =ℎ´è]ó

= 0.332P6´¨Ñs8

¨+forPr > 0.6

LocalNuandhforturbulentflowoverflatplate

ò=´ =ℎ´è]ó

= 0.0296P6´Æõs8

¨+for0.6 < Pr < 60

AverageNuandhforlaminarflowoverflatplate

ò=´ =ℎ´è]ó

= 0.664P6´¨Ñs8

¨+forPr > 0.6

AverageNuandhforturbulentflowoverflatplate


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ò=´ =ℎ´è]ó

= 0.037P6´Æõs8

¨+for0.6 < Pr < 60

AverageNuandhformixedboundarylayer

ò=û = (0.037P6ûÆõ−É)s8

¨+for0.6 < Pr < 60

É = 871748P6ÜC = 5 ∗ 10õ; É = 0.037P6ÜCÆõ − 0.644P6ÜC

¨Ñ

CorrelationsfortheaverageNufornaturalconvectionoververticalplate

ò=û =ℎè]ó

= ãP9ûá

Laminar: 10Æ ≤ P9û ≤ 10©ã = 0.59, n = 1/4

Turbulent: 10© ≤ P9û ≤ 10¨+ã = 0.1, n = 1/3

Mixedboundarylayer:

ò= = 0.825 +0.387P9û

¨≤

1 + 0.492/s8 ©/¨≤ ≥/Ñ¥

Ñ

radiationµ∂ = ∑.∏Æ.∏: surfacetemperature(K)

µ∂: blackbodyemissionpower(W/*Ñ)

∑: Stefan − Boltzmannconstant: 5.67x10Ω≥(Å/*Ñ`Æ)

µ = æ∑.∏Æ

æ: emissivity(0to1)

¢E∂∏ = ß¢

¢E∂∏: absorbedradiation(W/*Ñ)

ß: absorptivity(0to1)

�CEB = µ − ß¢ = æ∑(.∏Æ − .∏øCCÆ ) ÄCEB = æ∑É∏(.∏Æ − .∏øCCÆ )�CEB: radiationheatflux(W/*Ñ)

ÄCEB: radiationheatflowrate(W)É∏: surfacearea(*Ñ)

.∏øCC: surroundingsurfacetemperature, treatedasablackbody(K)

ÄCEB = ℎCÉ∏(.∏ − .∏øCC) ℎC: radiationheattransfercoefficient(Å/*ÑK)

ℎC = æ∑(.∏ − .∏øCC)(.∏Ñ − .∏øCCÑ )


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PL¿ø1M,NECE¡¡L¡ = ( ¨

¬√)Ω¨

PL¿ø1M,NECE¡¡L¡: equivalentresistanceforresistorsinparallel

masstransfer !1 =

ƒ√

≈

!1:massconcentration(g/cm3) *1:massfospecies(g) ã1 =

á√≈

ã1:molarconcentration(mol/m3) !1 = A1ã1

j = −« B»

B´ j: molardiffusionflux(mol/cm2s)

D: diffusioncoefficient(cm2/s)

j = ℎƒ(ãñ − ã") J = ℎƒÉ∏(ãñ − ã") J:netmolartransportrate(mol/s)

ã∏: surfacemolarconcentration(mol/m3)

ã": bulk/freestreammolarconcentration(mol/m+)

ℎƒ: convectionmasstransfercoefficient(m/s)

ã∏ = À(ÃÕ)

P.- !∏ =

À(ÃÕ)Œ

P.-

œℎû =–—û

“ œℎû ∶ averageSherwoodnumber

Sc = ”

“ Sc:Schmidtnumber

Le = ‘’

÷◊ Le:Lewisnumber

Shcorrelations:replaceNuw/ShandPrw/Sc(viaheat&masstransferanalogy)

ÿ

–—= !: è6(¨Ωá) ntypically=1/3

C∏O¡1B = ⁄sM

C∏O¡1B: solid − phaseconcentration(kmol/*+) ⁄: solubility(kmol/m3bar)

€ = ⁄D €:permeability(kmol/s-bar)

ℳ = €

û ℳ:permeance(kg/s-m2-Pa)

JM = ℳÉ(sM¨ − sMÑ) JM:watervapornettransportratethroughwall(kg/s)

RR

ASHR

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DRY BULB TEMPERATURE - °F

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12.5

13.0

13.5

14.0 VOLUME- CU.FT. PER LB. DRY AIR

14.5

15.0

HUMIDITY RATIO - POUNDS MOISTURE PER POUND DRY AIR

0

1.0

1.0

:-

2.0

4.0

8.0

-8.0

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120 E

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ALP

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KJ

PE

R K

ILO

GR

AM

OF

DR

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10

20

30

40

50

60

70

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100

ENTHALPY - K

J PER KILO

GRAM OF D

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C

5

10

15

20

25

30

35

40

45

50

DRY BULB TEMPERATURE - °C

.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

.011

.012

.013

.014

.015

.016

.017

.018

.019

.020

.021

.022

.023

.024

.025

.026

.027

.028

.029

.030

10%

REL

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20%

30%

40%

50%

60%

70%

80%

90%

5

5

10

10

15

15

20

20

25

25

30 W

ET B

ULB

TEM

PERA

TURE

- °C

30

0.78

0.80

0.82

0.84

0.86 VOLUME - CUBIC METER PER KG DRY AIR

0.88

0.90

0.92

0.94

HUMIDITY RATIO - KILOGRAMS MOISTURE PER KILOGRAM DRY AIR

0

1.0

1.0

:-

1.5

2.0

4.0

-4.0

-2.0-1.0

-0.5

-0.2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-5.0

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F

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75

80

85

90

95

100

105

110

115

120


.002

.004

.006

.008

.010

.012

.014

.016

.018

.020

.022

.024

.026

.028

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REL

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30%

40%

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60%

70%

80%

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35

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6065

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ET B

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TEM

PERA

TURE

- °F

85

90

12.5

13.0

13.5


14.5

15.0


0

1.0

1.0

:-

2.0

4.0

8.0

-8.0

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-2.0-1.0

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-0.3

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0.3

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HUM

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01.3

25 k

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AMER

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G, R

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ENG

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RS, I

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LEVE

L

1020

3040

5060708090100

110

110

120

120 E

NTH

ALP

Y -

KJ

PE

R K

ILO

GR

AM

OF

DR

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IR

10

20

30

40

50

60

70

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90

100

ENTHALPY - K

J PER KILO

GRAM OF D

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C

5

10

15

20

25

30

35

40

45

50


.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

.011

.012

.013

.014

.015

.016

.017

.018

.019

.020

.021

.022

.023

.024

.025

.026

.027

.028

.029

.030

10%

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20%

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40%

50%

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70%

80%

90%

5

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20

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30 W

ET B

ULB

TEM

PERA

TURE

- °C

30

0.78

0.80

0.82

0.84


0.88

0.90

0.92

0.94


0

1.0

1.0

:-

1.5

2.0

4.0

-4.0

-2.0-1.0

-0.5

-0.2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-5.0

-2.0

0.0

1.0

2.0

2.5

3.0

4.0

5.0

10.0

- ::

SENS

IBLE

HEA

TQ

sTO

TAL

HEAT

Qt

ENTH

ALPY

HUM

IDIT

Y RA

TIO

Dh

DW

RR

ASHR

AE P

SYCH

ROM

ETRI

C CH

ART

NO.1

NORM

AL T

EMPE

RATU

REBA

ROM

ETRI

C PR

ESSU

RE: 1

01.3

25 k

PaCo

pyrig

ht 1

992

AMER

ICAN

SO

CIET

Y O

F HE

ATIN

G, R

EFRI

GER

ATIN

G A

ND A

IR-C

OND

ITIO

NING

ENG

INEE

RS, I

NC.

SEA

LEVE

L

RR

ASHR

AE P

SYCH

ROM

ETRI

C CH

ART

NO.1

NORM

AL T

EMPE

RATU

REBA

ROM

ETRI

C PR

ESSU

RE: 2

9.92

1 IN

CHES

OF

MER

CURY

Copy

right

199

2AM

ERIC

AN S

OCI

ETY

OF

HEAT

ING

, REF

RIG

ERAT

ING

AND

AIR

-CO

NDIT

IONI

NG E

NGIN

EERS

, INC

.

SEA

LEVE

L

1015

2025

303540455055

55

60

60

EN

THA

LPY

- B

TU P

ER

PO

UN

D O

F D

RY

AIR

15

20

25

30

35

40

45

50

ENTHALPY - B

TU PER POUND OF D

RY AIR


F

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

115

120


.002

.004

.006

.008

.010

.012

.014

.016

.018

.020

.022

.024

.026

.028

10%

REL

ATIV

E H

UM

IDIT

Y

20%

30%

40%

50%

60%

70%

80%

90%

35

3540

4045

4550

5055

5560

6065

65

70

70

75

75

80

80

85 W

ET B

ULB

TEM

PERA

TURE

- °F

85

90

12.5

13.0

13.5


14.5

15.0


0

1.0

1.0

:-

2.0

4.0

8.0

-8.0

-4.0

-2.0-1.0

-0.5-0.4

-0.3

-0.2

-0.1

0.1

0.2

0.3

0.4

0.5

0.6

0.8

-200

0-1

000

0

500

1000

1500

2000 3000

5000

- ::

SENS

IBLE

HEA

TQ

sTO

TAL

HEAT

Qt

ENTH

ALPY

HUM

IDIT

Y RA

TIO

Dh

DW

RR

ASHR

AE P

SYCH

ROM

ETRI

C CH

ART

NO.1

NORM

AL T

EMPE

RATU

REBA

ROM

ETRI

C PR

ESSU

RE: 2

9.92

1 IN

CHES

OF

MER

CURY

Copy

right

199

2AM

ERIC

AN S

OCI

ETY

OF

HEAT

ING

, REF

RIG

ERAT

ING

AND

AIR

-CO

NDIT

IONI

NG E

NGIN

EERS

, INC

.

SEA

LEVE

L

RR

ASHR

AE P

SYCH

ROM

ETRI

C CH

ART

NO.1

NORM

AL T

EMPE

RATU

REBA

ROM

ETRI

C PR

ESSU

RE: 1

01.3

25 k

PaCo

pyrig

ht 1

992

AMER

ICAN

SO

CIET

Y O

F HE

ATIN

G, R

EFRI

GER

ATIN

G A

ND A

IR-C

OND

ITIO

NING

ENG

INEE

RS, I

NC.

SEA

LEVE

L

1020

3040

5060708090100

110

110

120

120 E

NTH

ALP

Y -

KJ

PE

R K

ILO

GR

AM

OF

DR

Y A

IR

10

20

30

40

50

60

70

80

90

100

ENTHALPY - K

J PER KILO

GRAM OF D

RY AIR


C

5

10

15

20

25

30

35

40

45

50


.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

.011

.012

.013

.014

.015

.016

.017

.018

.019

.020

.021

.022

.023

.024

.025

.026

.027

.028

.029

.030

10%

REL

ATIV

E H

UM

IDIT

Y

20%

30%

40%

50%

60%

70%

80%

90%

5

5

10

10

15

15

20

20

25

25

30 W

ET B

ULB

TEM

PERA

TURE

- °C

30

0.78

0.80

0.82

0.84


0.88

0.90

0.92

0.94


0

1.0

1.0

:-

1.5

2.0

4.0

-4.0

-2.0-1.0

-0.5

-0.2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-5.0

-2.0

0.0

1.0

2.0

2.5

3.0

4.0

5.0

10.0

- ::

SENS

IBLE

HEA

TQ

sTO

TAL

HEAT

Qt

ENTH

ALPY

HUM

IDIT

Y RA

TIO

Dh

DW

RR

ASHR

AE P

SYCH

ROM

ETRI

C CH

ART

NO.1

NORM

AL T

EMPE

RATU

REBA

ROM

ETRI

C PR

ESSU

RE: 1

01.3

25 k

PaCo

pyrig

ht 1

992

AMER

ICAN

SO

CIET

Y O

F HE

ATIN

G, R

EFRI

GER

ATIN

G A

ND A

IR-C

OND

ITIO

NING

ENG

INEE

RS, I

NC.

SEA

LEVE

L

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