Solution manual heat and mass transfer a practical approach 3rd edition cengel CH10 2

10-81 Saturated ammonia vapor at a saturation temperature of Tsat = 25°C condenses on the outer surfaces of a tube bank in which cooling water flows.. The rate of condensation of ammonia

Review Problems

10-79 Water is boiled at Tsat = 100°C by a spherical platinum heating element immersed in water The

surface temperature is Ts = 350°C The boiling heat transfer coefficient is to be determined

Assumptions 1 Steady operating conditions exist 2 Heat losses from the heater and the boiler are

negligible

Properties The properties of water at the saturation temperature of 100°C are (Table A-9)

3 3

kg/m9.957

J/kg102257

The properties of water vapor at (350+100)/2 = 225°C

are (Table A-16)

C W/m03581.0

CJ/kg1951

skg/m10749

1

kg/m444.0

5 3

Analysis The film boiling occurs since the temperature difference between the surface and the fluid The

heat flux in this case can be determined from

5

3 3

sat

4 / 1

sat

sat 3

film

W/m386

,

27

)100350()

100350)(

15.0)(

10749.1(

)100350)(

1951(4.0102257)444.09.957)(

444.0()03581.0)(

81.9(67

0

)(

)(

)(

4.0)(

−

=

−

T T T

T D

T T c h

gk

s v

s pv fg

v l v v

μ

ρρρ

&

The boiling heat transfer coefficient is

C W/m

W/m386,27)

(

2 sat

film sat

q h T

T h q

s

&

10-80 Water is boiled at Tsat = 120°C in a mechanically polished stainless steel pressure cooker whose

inner surface temperature is maintained at Ts = 130°C The time it will take for the tank to empty is to be

1

Pr

CJ/kg4244N/m

0550

0

skg/m10232.0kg/m

121

1

J/kg102203kg/m

4.943

3 3

3 3

fg l

c

h

σ

μρ

ρ

Heating

130 °C

120 °C Water

Also, 0.0130 and n = 1.0 for the boiling of water on a

mechanically polished stainless steel surface (Table 10-3) Note

that we expressed the properties in units specified under Eq 10-2

in connection with their definitions in order to avoid unit

2

3 3

1/2 3

3

3 sat ,

2 / 1 nucleate

W/m400,228

44.1)102203(0130.0

)120130(42440550

.0

1.121)-9.8(943.4)

10)(220310

232.0(

Pr

)(

)(

s l p v

l fg l

h C

T T c g

h q

σ

ρρμ

&

The rate of heat transfer is

W7174) W/m400,228(m)20.0(4

W71743

kg/m4.943(2

12

kg446.4evap evap

m

m m

t

&

&

10-81 Saturated ammonia vapor at a saturation temperature of Tsat = 25°C condenses on the outer surfaces

of a tube bank in which cooling water flows The rate of condensation of ammonia, the overall heat transfer coefficient, and the tube length are to be determined

Assumptions 1 Steady operating conditions exist 2 The tubes are isothermal 3 The thermal resistance of

the tube walls is negligible

Properties The properties of ammonia at the saturation temperature of 25°C are hfg = 1166×103

J/kg and

ρv = 7.809 kg/m3 (Table A-11) We assume that the tube temperature is 20°C Then, the properties of liquid ammonia at the film temperature of T f =(Tsat+T s)/2=(25 + 20)/2 = 22.5°C are (Table A-11)

C W/m4869

0

CJ/kg4765

skg/m10479

1

kg/m5.606

4 3

0

skg/m10124

1

CJ/kg4185

kg/m0.999

3 3

=

C)20C(25J/kg47650.68+J/kg101166

)(

68.0

3 3 sat

9280

m)C(0.025)

2025(s)kg/m10479.1(

)C W/m4869.0)(

J/kg101182)(

kg/m809.7)(606.5kg/m

5.606)(

m/s8.9(

729

0

)(

)(

729.0

2

4 / 1

4

3 3

3 3

2

4 / 1

k h g

h

h

s l

l fg v l l

μ

ρρρ

Then the average heat transfer coefficient for a 4-pipe high vertical tier becomes

C W/m6562C) W/m9280(4

1

4 / 1 tube 1 horiz, 4 / 1 tubes N

N h

h o

The rate of heat transfer in the condenser is

W 10 970 1 ) 14 17 )(

C J/kg 4185 )(

kg/s 69 15 ( ) (

kg/s 69 15 ) m/s 2 ( ) m 025 0 )(

25 0 ( ) kg/m 999 ( 16 16

5 in

out

2 3

m

Q

A m

W 10 970 1

3 5

* cond

(b) For the calculation of the heat transfer coefficient on the inner surfaces of the tubes, we first determine

the Reynolds number

440 , 44 s

kg/m 10 1.124

) kg/m m)(999.0 m/s)(0.025

2 ( Re

3 -

98 7 ( ) 440 , 44 ( 023 0 Pr Re 023

=

Nu

C W/m 6511 ) 9 275 ( m 0.025

C) W/m 590 0

) 25 )(

6562 ( ) 5 15 )(

6511

(

tube

tube tube

T

T T

T h T

h i i o o

which is sufficiently close to the assumed value of 20°C Disregarding thermal resistance of the tube walls, the overall heat transfer coefficient is determined from

C W/m

1

o

i h h

U

(c) The tube length may be determined from

m 5.05

) 17 14 ( 2

1 25 m) (0.025 C)(16) W/m

3268 ( W 10

970

.

&

10-82 Steam at a saturation temperature of Tsat = 40°C condenses on the outside of a thin horizontal tube Heat is transferred to the cooling water that enters the tube at 25°C and exits at 35°C The rate of

condensation of steam, the average overall heat transfer coefficient, and the tube length are to be

determined

Assumptions 1 Steady operating conditions exist 2 The tube can be taken to be isothermal at the bulk mean fluid temperature in the evaluation of the condensation heat transfer coefficient 3 Liquid flow through the tube is fully developed 4 The thickness and the thermal resistance of the tube is negligible

Properties The properties of water at the saturation

temperature of 40°C are hfg = 2407×103

J/kg and

ρv = 0.05 kg/m3 The properties of liquid water at

the film temperature of

(50+20)/2 = 35°C and at the bulk fluid temperature of

=+

=( sat s)/2

T

=+

=(Tin Tout)/2

+ 35)/2 = 30°C are (Table A-9),

C W/m

623

0

CJ/kg

4178

skg/m10720

0

kg/m0

994

3 3

C W/m615.0

CJ/kg4178

/sm10801.0/

kg/m0.996

2 6 3

l l l l

k c

ρμνρ

: C 30

At

Steam 40°C

=C25)C)(35J/kgkg/s)(4178408

.1()(

kg/s408.1]4/m)03.0(m/s)[

)(2kg/m996

c T T c

=C0)3C(40J/kg41780.68+J/kg102407

)(

68.0

3 3

m)C(0.03)3040(s)kg/m10720.0(

)C W/m623.0)(

J/kg102435)(

kg/m05.0994)(

kg/m994)(

m/s8.9(729

0

)(

)(

729.0

2

4 / 1

3

3 3

3 3

2

4 / 1

k h g

h

h

s l

l fg v l l

ρρρ

The average heat transfer coefficient for flow inside the tube is determined as follows:

C W/m7357m

0.03

359C) W/m615.0(Nu

359)

42.5()906,74(023.0PrRe023

0

Nu

906,7410

0.801

m)m/s)(0.032

(Re

2

4 0 8 0 4

0 8 0

6 - avg

i

ν

Noting that the thermal resistance of the tube is negligible, the overall heat transfer coefficient becomes

C W/m

4106 2 °

=+

=+

=

9292/17357/1

1/

1/

1

1

h h U

The logarithmic mean temperature difference is:

C10.9)5/15ln(

515)/ln(

ΔΔ

Δ

−Δ

=

Δ

o i

e i

T T

T T T

The tube length is determined from

m 16.7

=

→Δ

=

C)10.9)(

m03.0()C W/m4106(

W820,58)

(

2 ln

ln

π

πD T h

Q L

T hA

&

Note that the flow is turbulent, and thus the entry length in this case is 10D = 0.3 m is much shorter than

the total tube length This verifies our assumption of fully developed flow

10-83 Saturated ammonia at a saturation temperature of Tsat = 25°C condenses on the outer surface of vertical tube which is maintained at 15°C by circulating cooling water The rate of heat transfer to the

coolant and the rate of condensation of ammonia are to be determined

Assumptions 1 Steady operating conditions exist 2 The tube is isothermal 3 The tube can be treated as a vertical plate 4 The condensate flow is turbulent over the entire tube (this assumption will be verified) 5

The density of vapor is much smaller than the density of liquid, ρv <<ρl

Properties The properties of ammonia at the saturation temperature of 25°C are hfg = 1166×103 J/kg and ρv

= 7.809 kg/m3 The properties of liquid ammonia at the film temperature of T f =(Tsat+T s)/2=(25 + 15)/2 = 20°C are (Table A-11),

463

1

Pr

C W/m4927

0

CJ/kg4745

/sm102489.0/

skg/m10519

1

kg/m2.610

2 6

4 - 3

ν

μ

ρ

Ammonia25°C

=C)15C(25J/kg47450.68+J/kg101166

)(

68.0

3 3

463.1(151)

s/m102489.0(

81.9J/kg)

1098kg/m.s)(1110

0

253Pr

151)

(Pr0690.0Re

Re

3 / 4

5 0 3

/ 1

2 2 6 3

4

5 0

3 / 4

5 0 3

/ 1

2

*

5 0

turb vertical,

l

s sat l

v

g h

T T Lk

/sm102489.0(

m/s81.9)

2532142

(463.1588750

C) W/m4927.0(2142

)253(Re

Pr588750

Re

2 3

/ 1

2 2 6 2

75 0 5 0

3 / 1

2 75

0 5 0 turbulent

J/s98003

* on condensati

10-84 There is film condensation on the outer surfaces of 8 horizontal tubes arranged in a horizontal or

vertical tier The ratio of the condensation rate for the cases of the tubes being arranged in a horizontal tier

versus in a vertical tier is to be determined

Assumptions Steady operating conditions exist

Horizontal tier

Analysis The heat transfer coefficients for the

two cases are related to the heat transfer

coefficient on a single horizontal tube by

Horizontal tier: hhorizontal tier ofN tubes =hhorizontal1 tube

Vertical tier

Vertical tier:

4 / 1 tube 1 horizontal tubes

N of tier vertical

=

/Ratio

1/4

4 / 1

4 / 1 tube 1 , horizontal

tube 1 , horizontal

tubes N of tier vertical

tubes N of tier horizontal

tubes N of tier vertical

tubes N of tier horizontal

N

N h

h h h m m

10-85E Saturated steam at a saturation pressure of 0.95 psia and thus at a saturation temperature of Tsat = 100°F (Table A-9E) condenses on the outer surfaces of 144 horizontal tubes which are maintained at 80°F

by circulating cooling water and arranged in a 12 × 12 square array The rate of heat transfer to the cooling water and the rate of condensation of steam are to be determined

Assumptions 1 Steady operating conditions exist

2 The tubes are isothermal

Properties The properties of water at the

saturation temperature of 100°F are hfg = 1037

Btu/lbm and ρv = 0.00286 lbm/ft3 The properties

of liquid water at the film temperature of

(100 + 80)/2 = 90°F are (Table A-9E),

=+

358

0

FBtu/lbm

999

0

/hft02965.0/

hlbm/ft842.1slbm/ft10

Saturated steam

Btu/lbm1051

=

F)80F)(100Btu/lbm

999.0(0.68+Btu/lbm1037

)(

68

1562

ft)F(1.2/12)

80100)(

hlbm/ft842.1](

s)3600h/

1[(

)FftBtu/h358.0)(

Btu/lbm1051)(

lbm/ft00286.012.62)(

lbm/ft12.62)(

ft/s2

)(

2

3 3

3 2

4 / 1

k h g

h

h

s l

l fg v l l

μ

ρρρ

Then the average heat transfer coefficient for a 4-tube high vertical tier becomes

FftBtu/h839F)ftBtu/h1562(12

1

4 / 1 tube 1 horiz, 4 / 1 tubes

N

N h

The surface area for all 144 tubes is

2 totalπ =144π(1.2/12ft)(15ft)=678.6ft

A s

Then the rate of heat transfer during this condensation process becomes

Btu/h 11,387,000

=

=

=

Btu/lbm1051

Btu/h000,387,11

* on condensati

10-86E Saturated steam at a saturation pressure of 0.95 psia and thus at a saturation temperature of Tsat = 100°F (Table A-9E) condenses on the outer surfaces of 144 horizontal tubes which are maintained at 80°F

by circulating cooling water and arranged in a 12 × 12 square array The rate of heat transfer to the cooling water and the rate of condensation of steam are to be determined

Assumptions 1 Steady operating conditions exist

2 The tubes are isothermal

Properties The properties of water at the

saturation temperature of 100°F are hfg = 1037

Btu/lbm and ρv = 0.00286 lbm/ft3 The properties

of liquid water at the film temperature of

(100 + 80)/2 = 90°F are (Table A-9E),

=+

358

0

FBtu/lbm

999

0

/hft02965.0/

hlbm/ft842.1slbm/ft10

Saturated steam

Btu/lbm1051

=

F)80F)(100Btu/lbm

999.0(0.68+Btu/lbm1037

)(

68

1374

ft)F(2.0/12)

80100)(

hlbm/ft842.1](

s)3600h/

1[(

)FftBtu/h358.0)(

Btu/lbm1051

)(

lbm/ft00286.012.62)(

lbm/ft12.62)(

ft/s2.32

)(

729.0

2

4 / 1

2

3 3

3 2

4 / 1

k h g

h

h

s l

l fg v l l

μ

ρρρ

Then the average heat transfer coefficient for a 4-tube high vertical tier becomes

FftBtu/h739F)ftBtu/h1374(12

1

4 / 1 tube 1 horiz, 4 / 1 tubes

N

N h

The surface area for all 144 tubes is

2 totalπ =144π(2/12ft)(15ft)=1131ft

A s

Then the rate of heat transfer during this condensation process becomes

Btu/h 16,716,000

=

=

=

Btu/lbm1051

Btu/h000,716,16

* on condensati

10-87 Water is boiled at Tsat = 100°C by a chemically etched stainless steel electric heater whose surface

temperature is maintained at Ts = 115°C The rate of heat transfer to the water, the rate of evaporation of water, and the maximum rate of evaporation are to be determined

Assumptions 1 Steady operating conditions exist 2 Heat losses from the heater and the boiler are

negligible

Properties The properties of water at the saturation temperature of

100°C are (Tables 10-1 and A-9)

Water, 100°C

115°C

Steam 100°C

75

1

Pr

N/m0589

0

kg/m60

0

kg/m9.957

3 3

m/skg10282.0

J/kg102257

3 3

Also, 0.0130 and n = 1.0 for the boiling of water on a chemically etched stainless steel surface

(Table 10-3) Note that we expressed the properties in units specified under Eq 10-2 in connection with

their definitions in order to avoid unit manipulations

2

3

3

1/2 3

3

3 sat ,

2 / 1

nucleate

W/m900,474

75.1)102257(0130.0

)100115(42170589

.0

0.60)9.8(957.9)

10)(225710

282.0(

Pr

)(

)(

s l p v

l fg l

h C

T T c g

h q

σ

ρρμ

&

The surface area of the bottom of the heater is A s =πDL=π(0.002m)(0.8m)=0.005027m2

Then the rate of heat transfer during nucleate boiling becomes

W 2387

=

=

= nucleate (0.005027m2)(474,900 W/m2)boiling A q

Q& s&

The rate of evaporation of water is determined from

kg/h 3.81

= kg/s 10 1.058× −3

J/s23873

boiling n

*12.0

1.2

<

399.00589

.0

60.09.957(8.9)001.0()(

*

25 0 25

0

2 / 1 2

/ 1

g L

L

cr

v l

σ

ρρ

Then the maximum or critical heat flux is determined from

2

kW/m 1280

3 4

/ 1 2

max

W/m1,280,000

)]60.09.957()6.0(8.90589.0)[

102257(151.0)]

(

fg

cr h g C

10-88E Steam at a saturation temperature of Tsat = 100°F condenses on a vertical plate which is maintained

at 80°C The rate of heat transfer to the plate and the rate of condensation of steam per ft width of the plate are to be determined

Assumptions 1 Steady operating conditions exist 2 The plate is isothermal 3 The condensate flow is

wavy-laminar over the entire plate (this assumption will be verified) 4 The density of vapor is much

smaller than the density of liquid, ρv <<ρl

Properties The properties of water at the saturation temperature of 100°F are hfg = 1037 Btu/lbm and ρv = 0.00286 lbm/ft3 The properties of liquid water at the film temperature of T f =(Tsat+T s)/2=(100 + 80)/2

= 90°F are (Table A-9E),

FftBtu/h358

0

FBtu/lbm999

0

/hft02965.0/

hlbm/ft842.1slbm/ft10

117

5

lbm/ft12.62

2 4

Analysis The modified latent heat of vaporization is

999.0(0.68+Btu/lbm

1037

)(

1(

s)3600()h/ft02965.0(

ft/s2.32)

Btu/lbm1051

)(

hlbm/ft842.1(

F)80100(F)ftBtu/h358.0(ft)6(70

70.381.4Re

Re

82 0 3 / 1

2 2

2 2 2

820 0 3 / 1

2

*

sat wavy

=

=

l fg

νμ

which is between 30 and 1800, and thus our assumption of wavy laminar flow is verified Then the

condensation heat transfer coefficient is determined from

FftBtu/h811h)

1(

s)3600()h/ft02965.0(

ft/s2.322

.5)201(08.1

F)ftBtu/h358.0(201

2.5Re08.1Re

2 3

/ 1

2 2

2 2 2

22 1

3 / 1

2 22

1 wavy

h

ν

The heat transfer surface area of the plate is

2ft4ft)ft)(14

=

=

= 64,880Btu/hon

condensati

Q

&

10-89 Saturated refrigerant-134a vapor condenses on the outside of a horizontal tube maintained at a

specified temperature The rate of condensation of the refrigerant is to be determined

Assumptions 1 Steady operating conditions exist 2 The tube is isothermal

Properties The properties of refrigerant-134a at the saturation temperature of 35°C are hfg = 168.2×103

J/kg and ρv = 43.41 kg/m3 The properties of liquid R-134a at the film temperature of

(35 + 25)/2 = 30°C are (Table A-10),

=+

=( sat s)/2

T

C W/m

0808

0

CJ/kg

1448

kg/m.s10

888

1

kg/m1188

4 3

=C)25C(35J/kg14480.68+J/kg102.168

)(

68.0

3 3

h

R-134a 35°C

1880

m)C(0.015)

2535(s)kg/m10888.1(

)C W/m0808.0)(

J/kg100.178)(

kg/m41.43)(1188kg/m1188)(

m/s81

)(

729.0

2

4 / 1

4

3 3

3 3

2

4 / 1

k h g

h

h

s l

l fg v l l

μ

ρρρ

The heat transfer surface area of the pipe is

2m3299.0m)m)(7015.0

m3299.0)(

C W/m1880()

J/s62003

* on condensati