978-0073398198 Chapter 11 Part 6

11-101

11-123 Oil in an engine is being cooled by air in a cross-flow heat exchanger, where both fluids are unmixed; (a) the heat

transfer effectiveness and (b) the outlet temperature of the oil are to be determined.

W/K22.53)KJ/kg 2047)(kg/s 026.0( === phhh cmC 

The capacity ratio is

2516.0

W/K11.52

W/K3.225

max

min ====

c

h

C

c

11-103

11-125 Exhaust gases are used in a recuperative cross flow heat exchanger to heat air. For the given values of flow condition,

heat transfer coefficients and the fouling resistance, the air exit temperature and the area of heat exchanger is to be

determined.

Assumptions 1 Steady state conditions exist. 2 Heat exchanger is well insulated. 3 Fluid properties are constant.

Analysis (a) For the given flow conditions the energy balance between the two fluid streams gives,

U = 182.92 W/m2·K.

The heat capacity rate of the cold fluid (air) is

max

CW/K16035K)J/kg1069)(kg/s15(→=== pccc cmC 

The heat capacity rate of the hot fluid (exhaust gas) is,

min

CW/K8017.5K)J/kg1069()kg/s5.7( →=== phhh cmC 

Thus the capacity ratio is

5.0

16035

5.8017

max

min === C

C

c

The effectiveness of the heat exchanger is

383.0

)30500(

)320500(

)(

,,min

,,

max

=

−

=

−

== C

C

TTC

Q

o

incinh

outhinhh





Now the number of transfer units (NTU) for both fluids unmixed are obtained from Figure 11-27(e),

NTU = 0.6

11-104

Change in air exit temperature with change in the air mass flow rate.

11-105

11-126 Single pass cross flow heat exchanger uses water (mixed) to heat methanol (unmixed) initially at 10C. The heat

exchanger area corresponding to the effectiveness of 0.5 is to be determined. Further, the effect of mass flow rate of water on

)(

5.0

,,min

,,

max incinh

incoutcc

TTC

Q

−

== 



kW 5005.0/250

max == kWQ



11-106

(b)

Variation of the total heat transfer rate with change in water mass flow rate

As shown in the figure above, a variation of ±30% in the water mass flow rate causes the heat transfer rate to vary by 85%.

11-107

Variation of overall heat transfer coefficient with change in water mass flow rate.

11-109

K/Wm )10652.110169.41034.4(

1

KW/m3.056

1

K)W/m250(2

)023.0/025.0ln()025.0(

m)0.023(K)W/m(2500

m0.025

1

2

)/ln(

1

2364

22

++=



+



+



=

++=

−−−

U

m

hk

DDD

Dh

D

Uo

ioo

ii

o

11-110

11-128 Water is heated by steam condensing in a condenser. The required length of the tube is to be determined.

Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings

is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic

C100=C20C120

C40=C80C120

,,2

,,1

−=−=

incouth

outcinh

TTT

120C

Steam

20C

2.2 kg/s

11-111

11-129 Ethanol is vaporized by hot oil in a double-pipe parallel-flow heat exchanger. The outlet temperature and the mass

flow rate of oil are to be determined using the LMTD and NTU methods.

Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings

is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic

11-112

11-130 Saturated water vapor condenses in a 1–shell and 2-tube heat exchanger, (a) the heat transfer effectiveness, (b) the

outlet temperature of the cold water, and (c) the heat transfer rate for the heat exchanger are to be determined.

Assumptions 1 Steady operating condition exists. 2 The heat exchanger is well-insulated so that heat loss to the surroundings

is negligible. 3 Fluid properties are constant. 4 Changes in the kinetic and potential energies of fluid streams are negligible.

11-115

D

[cm]

Q



[kW]

cond

m



[kg/s]

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

2

30.65

0.01261

1 1.2 1.4 1.6 1.8 2

30

30.25

30.5

30.75

31

0.012

0.0125

0.013

0.0135

0.014

D [cm]

Q [kW]

mcond [kg/s]

Qdot

mcond

11-117

11-134 Saturated steam flows over tubes in a shell and tube heat exchanger at specified conditions. Effectiveness of the heat

exchanger, length of the tube and the rate of steam condensation are to be determined.

Assumptions 1 Steady state conditions exist. 2 Fluid properties are constant. 3 Heat exchanger is well insulated.

Properties The properties of water are evaluated at an average temperature of (60 + 20)°C/2 = 40°C from Table A–9:

ρ = 992.1 kg/m3, μ = 0.653 × 10−3 kg/m·s, cp = 4179 J/kg·K, k = 0.631 W/m·K, and Pr = 4.32

𝑄̇max =𝐶𝑐(𝑇𝑐,out −𝑇𝑐,in)

𝐶min(𝑇ℎ,in −𝑇𝑐,in)=60−20

130−20 = 𝟎.𝟑𝟔𝟑𝟔𝟒

(b) Cmin is calculated as

𝐶min = 𝑚̇𝑐𝑐𝑝𝑐 = 4(0.25 kg/s)(4179 J/kg⋅K)=4179 W/K

For a phase change process, the number of transfer units (NTU) is calculated as

NTU = −ln(1−𝜀)= −ln(1 − 0.36364)= 0.45199

The convection heat transfer coefficient for water through the tubes is

ℎ𝑖=Nu 𝑘

𝐷=(194.42)(0.631 W/m⋅K)

0.0125 m =9814.3 W/m2⋅K

Thus the overall heat transfer coefficient is

𝑈 = (1

=981.78 W/m2⋅K

Therefore the length of heat exchanger tube is calculated as

𝐿 = NTU𝐶min

11-119

mass flow rate of cooling water has to be increased to account for this heat transfer reduction. Thus the new mass flow rate of

11-120

Selection of the Heat Exchangers

11-137C The first thing we need to do is determine the life expectancy of the system. Then we need to evaluate how much

11-138C 1) Calculate heat transfer rate, 2) select a suitable type of heat exchanger, 3) select a suitable type of cooling fluid,

and its temperature range, 4) calculate or select U, and 5) calculate the size (surface area) of heat exchanger

11-139 Oil is to be cooled by water in a heat exchanger. The heat transfer rating of the heat exchanger is to be determined and

a suitable type is to be proposed.

Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings