Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

The velocities involved in pipe and duct flow are relatively low, and the
kinetic energy changes are usually insignificant. This is particularly true when
the pipe or duct diameter is constant and the heating effects are negligible.
Kinetic energy changes may be significant, however, for gas flow in ducts
with variable cross-sectional areas especially when the compressibility effects
are significant. The potential energy term may also be significant when the
fluid undergoes a considerable elevation change as it flows in a pipe or duct.

EXAMPLE 5–11 Electric Heating of Air in a House

The electric heating systems used in many houses consist of a simple duct

with resistance heaters. Air is heated as it flows over resistance wires. Con-

sider a 15-kW electric heating system. Air enters the heating section at 100

kPa and 17°C with a volume flow rate of 150 m^3 /min. If heat is lost from

the air in the duct to the surroundings at a rate of 200 W, determine the exit

temperature of air.

Solution The electric heating system of a house is considered. For speci-

fied electric power consumption and air flow rate, the air exit temperature is

to be determined.

Assumptions 1 This is a steady-flow process since there is no change with

time at any point and thus mCV0 and ECV0. 2 Air is an ideal gas

since it is at a high temperature and low pressure relative to its critical-point

values. 3 The kinetic and potential energy changes are negligible, ke 

pe 0. 4 Constant specific heats at room temperature can be used for air.

Analysis We take the heating section portion of the ductas the system

(Fig. 5–41). This is a control volumesince mass crosses the system bound-

ary during the process. We observe that there is only one inlet and one exit

and thus m. 1 m. 2 m.. Also, heat is lost from the system and electrical

work is supplied to the system.

At temperatures encountered in heating and air-conditioning applications,

hcan be replaced by cp Twhere cp 1.005 kJ/kg · °C—the value

at room temperature—with negligible error (Fig. 5–42). Then the energy

balance for this steady-flow system can be expressed in the rate form as

Rate of net energy transfer Rate of change in internal, kinetic,

by heat, work, and mass potential, etc., energies

From the ideal-gas relation, the specific volume of air at the inlet of the

duct is

The mass flow rate of the air through the duct is determined from

m

#



V

#

1

v 1



150 m^3 /min

0.832 m^3 /kg

¬a

1 min

60 s

b3.0 kg/s

v 1 

RT 1

P 1



1 0.287 kPa#m^3 /kg#K 21 290 K 2

100 kPa

0.832 m^3 /kg

W

#

e,in
Q

#

outm

#

cp 1 T 2 
T 12

W

#

e,inm

#h

1 Q

#

outm

#h

2 ¬^1 since ¢ke¢pe^02

E

#

inE

#

out

E

#

in
E

#

out^ ^ dEsystem>dt^ ^0

Chapter 5 | 245

0 (steady)

⎭⎪⎪⎬⎪⎪⎫ ⎭⎪⎪⎪⎬¡⎪⎪⎪⎫

T 2 =?

Q ̇out = 200 W

W ̇e, in = 15 kW

V 1 = 150 m^3 /min

P 1 = 100 kPa

T 1 = 17°C

̇

FIGURE 5–41

Schematic for Example 5–11.

AIR

–20 to 70°C

∆h = 1.005 ∆T (kJ/kg)

FIGURE 5–42

The error involved in hcpT,

where cp1.005 kJ/kg · °C, is less

than 0.5 percent for air in the

temperature range 
20 to 70°C.