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

except for the narrow Mach number range of Ma 1 in sub-

sonic flow (see Example 17–13). Both temperature and the Mach num-

ber increase with heating in subsonic flow, but Treaches a maximum

Tmaxat Ma 
 (which is 0.845 for air), and then decreases. It may

seem peculiar that the temperature of a fluid drops as heat is transferred

to it. But this is no more peculiar than the fluid velocity increasing in

the diverging section of a converging–diverging nozzle. The cooling

effect in this region is due to the large increase in the fluid velocity and

the accompanying drop in temperature in accordance with the relation T 0


TV^2 /2cp. Note also that heat rejection in the region Ma 

1 causes the fluid temperature to increase (Fig. 17–53).

5.The momentum equation PKV
constant, where K
rV
con-

stant (from the conservation of mass equation), reveals that velocity and

static pressure have opposite trends. Therefore, static pressure

decreases with heat gain in subsonic flow (since velocity and the

Mach number increase), but increases with heat gain in supersonic flow

(since velocity and the Mach number decrease).

6.The continuity equation rV
constant indicates that density and veloc-

ity are inversely proportional. Therefore, density decreases with heat

transfer to the fluid in subsonic flow (since velocity and the Mach num-

ber increase), but increases with heat gain in supersonic flow (since

velocity and the Mach number decrease).

7.On the left half of Fig. 17–52, the lower arm of the Rayleigh line is

steeper (in terms of s as a function of T), which indicates that the

entropy change corresponding to a specified temperature change (and

thus a given amount of heat transfer) is larger in supersonic flow.

The effects of heating and cooling on the properties of Rayleigh flow are

listed in Table 17–3. Note that heating or cooling has opposite effects on most

properties. Also, the stagnation pressure decreases during heating and increases

during cooling regardless of whether the flow is subsonic or supersonic.

1 > 1 k

1 > 1 k

1 > 1 k

Chapter 17 | 863

T 01

Supersonic

flow

Heating

T 02  T 01

T 1 T 2  T 1

T 01

Subsonic

flow

Heating

T 02  T 01

T 1

T 2  T 1 or

T 2  T 1

FIGURE 17–53

During heating, fluid temperature

always increases if the Rayleigh flow

is supersonic, but the temperature may

actually drop if the flow is subsonic.

TABLE 17–3

The effects of heating and cooling on the properties of Rayleigh flow

Heating Cooling

Property Subsonic Supersonic Subsonic Supersonic

Velocity, V Increase Decrease Decrease Increase

Mach number, Ma Increase Decrease Decrease Increase

Stagnation temperature, T 0 Increase Increase Decrease Decrease

Temperature, T Increase for Ma 1/k1/2 Increase Decrease for Ma 1/k1/2 Decrease

Decrease for Ma 1/k1/2 Increase for Ma 1/k1/2

Density, r Decrease Increase Increase Decrease

Stagnation pressure, P 0 Decrease Decrease Increase Increase

Pressure, P Decrease Increase Increase Decrease

Entropy, s Increase Increase Decrease Decrease

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