Thermodynamics

except for the narrow Mach number range of 1> 1k Ma 1 in subsonicflow (see Example 17–13). Both temperature and the Mach numberincrease with heating in subsonic flow, but T reaches a maximumT max at Ma 1> 1k (which is 0.845 for air), and then decreases. It mayseem peculiar that the temperature of a fluid drops as heat is transferredto it. But this is no more peculiar than the fluid velocity increasing inthe diverging section of a converging–diverging nozzle. The coolingeffect in this region is due to the large increase in the fluid velocity andthe accompanying drop in temperature in accordance with the relation T 0 T V 2 /2c p . Note also that heat rejection in the region 1> 1k Ma 1 causes the fluid temperature to increase (Fig. 17–53).5. The momentum equation P KV constant, where K rV constant(from the conservation of mass equation), reveals that velocity andstatic pressure have opposite trends. Therefore, static pressuredecreases with heat gain in subsonic flow (since velocity and theMach 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 velocityare inversely proportional. Therefore, density decreases with heattransfer to the fluid in subsonic flow (since velocity and the Mach numberincrease), but increases with heat gain in supersonic flow (sincevelocity and the Mach number decrease).7. On the left half of Fig. 17–52, the lower arm of the Rayleigh line issteeper (in terms of s as a function of T), which indicates that theentropy change corresponding to a specified temperature change (andthus a given amount of heat transfer) is larger in supersonic flow.The effects of heating and cooling on the properties of Rayleigh flow arelisted in Table 17–3. Note that heating or cooling has opposite effects on mostproperties. Also, the stagnation pressure decreases during heating and increasesduring cooling regardless of whether the flow is subsonic or supersonic.T 1T 01HeatingHeatingChapter 17 | 863SubsonicflowT 2 T 1 orT 2 T 1T 02 T 01T 1 SupersonicT 2 T 1flowT 01T 02 T 01FIGURE 17–53During heating, fluid temperaturealways increases if the Rayleigh flowis supersonic, but the temperature mayactually drop if the flow is subsonic.TABLE 17–3The effects of heating and cooling on the properties of Rayleigh flowHeatingCoolingProperty Subsonic Supersonic Subsonic SupersonicVelocity, V Increase Decrease Decrease IncreaseMach number, Ma Increase Decrease Decrease IncreaseStagnation temperature, T 0 Increase Increase Decrease DecreaseTemperature, T Increase for Ma 1/k 1/2 Increase Decrease for Ma 1/k 1/2 DecreaseDecrease for Ma 1/k 1/2 Increase for Ma 1/k 1/2Density, r Decrease Increase Increase DecreaseStagnation pressure, P 0 Decrease Decrease Increase IncreasePressure, P Decrease Increase Increase DecreaseEntropy, s Increase Increase Decrease Decrease