The Straight Line Law

A process that occurs frequently in refrigeration practice is the transfer of heat and mass (water) between air and a wetted surface, as shown in Fig. 6.25. The dry-bulb temperature of the air entering the section is ti and its moisture content is Wi.

Heat and mass transfer between air and a wetted surface.

At the water surface, the air is in equilibrium with the water, so the air is saturated and at the same temperature as the water, ts, and the moisture content of the air at the surface is the same as the saturated air, Ws. The temperature difference between the air and the wet surface is the driving force for the transfer of heat between them. The water vapor pressure is linearly proportional to the moisture content, W, so the difference between Wi andWs is the driving force for the transmission of water vapor at the entrance to the section.

The handy straight-line law explains numerous processes by predicting the path of the air conditions on the psychrometric chart. The straight-line law applies to the situation shown in Fig. 6.25, where air contacts a wetted surface.

The statement of the straight-line law is

The straight-line law:

The path on the psychrometric chart drives toward the saturation line at the temperature of the wetted surface.

The straight-line law is well verified by fundamental laws of heat and mass transfer. It shows that from the change in properties of the air shown on the psychrometric chart, the directions of heat transfer and water-vapor transfer are indicated by the changes in enthalpy and moisture content, respectively.

Figure 6.26 shows several different situations where entering air at condition i contacts a wet surface of temperature ts.

Several applications of the straight-line law

Figure 6.26a shows the situation prevailing in a cooling and dehumidifying coil where, even if the coil is dry when starting operation, moisture from the air condenses on the cold surface of the coil, such that thereafter the surface is wetted and the straight-line law applies. The air flowing across the surface changes state from i to o, and during that process the enthalpy indicates that it gives up heat to the coil and the refrigerant carries it away.

In Fig. 6.26b, the situation portrayed is that of evaporative cooling, as shown schematically in Fig. 6.27. Because no heat is added externally to the water, the energy balance requires that the enthalpy of entering air equals that leaving, thus hi=ho.

Evaporative cooler represented by Fig. 6.26b.

The process of constant enthalpy in Fig. 6.26b results in a drop in air temperature, but an increase in moisture content, W. Evaporative cooling is rare in industrial refrigeration practice, but Fig. 6.26b is a transition from the cooling and dehumidification process to the heating and humidification process of Fig. 6.26c.

Our interest in Fig. 6.26c lies not in the heating and humidification of the air, but in the removal of heat from the wetted surface. This is the process that occurs in a cooling tower and an evaporative condenser—a topic encountered again in Chapter 7 in the study of condensers.

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