Flow Processes or Heat Exchangers

5. Flow Processes or Heat Exchangers

Heat exchangers are used to transfer heat rather than to directly produce work. There- fore, the definition for availability efficiency that is just based on work is unsuitable for heat exchangers. Hence the availability efficiency for a heat exchanger must be defined in terms of its capability to maintain the work potential after heat exchange. Hence η Avail,f = (Exergy

leaving the system) ÷ (Exergy entering the system). A perfect heat exchange will have η avail,f =1 Since the stream exergy leaving a system equals that entering it minus the exergy loss

in the system, η Avail,f = 1 – ((Exergy loss in the system) ÷ (Exergy entering the system)).

a. Significance of the Availability or Exergetic Efficiency For instance, heat is transferred in a boiler from hot gases to water in order to produce steam. However, the steam may be used for space heating and/or to produce work, and the higher the η Avail value in the boiler, the higher will be the potential of the steam to perform

work in a subsequent work–producing device. The availability efficiency represents the ratio of the exiting exergy to the entering exergy.

Assume that a home is to be warmed by a gas heater to a 25ºC temperature during the winter when the ambient temperature is 0ºC. Assume, also, that the heater burns natural gas as fuel and produces hot combustion gases at a temperature of say 1800 K. These hot gases are used to heat cooler air in a heat exchanger. The flow through the house is recirculated through the heater in which the cold air enters at a temperature of say 10ºC and leaves at 25ºC. Conse- quently, the hot gases transfer heat to the colder air and leave the heat exchanger at a 500 K temperature. Extreme irreversibilities are involved. Typically η Avail is very low indicating a

large loss in work potential. “Smart” engineering systems can be designed to heat the home and at the same time provide electrical power to it for the same conditions as in the previous gas heater arrange- ment. Assume that the hot product gases at 1800ºK are first cooled to the dead state (at 273 K) using a Carnot engine to produce work equal to Ψ g,1800 . The cold air at 283 K can also be

cooled to the dead state to run another Carnot engine that produces work, Ψ a,283 . The work produced from both engines Ψ g,1800 + Ψ a,283 can then be used to run a heat pump that raises the temperature of the air from the dead state to the desired temperature (298 K) and, conse-

quently, increases the exergy contained in the air and raises the temperature of the product gases from the dead state to the exiting gas temperature (500 K). We will still be left with a potential to do work (= exergy of hot gases and cooler air entering the heat exchanger – exergy due to the cooled gases and heated air leaving the heat exchanger) which can be used to pro- vide electricity to the home.

b. Relation Between η Avail,f and η Avail,0 for Work Producing Devices If the exit state from a work producing device is the dead state, then the availability efficiency is η Avail,0 = (work output) ÷ (input exergy). This ratio informs us of the extent of the conversion of the input exergy into work, but gives no indication as to whether the exergy is lost as a result of irreversibility or with the exit flow. The flow availability efficiency η Avail,f , which compares the exergy ratio leaving a system to that entering it, is able to convey that in- formation.