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.
Parts
» COMPUTATIONAL MECHANICS and APPLIED ANALYSIS
» Explicit and Implicit Functions and Total Differentiation
» Exact (Perfect) and Inexact (Imperfect) Differentials
» Intermolecular Forces and Potential Energy
» Internal Energy, Temperature, Collision Number and Mean Free Path
» Vector or Cross Product r The area A due to a vector product
» First Law for a Closed System
» First Law For an Open System
» STATEMENTS OF THE SECOND LAW
» Cyclical Integral for a Reversible Heat Engine
» Irreversibility and Entropy of an Isolated System
» Degradation and Quality of Energy
» SINGLE–COMPONENT INCOMPRESSIBLE FLUIDS
» Evaluation of Entropy for a Control Volume
» Internally Reversible Work for an Open System
» MAXIMUM ENTROPY AND MINIMUM ENERGY
» Generalized Derivation for a Single Phase
» LaGrange Multiplier Method for Equilibrium
» Absolute and Relative Availability Under Interactions with Ambient
» Irreversibility or Lost Work
» Applications of the Availability Balance Equation
» Closed System (Non–Flow Systems)
» Heat Pumps and Refrigerators
» Work Producing and Consumption Devices
» Graphical Illustration of Lost, Isentropic, and Optimum Work
» Flow Processes or Heat Exchangers
» CLASSICAL RATIONALE FOR POSTULATORY APPROACH
» Generalized Legendre Transform
» Van der Waals (VW) Equation of State
» Other Two–Parameter Equations of State
» Compressibility Charts (Principle of Corresponding States)
» Boyle Temperature and Boyle Curves
» Three Parameter Equations of State
» Empirical Equations Of State
» State Equations for Liquids/Solids
» Internal Energy (du) Relation
» EXPERIMENTS TO MEASURE (u O – u)
» Vapor Pressure and the Clapeyron Equation
» Saturation Relations with Surface Tension Effects
» Temperature Change During Throttling
» Throttling in Closed Systems
» Procedure for Determining Thermodynamic Properties
» Euler and Gibbs–Duhem Equations
» Relationship Between Molal and Pure Properties
» Relations between Partial Molal and Pure Properties
» Mixing Rules for Equations of State
» Partial Molal Properties Using Mixture State Equations
» Ideal Solution and Raoult’s Law
» Completely Miscible Mixtures
» DEVIATIONS FROM RAOULT’S LAW
» Mathematical Criterion for Stability
» APPLICATION TO BOILING AND CONDENSATION
» Physical Processes and Stability
» Constant Temperature and Volume
» Equivalence Ratio, Stoichiometric Ratio
» Entropy, Gibbs Function, and Gibbs Function of Formation
» Entropy Generated During an Adiabatic Chemical Reaction
» MASS CONSERVATION AND MOLE BALANCE EQUATIONS
» Evaluation of Properties During an Irreversible Chemical Reaction
» Criteria in Terms of Chemical Force Potential
» Generalized Relation for the Chemical Potential
» Nonideal Mixtures and Solutions
» Gas, Liquid and Solid Mixtures
» Availability Balance Equation
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