Page 334 - Design and Operation of Heat Exchangers and their Networks
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320   Design and operation of heat exchangers and their networks


          today, modern control theories and techniques are also developed to control
          thermal systems using real-time dynamic models of heat exchangers (Guan
          et al., 2004).
             Dynamic analysis of heat exchangers also has significant meaning for the
          fault diagnosis of a thermal system. If an equipment in the system is defective
          or a pipeline is broken, according to the measured temperature responses of
          the system, one can determine the type and position of the fault by means of
          computer dynamic simulation of the system and fault diagnosis technique.
             The task of the dynamic analysis of a heat exchanger is to obtain the
          dynamic response characteristics of the outlet fluid temperatures to the var-
          iations of various operating conditions (mainly the flow rates, supply tem-
          peratures of streams, and heating/cooling loads) with theoretical or
          experimental methods. There are a number of other factors affecting the
          transient behavior of heat exchangers and their networks such as heat transfer
          coefficients, size and structure of heat exchangers, flow arrangement, ther-
          mal properties of fluid streams and exchanger materials, environmental tem-
          perature, and fouling. Some of them may not appear in the steady-state
          simulation procedure. A comprehensive algorithm of dynamic simulation
          will contain many such factors to provide an accurate modeling and simu-
          lation of the exchanger dynamics.
             The dynamic analysis of heat exchangers can be performed either exper-
          imentally or theoretically. For the dynamic simulation, two approaches have
          often been used, that is, the lumped parameter model and the distributed
          parameter model. These models can usually be described mathematically
          by mixed sets of differential and algebraic equations and can be solved by
          means of analysis methods or numerical methods such as finite-difference
          methods, finite-element methods, numerical inversion of the Laplace trans-
          form, and numerical inversion of the Fourier transform. In addition, the
          dynamic behavior of a heat exchanger can be described with its transfer
          functions giving the corresponding output values for each possible value
          of the input to the exchanger, which is especially helpful for control. The
          experimental investigation is often used for the validation of the dynamic
          models or the determination of the parameters used in the models.
             The earliest study on transient behavior of heat exchangers can be dated
          from 1926. Anzelius (1926), Nusselt (1927), Hausen (1929), and Schumann
          (1929) investigated heat transfer between a porous medium and a fluid pass-
          ing through it and obtained the outlet fluid temperature response to a sudden
          change in the inlet fluid temperature, which is known as single-blow prob-
          lem. Furnas (1932) would be the first one to use the Schumann’s model for
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