Fluid temperature dynamics in incompressible fluid heat exchange systems
Colburn, Johnnie W
Chapman, Alan J.
Master of Science
Linearized partial differential equations for incompressible fluid temperature dynamics in pipes and single-pass heat exchangers are derived. Laplace transform methods are employed to obtain temperature transfer functions (for pipes) and transfer matrices (for heat exchangers). Using a power series approximation for the individual transfer functions of a heat exchanger transfer matrix, Fourier transforms (in Euler form) are obtained for evaluation of frequency response. Using these models, analysis of multiple heat exchanger systems is described in terms of multiplication of a sequence of suitable transfer matrices (either geometric or causal). The effect of piping on temperatures in heat exchanger systems is shown to be negligible in the steady state and dependent on the static effectiveness of the individual heat exchangers of the system in the transient state. For analysis of load changes in process design, it is suggested that dynamics of heat exchanger systems be characterized by the overall steady state gain and a single time constant (for each transfer function) determined by evaluation of the phase frequency response of the heat exchanger system.