Response of Counterflow Heat Exchangers to Step Changes of Flow Rates

Abstract

The response of heat exchangers to changes of mass flow rates is of interest for control of systems containing heat exchangers. The purpose of this note is to find the responses of the outlet temperatures of counterflow exchangers to step changes of either or both flow rates. The problem is an initial value problem. Initially the exchanger operates in the steady-state condition for which the initial wall and fluid temperature distributions are computed using simple relations. At time zero either or both flow rates are abruptly changed without a change of fluid inlet temperatures. The ensuing transient occurs as the fluid and wall temperature distributions change from initial to final values. The governing differential equations are linear and homogeneous with constant coefficients after the flow rate changes. If the inlet temperatures vary after or at the time of flow rate steps then responses to inlet temperature variations are additive to responses caused by the flow rate steps. Responses to inlet temperature variations have been given, for example, by Romie (1984) and Roetzel and Xuan (1992a). Ontko and Harris (1990) use finite difference methods and Xuan and Roetzel (1993) use the Graver-Stehfest algorithm for numerical inversion of Laplace transforms to findmore » combined responses to step changes of flow rates and inlet temperature variations. Although the response to step changes of flow rates is implicit in both references, the effect of flow rate excitation taken alone has not been made evident. Hence this note.« less