The modelling and dynamic analysis of shell and tube heat exchangers will be considered in this contribution. Procedures which incorporate the heat transfer and the fluid flow system properties, for these processes, will be developed. An incremental, energy balance yielding the system, partial differential equations presents the governing process. The multivariable, multi-dimensional, Laplace transformed, distributed parameter formulation of heat exchanger representations, are provided. A frequency domain description of the system model is derived enabling the recovery of Laplace function rationality for both parallel and counter flow heat exchanger models. Suitable feedback control techniques are identified, as a prelude to closed loop design studies. The dynamics, for tubular heat exchangers are computed, for purposes of comparison with alternative response and regulation approaches. A typical application study is outlined.

Introduction

Heat exchangers are used in many industries where fluid heat transfer is required, see for example Saunders E.A (1). In this operation heat energy is transferred from a hot to a cooler fluid flow stream by a carrier type, energy conversion process, as in Hewitt G et al (2) and Coulson. H. G and Richardson J. (3). This involves coupled fluid flow and thermal interactions where heat is transferred along with the fluid flow through the containing volumes and across the separating, heat exchanger, tube walls. The heating of materials during conveyancing operations would also be equivalent to a carrier flow, heat transfer, percolation process. Continuous conveyor fed food preparation systems and the fluid drainage from the pulp-fibre suspensions, in the paper and board manufacturing industries, as detailed in Smith B.W (4), for example, also comprise percolation, heat and mass transfer processes. However, in this compilation the large scale, tubular heat transfer units commonly employed in the oil, gas and chemical industries, as discuss in Sadik K and Liu H. (5), and Smith E.M (6) will be the focus of the formulation, analysis and simulation studies presented herein. These devices are also used in ventilation, air conditioning and battery cooling systems, as detailed in Whalley R and Ameer A (7), Roetzel, W. and Xuan, Y. (8) in refrigeration units, in fossil fuel boilers, see for example Whalley R (9) and in nuclear, electrical power generation plant, as shown in Schultz M.A. (10). Generally, tubular heat transfer units are configured to work in series with a fluid source of supply and a suitable coolant or heating, fluid stream. A continuous process is employed thereafter to simultaneously achieve, the parallel or counter flow, heating or cooling effect required.