scope:

INTRODUCTION

In the design of thermal systems, predicting the heat transfer rate of heat exchangers under prescribed operating conditions is necessary. For a given device exchanging heat between two fluids, the heat transfer rate depends on the flow rates and the inlet temperatures of each fluid. Currently, most calculations are done on the basis of manufacturers' data for specific fluids that give the heat transfer rate as a function of the two flow rates and the two inlet temperatures. This is a four-variable function and difficult to represent completely. In principle the functional relation depends on the geometry of the heat exchanger, the materials with which it is made, the surface conditions, the fluids used, etc. The relationship completely characterizes the heat exchanger and is the information that must be transferred in some form from the manufacturer to the design engineer.

It would be advantageous to be able to compress the information contained in the heat transfer rate function so that it can later be accurately recovered. For instance, if the internal and external heat transfer coefficients are provided, the heat transfer for any flow rate, inlet temperature, or fluid can be easily determined. The situation is complicated by the fact that the heat transfer coefficients vary considerably with flow rates and fluid properties. Dimensional analysis can reduce the number of variables to the internal and external Nusselt (or Stanton) numbers as functions of the corresponding Reynolds and Prandtl numbers. If such correlations could be determined from experimental measurements, an acceptable procedure can be devised. In practice, without accurate tube wall temperature measurements, it is difficult to separate the experimentally determined overall thermal resistance into its internal and external components. Furthermore, property variations, especially the variation of liquid viscosity, make any correlation obtained highly dependent on fluid temperatures. Procedures that take this variation into account, become very complex and potentially lose generality. In any case the user of the information, the system designer, is usually interested only in the heat transfer rate, and not in intermediate variables such as the heat transfer coefficients. For this purpose a straightforward interpolation of the original experimental data would probably be more useful, but would be inconvenient.

The artificial neural network (ANN) technique offers an alternative approach to the problem of information compression for heat exchangers. It is a procedure that is usually used for predicting the response of a physical system that cannot be easily modeled mathematically. The network is first "trained" by experimentally obtained input-output sets of data, after which it can be used for prediction. The manufacturer can train a network using the experimental data; the constants or parameters of the trained network can then be transferred to the user who can calculate the performance of the heat exchanger under any other flow rate or inlet temperature conditions.

ANNs are an established technique; see, for example, Haykin (1994) for an account of the history and mathematical background. There have been a few applications to heat transfer problems. One is in the area of liquid crystal thermography to determine heat transfer coefficients (Jambunathan et al. 1996). The generalization capacity of the ANN has been used to design a finned heat exchanger (Lavric et al. 1994, Lavric et al. 1995). Huang and Nelson (1994) also applied this technique to determine the delay time for a HVAC plant to respond to control actions. Ding and Wong (1990) controlled a simulated hydronic system using an ANN. In a previous paper Díaz et al. (1996) applied ANNs to analyze experimental heat-exchanger data.

The goal of the present study is to represent heat exchangers using ANNs. The procedure used to set up and train the network is described first. Then a series of problems of increasing complexity are formulated to facilitate understanding. These problems are: one-dimensional conduction, convection with one heat transfer coefficient, convection with two heat transfer coefficients, and single-row plate-fin heat exchanger. Artificial data bases are generated for the first three problems. Finally, an experimental data base will be used for the fourth problem and the results of the ANN analysis presented.