Conclusion
In this contribution the dynamic modelling process for tube and shell, heat exchangers, was outlined. The complexity of the representations for these devices, arises from the fact that under independent, fluid flow and input-output temperature conditions, the analytical procedures result in multivariable, irrational, two dimensional models. This inhibits direct Laplace inversion to the time domain whilst restricting simulation and analytical evaluation. It is true, that in principle the Laplace error function and contour integration could be employed to achieve the time domain functions required. However, this process becomes increasingly challenging when considering the mixed, lumped and distributed parameter models, employed herein. These models exhibit Laplace function singularities, further limiting investigation, under general tube and shell, fluid/ gas flow and temperature variation conditions. This impedes simulation, design and the application of feedback regulation with the result that the prediction of optimum, continuous operational, dynamic performance, is difficult. With the use of frequency response, Bode analysis procedures, it was demonstrated that Laplace rationality can be restored with the result that design and simulation becomes easier opening the route to feedback regulation and optimization studies. The key to this depends on achieving a suitable low frequency fit, for the parallel and counter flow model, ( ) ( ) and functions, p c s s respectively. In doing so, the complex frequency domain, branch point problem is avoided with the restoration of Laplace function completeness. As shown in sections 7 and 8 and in sections 13 and 14, of this contribution, the dynamic simulation of both parallel and counter flow, tubular heat exchanger models following this enhancement becomes routine enabling the application of conventional analysis and simulation methods and the advancement of the design and feedback control problems.
