A thermal model for prediction of the Nusselt number in a pipe with chaotic flow

It is currently well established that Lagrangian chaos intensifies heat transfer significantly [J. Fluid Mech. 209 (1989) 335]. It thus appears to be a promising technique for the design of compact, high-performance heat exchangers and heat exchanger-reactors. However, the design of such apparatus requires extensive calculations. The objective of this work is to implement a simplified thermal model with which to simulate heat transfer in a twisted pipe (of a shell and tube heat exchanger) of two tube configurations, helically coiled or chaotic, without requiring the heavy calculations needed in the numerical resolution of the Navier–Stokes and energy equations. The large database obtained from the parametric study of the variation of the Nusselt number using the heat transfer model developed here, allows one to correlate Nu with Re, Pr, Nbends: Nu=1.045 Re0.303 Pr0.287 Nbends−0.033. This correlation is valid for coil geometry with alternating planes of curvature, i.e. chaotic configuration and the range of validity of the correlation is Re∈[100;300], Pr∈[30;100] and Nbends∈[3;13]