Analysis of the Nusselt number in pulsating pipe flow

Much attention has been given to the possibility of enhancing the heat transfer rate by superimposing pulsation on a mean flow inside a confined passageway. Industrial applications can be found in Stifling engines and reciprocating cycles, to name a few. A perusal of the relevant literature reveals that pulsating flows in a pipe and the attendant heat transfer have been the subject of several analytical [1,2] and experimental investigations [3, 4]. However, the available published data have been inconclusive and they often show conflicting results. Some investigators reported heat transfer enhancements [4, 5], whereas heat transfer reductions were also noted by some workers [6]. In some instances, both heat transfer augmentation and reduction were detected in a single experiment [3]. Some of these discrepancies can be traced to differences in the parameter spaces that were examined, as well as the nonuniformities in experimental methodologies utilized in various research efforts. However, an analysis of these discrepancies is of vital importance for a more complete application to pulsating heat transfer problems, The present Technical Note addresses this technical issue. One promising avenue to cope with these discrepancies is to reevaluate the Nusselt numbers used in prior published works. It is found that many versions of the Nusselt number were devised to account for the results of the analyses. For a small-amplitude pulsating flow, the Nusselt numbers in various forms are shown to lead to inconsistent results. In addition, if the pulsation amplitude is appreciable, a reverse flow is produced. In this case, difficulties arise in defining the bulk temperature or the time-dependent Nusselt number over a cycle, The present Technical Note aims to examine the consequences of using various forms of the Nusselt number. Special attention is paid to the case of a large-amplitude pulsation flowrate (Af/> 1), which causes reverse flows at the cross section in a pipe. A new definition of the Nusselt number is proposed in the present study. By adopting this definition, the influence of the pulsation amplitude and frequency on heat transfer is scrutinized.