Influence of developing flow on the heat transfer in laminar oscillating pipe flow

A theoretical analysis was performed to evaluate the influence of developing flow on the heat transfer associated with laminar oscillating pipe flow. Simplified analytical approaches are briefly discussed before an investigation based on the numerical solution of the conservation equations for mass, momentum and energy is presented, assuming constant wall temperature and an incompressible viscous fluid. Focusing on operating conditions as found in heat exchangers of regenerative thermal machines, like Stirling engines or Vuilleumier heat pumps, numerous calculations of the flow field and the heat transfer have been executed covering wide ranges of the characteristic dimensionless groups. The results are presented in tems of correlations of the mean Nusselt number averaged on the pipe length and a distribution function describing the local heat transfer. Furthermore, it is shown that the derived correlations are also applicable to compressible fluid flow, provided that the relative pressure amplitude is within the limits typical of regenerative thermal machines.