Conformal mapping as an analytical tool for hydrodynamic analysis in corrugated pipe flows

An investigation of steady laminar flow in transversely corrugated conduits is presented, with the velocity distribution and frictional resistance being characterized for the fully developed region, while the incremental pressure drop, and hydrodynamic entrance length are examined for the developing region. The velocity field throughout both flow regimes is modeled using an innovative analytical approach based on epitrochoidal coordinate transformations. It is demonstrated that in fully developed flow, the Fanning friction factor is reduced with either an increase in corrugation count at fixed amplitude or with larger corrugation amplitude at fixed wave number. Conversely, in the developing flow region, both the incremental pressure drop, and entrance length are found to increase with greater corrugation amplitude or number of boundary waves. These findings are shown to provide valuable insights for the optimization of corrugated conduit designs in applications where entrance effects are significant, such as in compact heat exchangers and microfluidic systems.