A numerical study of laminar forced convection in sinusoidal ducts with arc lower boundaries under uniform wall temperature

Laminar flow in ducts of irregular cross-sectional shapes is of importance to heat recovery heat exchangers. In this article, heat trasfer and pressure drop characteristics in corrugated sinusoidal ducts with arc lower boundaries are studied for a hydrodynamically fully developed, thermally developing flow under uniform temperature conditions. The numerical method is of high-order accuracy, is numerically implicit, and is unconditionally stable. The cross-derivative term is treated as a source term and is solved by iterations in which a varying axial step size ensures a fast convergence without sacrificing details near the inlet of the thermal entry region. This method allows for the simulation of unevenly distributed nodes on boundaries, in combination with the transformation of the special duct geometry to a rectangular computational domain. The detailed finite difference discretization of the governing momentum and energy equations is provided. The values of (f · Re) and local and mean Nusselt numbers are calculated for different aspect and bending ratios. The velocity and temperature profiles are plotted. The results would be helpful to estimate the performances of honeycomb-type regenerative wheels.