Mathematical and numerical predictions for optimum perfect mixing by bulk convective oscillatory exchange

Abstract

The mixing quality for bulk convective oscillatory exchange are analyzed, modeled, and simulated for 24 cases mathematically and numerically. A new mathematical model has been derived for heat and mass transfer between two reservoirs to predict the perfect and optimum mixing quality. Two-dimensional axisymmetric simulations are carried out for incompressible viscous oscillatory flows. The computations are run for two reservoirs that are connected by a short duct over a unique range of the fluid’s axial displacements. From the mathematical model, two new equations for the instantaneous temperature in each reservoir have been derived to predict the perfect mixing quality for any bulk convective oscillatory exchange. According to the computational predictions, the mass exchange between the two reservoirs has been classified into five different regions depending on their mixing quality. Optimum perfect mixing conditions were obtained at a normalized fluid’s axial tidal displacement with mixing ratio ranged from . A new correlation for predicting the rate of heat transfer enhancement by the bulk convective oscillatory exchange is suggested. It is observed that the effective thermal conductivity has been enhanced by up to compared with the molecular conductivity of the fluid. Also, the mixing quality for specific mass exchange conditions has enhanced up to compared with the perfect mixing case.