Numerical simulation of thin film flowing down a vertical uniformly heated plane using the regularized weighted residuals model

Abstract With the developed three-dimensional Regularized Weighted Residuals Model (RM), discussion on its accuracy and simulation work are conducted. It is shown that for small to moderate Reynolds number, the accuracy of RM decreases with increasing Marangoni number and decreasing Biot number of the plane. The streamwise error ratios are larger than spanwise ones and reach a maximum when Reynolds number equals 3, which is due to underestimate of Marangoni instability. The increase of Reynolds number or introducing streamwise most unstable disturbance makes film duration time longer. With increasing Reynolds number, the early stage of wave evolution becomes faster and ripples are more intensive; the final pattern is more unstable and disordered. Heat transfer efficiency reaches two peaks with increasing Reynolds number, one due to the interaction between thermal condition and flow rate, the other due to film no-rupture. Introducing streamwise most unstable disturbance makes the early stages of wave evolution longer and wave amplitude smaller in later stages. Unless Reynolds number is small enough, heat transfer efficiency decreases with the introduction of streamwise most unstable disturbance.