A theoretical analysis about the effect of aspect ratio on single-phase laminar flow in rectangular ducts

Abstract Effects of the aspect ratio on single-phase laminar flow resistance in rectangular duct are theoretically studied by way of analyzing the wall shear stress. And the transition Reynolds number with different aspect ratios is also investigated by energy gradient method. The results show that the Poiseuille number increases as the aspect ratio decreases. And the contribution of the skin friction due to the wide side to the total frictional resistance is increased evidently with the decreasing of the aspect ratio. Although the aspect ratio has limited influences on shear stress occurs on narrow side, the decrease of the aspect ratio leads the distribution of local shear stress on wide side transforms from parabola to trapezia gradually and the mean shear stress increases significantly, if the hydraulic diameter is constant. A simplified expression for Poiseuille number is acquired by approximately displacing the infinite series, showing good agreement with the experiments for mini/micro ducts and the correlation of Shah & London. In addition, an approximate correlation is also given for narrow rectangular duct with the aspect ratio less than 0.2. Finally, a polynomial correlation for transition Reynolds number is achieved by energy gradient method, which is consistent with the previous work and experimental data.