Buoyancy effects in vertical 2-D and 3-D T-channels on the onset of flow reversal of power-law fluids in the side branch

Abstract

The primary goal of the present study is to investigate the flow reversal in the side branch of a T-channel for the flow of power-law fluids. The governing equations have been solved over wide ranges of conditions as: channel Reynolds number, 20 ≤ Re ≤ 100, Prandtl number, 1 ≤ Pr ≤ 100, Richardson number, 0 ≤ Ri ≤ 10, power-law index, 0.2 ≤ n ≤ 1.4, together with the conditions of equal exit pressure (EEP) and specified flow split (SFS). The flow reversal occurs in the side branch of the T-channel at a critical value of the Richardson number for the equal exit pressure condition, and this can be eliminated by using the specified flow rates as 10 ≤ βMB (%) ≤ 99 where, βMB is the value of the specific flow rate at the main branch outlet for a particular case. The results are interpreted in terms of velocity and temperature fields, exit flow rates, the required pressure to maintain the specific flow rate, recirculation lengths and the local Nusselt number. As the power-law index and/or Reynolds number is increased, the flow reversal is encountered at lower Richardson and Prandtl numbers. The flow rate from the main branch increases with Re, n, Ri while it decreases with Pr. Furthermore, the required pressure to maintain the flow rate shows a positive dependence on n, Ri and Pr whereas it shows an inverse dependence on Re and specified flow rates (βMB). Also, the rate of heat transfer rises with an increase in Re, Ri, Pr and β while it is promoted in shear-thinning fluids and impeded in shear-thickening fluids. Furthermore, the present work also compares the critical value of Richardson number of the 2-D model with that of the 3-D model for aspect ratio as 0.5 ≤ AR ≤ 10. The results show that for AR ≥ 5, the three-dimensional effects are small. Qualitative trends of the critical Richardson number e.g., with respect to Prandtl number obtained from the 3-D model are the same as from the 2-D model irrespective of the values of the aspect ratio.