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.
