Transition to periodic unsteady and effects of Prandtl and Richardson numbers on the flow across a confined heated trapezoidal prism

Abstract

The effects of wall confinements (?) and of Prandtl numbers (Pr) on the laminar flow around a heated trapezoidal prism are investigated numerically for Pr = 0.71–100 and ? = 12.5–50 % at low Reynolds numbers (Re). The critical value of the Reynolds number (i.e., the transition from a steady to a time-periodic regime) is calculated and it exists between Re = (36 and 37), (60 and 61) and (91 and 92) for the blockage ratios of 12.5, 25 and 50 %, respectively. The average Nusselt number increases with increasing Re and/or Pr and/or blockage ratio. The variation of local Nusselt number on each surface of the obstacle and the representative isotherm contours are presented to elucidate the role of Pr and blockage ratio on the heat transfer from the trapezoidal prism. The maximum heat transfer enhancement with respect to a square prism on the basis of equal projected area is found to be approximately 31 and 45 % for the blockage ratios of 12.5 and 25 %, respectively, for Pr = 0.71 and Re = 1. The Colburn heat transfer factor correlations are also obtained for the preceding range of settings. Finally, the influence of Richardson number (Ri = 0–1) on the flow and heat transfer characteristics has been studied for air as working fluid. © 2014, The Brazilian Society of Mechanical Sciences and Engineering.