Search

Flow around an isolated generic sharp-edged object with varying height ratio (β = 0–1) i.e. height from the rear end of the object to the front end ( β = H 2 / H 1 ) has been investigated in cross-flow configuration covering steady and periodic regimes at Reynolds number (Re) from 1 to 150 using air as a working fluid. Flow separation is delayed with a decrease in β. Wake formed is the highest for β = 1 (square object) and progressively decreases with the decrease in β. The vortex shedding effect has been demonstrated on the heat transfer phenomena around the objects. For all the cases of height ratios, as Re increases the flow undergoes supercritical Hopf bifurcation to periodic state as steady-state condition loses its stability. Stuart-Landau theory has been used to determine the value of critical Re or the onset of vortex shedding for all the cases of height ratios. As β increases from 0 to 0.7, the value of critical Re increases. Influence of surface vorticity and surface pressure on the overall drag coefficient ( C D ) has been explored. Effect of β on the Strouhal number (St) has been investigated and the findings are in agreement with previous results. Finally, correlations relating Lr, C D , Nu ‾ and St with Re and β have been developed.

Numerical computations have been carried out to explore the influence of mixed convection heat transfer from heated trapezoidal geometries of two different configurations namely converging and diverging cylinders in a vertical domain. The recirculation length of the diverging cylinder is found to be more than that of the converging cylinder for all values of Re (5 to 40) considered in this study and this length decreases after introducing buoyancy effect. Drag coefficients decrease with increase in Re for a fixed Ri. However, drag increases for the increasing values of Ri (values considered up to 1). The drag coefficient is found to be the smaller for diverging cylinder than that of converging one. Local Nusselt number shows significant increase as Re and Ri values increase, which results in enhanced heat transfer. Keeping Ri fixed and increasing the value of Re results in the augmentation of heat transfer and is around 15% at Re = 5 and 23% at Re = 40 for Ri = 0 for a square cylinder with respect to diverging cylinder. Under the influence of aiding buoyancy, the values of average Nusselt number ( $$ \overline{Nu} $$ ) for the diverging cylinder are higher compared to that of converging cylinder. A correlation expressing functional relationship of $$ \overline{Nu} $$ with Re and Ri has also been generated.

Two-dimensional numerical simulations are carried out to understand the effects of cross-buoyancy on the confined flow and heat transfer characteristics over an equilateral triangular bluff body at low and intermediate Reynolds numbers (Re). For a fixed Richardson number (Ri), an average cylinder Nusselt number increases with increasing Re. However, the average Nusselt number shows a soft response toward increasing Ri. The critical Re for the onset of periodic unsteady flow increases with increasing cross-buoyancy (Ri). A simple heat transfer correlation is also obtained to relate the values of average cylinder Nusselt number, Re, and Ri.

The effects of wall confinements (β) and of Prandtl numbers (Pr) on the laminar flow around a heated trapezoidal prism are investigated numerically for Pr = 0.71–100 and β = 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.