Laminar Momentum and Heat Transfer in a Channel with a Built‐In Tapered Trapezoidal Bluff Body

Abstract

Effects of wall confinements on the laminar flow and heat transfer around a heated tapered trapezoidal bluff body are investigated numerically in the confined domain (Reynolds number, Re = 1 to 40; blockage ratio = 0.125 to 0.5; and Prandtl number, Pr = 0.71). The onset of flow separation is found between Re = 4 and 5 for the blockage ratio of 0.125 and between Re = 5 and 6 for the blockage ratios of 0.25 and 0.5. If compared with a long circular obstacle on the basis of equal projected area, the total drag coefficient of the trapezoidal cylinder is found to be larger than the circular one, but an opposite trend is observed for the heat transfer. The augmentation in heat transfer for trapezoidal and circular cylinders is found to be approximately 46, 72, 74, and 65 percent for Re = 1, 5, 10, and 40, respectively for the blockage ratio of 0.25. The maximum enhancement in heat transfer for a tapered trapezoidal bluff body with respect to a square bluff body is found to be approximately 104 percent and 101 percent for blockage ratios of 0.25 and 0.5, respectively. Finally, simple correlations of wake length, drag, and average cylinder Nusselt number are established.

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

“…Exceptional concurrence can be seen between the present results and the values reported in the literature [19][20][21][22] and the maximum deviation can be seen of the order of 0.1 % for drag coefficient and less than 0.3 % for Nusselt number, and hence this validates the present numerical methodology. Extensive details on the forced flow (Ri = 0) of air (Pr = 0.71) around a trapezoidal prism in a channel can be found in our recent study [17] and are not replicated here. Briefly, as the Reynolds number increases, the flow separates at the trailing edge of the trapezoidal prism.…”

“…The fully developed velocity profile at the channel inlet is incorporated using user-defined functions available in Ansys [18]. The second-order implicit time-integration method is used here and the dimensionless time step is set to 0.01 [5,17]. The resulting algebraic equations are solved by Gauss-Siedel iterative method in conjunction with Algebraic Multi-Grid solver.…”

“…[17] and for the purpose of brevity, it is not shown. Briefly, the computational grid structure consists of both uniform and non-uniform grid distributions with the smallest grid size of 0.002b (near the obstacle and near the top and bottom walls of the channel) and the coarsest grid size of 0.4b with 100 control volumes (CVs) on each side of a trapezoidal prism.…”

“…and boundary conditions Figure 1 shows the geometrical configuration of 2-D incompressible and laminar flow over a long tapered trapezoidal prism having upstream face width and axial obstacle height b each, and downstream face width a (=0.5b) [5,17]. The domain is considered to be confined by employing the wall confinements (β) ranging from 12.5 to 50 %, where β = b/H.…”

“…Further, the study has been extended for the Ri effects on the flow and heat transfer around a trapezoidal prism. Furthermore, the present study is the natural extension of our recent work [17] on the forced momentum and heat transfer (Ri = 0) across a confined tapered trapezoidal prism for Re = 1-40 and β = 12.5-50 %, albeit at a fixed Pr = 0.71 (air).…”