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This article investigates the laminar flow of power-law fluids through two porous square cylinders in a side-by-side configuration. The effects of power-law index (n), Darcy number (Da), and gap ratio (g/W) are examined within ranges of g/W = 0.5–5, n = 0.4–0.8, and Da = 10−6–10−2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re = 1 where Darcy's law is applicable; second, for a viscous dominant flow at Re = 100, where Darcy–Forchheimer-extended model is exercised. Flow patterns behind the porous cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular nonperiodic vortex shedding characterized by a single large vortex street far off the downstream for g/W = 0.5. However, synchronized wake patterns were observed in either antiphase or in-phase modes for higher gap ratios. Leading-edge separation with two-side recirculation induces quasi-periodicity in the flow for all g/W. It was found that increasing the permeability can prevent the leading edge separation. Additionally, a transition from antiphase to in-phase mode occurs when the permeability is altered while maintaining constant flow-time. The presence of a jet-like flow between cylinders significantly impacts unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. A jump in some flow parameters was observed at higher Re for the midrange Darcy number, but no such increase was noted for the high shear-thinning behavior. These findings provide a potential approach for improving the design of fluidic systems involving porous cylinders. [ABSTRACT FROM AUTHOR]

The article examines the consequence of thermal buoyancy-driven cross-flow and heat transfer for shear-thinning power-law fluids on the tandem orientation of two cylinders. Finite volume methodology is used to investigate the effect of the gap ratio (2.5 = S/D = 5.5), power-law index (0.2 = n = 1), and Richardson number (0 = Ri = 1) on flow and thermal output parameters at Reynolds number Re = 100 and Prandtl number Pr = 50 in a confined channel. An unprecedented jump has been witnessed in the flow/thermal parameters at the critical gap ratio (critical spacing). At forced convection (Ri = 0), this critical spacing keeps on increasing with shear-thinning character, from S/D = 3.9 (at n = 1) to 4.9 (at n = 0.2). On the contrary, an increase in shear-thinning characteristic leads to a decrease in critical spacing from S/D = 3.9 (at n = 1) to 2.8 (at n = 0.4) for Ri = 1 (mixed convection). The heat transfer rate increases with shear-thinning behavior, with a maximum heat transfer, noted at n = 0.2. A higher unprecedented increment for flow/thermal parameters is seen at critical spacing for the downstream cylinder than the upstream cylinder. At the highest gap ratio, the output parameters for the upstream cylinder approximate that of an isolated cylinder. The time-variant fluctuations in lift coefficients for a shear-thinning flow in a tandem arrangement provide a new understanding of coshedding and extended body flow regimes. [ABSTRACT FROM AUTHOR]

In this article, investigations have been carried out to decipher the effect of thermal buoyancy in a viscosity stratified flow field for a shear-thinning fluid flowing past a pair of heated side-by-side square cylinders, which is an extension part of our recent study [Sanyal, A. and Dhiman, A., "Wake interactions in a fluid flow past a pair of side-by-side square cylinders in presence of mixed convection," Phys. Fluids 29, 103602 (2017)]. It is found that the leading-edge flow-separations from the square cylinders influence the near-wake structures and vortex shedding patterns in the presence of shear-thinning effects, which is otherwise missing for Newtonian fluid flow at Reynolds number Re = 40 and Richardson number Ri = 1. The distribution of wall-viscosity η along the inner surfaces of the side-by-side square cylinders, at different values of transverse spacings s/d and flow-behavior indices n, hints at large dependency on the inflections in the velocity profile within the gap-flow region. Under thermal buoyancy-driven mild shear-thinning flow conditions (n = 0.6 and 0.8), the gap-flow characteristics have been classified into "pressure-driven" and "momentum-driven" flow regimes, which provides a good explanation for the aberrations noted in the distribution pattern of η. The root-mean-square fluctuations of the velocity-magnitude and vortex shedding phenomenon are found to reciprocate a consistent flow physics associated with a shear-thinning flow at near and far-field downstream. The single body deflected type flow is primarily seen under predominant shear-thinning flow conditions (n = 0.4), compared to chaotic or quasi-periodic flow under mild shear-thinning conditions. Besides, the evolution of non-linear dynamics-based flow regimes (classified with respect to s/d using power spectrum density analysis) at different values of n and s/d is thoroughly summarized. The time-variant fluctuations of lift and drag force parameters are also found to be unified through cause and effects. [ABSTRACT FROM AUTHOR]

The dynamics of a shear-thinning fluid flowing past a pair of mildly heated side-by-side square cylinders, in a confined horizontal flow channel at low Reynolds number (Re), has been investigated. A detailed probe for flow physics in terms of vortex shedding patterns, near-wake streamlines and stretch of isotherms are carried out at Re = 1 and 100 (signifying two-dimensional unseparated steady flow and transient flow). The power-law index (n) is varied from 0.4 to 1 and the side-by-side transverse gap ratio (s/d) ranges from 1 (pressure-driven flow regime) to 5 (momentum-driven flow regime) at a constant value of Prandtl number (Pr) = 50. When the shear-thinning effects in the flow are increased (in the present numerical framework) at Re = 100, the time-averaged streamlines depict an early onset of leading edge flow separations from the pair of side-by-side square cylinders. One can infer from the phase space plots that the flow becomes chaotic with the increase in shear-thinning effect from n = 0.8 to 0.4 and decrease in s/d from 5 to 1. An anti-phase vortex shedding can be characterized by the occurrences of symmetrical structures of negative ζ (where ζ quantifies the accumulation and propagation of the vortices) contours in the downstream and this is realized at Re = 100, n = 0.8 and s/d ≥ 1.7. An in-phase vortex shedding (which occurs at Re = 100, n = 0.4 and all values of s/d) is characterized by asymmetrical occurrences of negative ζ contours which have a tendency of dying down early in the downstream with the increase in the nearness of the side-by-side square cylinders. This is more clearly realized at enhanced shear-thinning effects in the flow. Finally, the variation of time and space-averaged drag flow parameter (CD) and Nusselt number (Nu) with respect to shear-thinning effects in the flow has been extensively determined. [ABSTRACT FROM AUTHOR]

In this research article, we investigated the phenomena of a buoyancy-driven cross-flow impinging on a bulk flow from the inlet for a flow past a pair of side-by-side square cylinders in a confined channel wall (which are kept in an adiabatic condition), a special case of an "internal flow" type problem. The density difference in the flow was achieved through a subtle temperature difference between the ambient fluid and the solid walls present in the domain. The study has been carried out at the Reynolds number Re = 1-40 for a transverse gap ratio s/d = 0.7-10 and the Richardson number Ri = 0-1 at a constant value of the Prandtl number Pr = 50. During a rigorous parametric study, we found that the mixed convection not only brings an early unsteadiness in the flow but also fetches an early formation of different flow regimes at Re = 40. An effort has been made to identify the precise near-wake formations leading to the vortex shedding processes in a mixed convection flow for a various range of s/d values. Different flow regimes can be identified efficiently through a unique combination of occurrences for dominant frequencies in terms of the Strouhal number St of primary, secondary, and harmonic frequencies in the flow. The time variant lift plots indicate that the unsteady periodicity in the flow varies from sinusoidal nature at s/d = 0.7 (single body type flow) to square wave (non-sinusoidal periodic waveform) for s/d = 1.5 (chaotic flow) and finally getting back to sinusoidal at s/d = 6 (non-interacting flow). We have also encountered the drastic pattern changes in the flow which occurred due to the onset of recirculation followed by the transition of steady to unsteady periodic nature with Re = 1-40 for all the values of s/d. This case is analyzed in detail through the study of various flow parameters. [ABSTRACT FROM AUTHOR]

Computations of incompressible fluid flow and heat transfer around a square obstacle with a nearby adiabatic wall have been performed in a horizontal plane. The ranges of dimensionless control parameters considered are Prandtl number (Pr) = 10-100, Reynolds number (Re) = 1-150 and gap ratio ( G) = 0.25-1. The steady-flow regime is observed up to Re = 121 for G = 0.5, and beyond this Re, time-periodic regime is observed. The shift to a time-periodic regime from a steady regime occurred at greater Re than that for an unconfined square obstacle. With increasing Pr, increase in average Nusselt number values is recorded for all Re and G studied. The heat transfer augmentation is approximately 1332% at Re = 150 (Pr = 100, G = 0.25) with regard to the corresponding values at Re = 1. Lastly, a correlation for j factor is determined for the preceded conditions. [ABSTRACT FROM AUTHOR]

Flow and heat transfer characteristics around a semi-circular cylinder placed in a confined channel are investigated in the unsteady regime. The two-dimensional simulations are carried out for varying values of control parameters: Reynolds number (Re) = 50–200 and Prandtl number (Pr) = 0.7, 10 and 100 at a fixed blockage ratio of 25% for Newtonian constant-property fluid. Continuity, Navier–Stokes and energy equations with appropriate boundary conditions are solved using the commercial computational fluid dynamics solver Ansys Fluent. The transition from steady to time-periodic flow occurs between Re = 69 and 70. The effect of Prandtl number on Nusselt number is pronounced; the ratio of Nusselt number values belonging to Pr = 100 and those belonging to Pr = 0.7 ranges from 6.3 to 6.5 over the Reynolds number domain investigated. Finally, the present numerical results are used to develop drag coefficient, Strouhal number and Nusselt number correlations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Confined flow and heat transfer phenomena across two long triangular bars in tandem arrangement in a horizontal channel have been studied for the range of Reynolds number (Re) = 1–40, Prandtl number (Pr) = 0.71–50 and gap ratio (S/B) = 1–4 for a fixed blockage ratio of 25%. The average Nusselt number of the first triangular cylinder is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Heat transfer correlations in terms of the Colburn jhfactor have been established in the steady regime. [ABSTRACT FROM PUBLISHER]