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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 present article focuses on the incompressible flow around two identical porous cylinders for a side-by-side configuration in a closed channel. The formation of various flow patterns behind permeable cylinders is more intriguing and further compelling to assimilate the underlying flow physics. The effects of three critical parameters, gap ratio (s/d), Reynolds number (Re), and the Darcy number (Da), on the flow behavior are investigated for the ranges of s/d = 1.5–6, Re = 5–100, and Da = 10−6–10−2. Both attached standing and detached vortices are observed in a steady flow regime. One secondary wake structure is also observed for s/d = 1.5, whose size gradually reduces with increased permeability. In an unsteady flow regime, the jet-like flow in the gap section mainly governs the unsteady wake patterns. In the low range of Darcy numbers (10−6–10−3), asymmetric flip-flopping patterns are observed for s/d = 1.5 and 2; and synchronized wake patterns either in anti-phase or in-phase mode are observed for higher gap ratios. The velocity profiles in the gap and free sides of the cylinders and pressure distribution along the porous surface are also discussed to facilitate the understanding of different wake patterns. Surprisingly, a case of pattern shifting from anti-phase to in-phase mode is observed when permeability is altered for the same flow-time. Symmetric and clustered strands of vorticity near the centerline are observed for all cases of s/d at Da = 10−2. The effects of Re, s/d, and Da on the drag coefficient and critical Reynolds number are also discussed. A jump in the drag values, a maximum of 13.9% for s/d = 3.5, is witnessed for the mid-range of Da at higher Re. [ABSTRACT FROM AUTHOR]

The steady flow of non‐Newtonian power‐law fluids across a periodic square array of infinitely long circular cylinders is studied numerically using an unstructured finite volume method. The local and global flow characteristics have extensively been explored by the systematic variations of the pertinent dimensionless parameters as follows: fluid volume fraction (ϕf =.70–.99), Reynolds number (Re = 1–40), and power‐law index (n =.4–1.8). Qualitatively, the dense and curved streamlines are seen with the increasing inertial forces and shear‐thinning behavior across all the fluid volume fractions. Further, the pressure coefficient over the surface of periodic cylinders is significantly influenced by the governing parameters and found to be maximum and minimum for the upstream and downstream cylinders, respectively. The individual and total drag coefficients have shown complex dependence on n, ϕf, and Re. For shear‐thinning fluids (n < 1), the pressure drag coefficient dominates over the friction drag coefficient, whereas an opposite response is seen for the shear‐thickening fluids (n > 1) except at Re = 40. Further, both individual and total drag coefficients are observed to increase and decrease in the ranges of ϕf of.70–.90 and.92–.99, respectively, with increasing n. The strong interactions between the periodic cylinders, at smaller ϕf, diminish with a corresponding increase in ϕf. In addition, simple predictive correlations for the pressure, friction, and total drag coefficients have been developed to gain further physical insights into the detailed flow kinematics. Finally, the present findings display a good agreement with the available literature. [ABSTRACT FROM AUTHOR]

Highlights • Mixed convection characteristics were explored across a periodic array of cylinders. • The dense and curved streamlines and isotherms were obtained. • Drag coefficients were diminished with rise in Reynolds number and fluid volume fractions. • Statistical correlations were developed for drag coefficient and Nusselt number. • The present results displayed an excellent agreement with the available literature. Abstract Aiding buoyancy mixed convection features of Newtonian fluids across a periodic array of heated cylinders have been studied numerically using a commercial CFD solver ANSYS FLUENT. The governing equations have been solved for the following ranges of physical parameters: Reynolds (1 ≤ Re ≤ 40), Prandtl (0.70 ≤ Pr ≤ 50) and Richardson (0 ≤ Ri ≤ 2) numbers and fluid volume fractions of 0.70–0.99. Qualitatively, the dense and curved streamlines and isotherms were seen with the increasing inertial (Re), viscous diffusion (Pr) and buoyancy parameter (Ri) across all the fluid volume fractions. The drag coefficients were observed to be diminished with an upturn in Re and fluid volume fractions, whereas an opposite behavior was noticed with rising in Pr and buoyancy parameter. The Nusselt numbers were found to be enhanced with Re and Pr numbers and moreover with fluid volume fractions also as in contrast to forced convection (Ri = 0) cases. Aiding buoyancy enhances flow as well as heat transfer features and yields unsteady behavior also at the higher fluid volume fractions and Re for all the values of Pr and Ri numbers. Moreover, statistical correlations have been developed for the total drag coefficient and average Nusselt number to gain the more physical insight of the results. Lastly, the findings have been compared with the literature which displayed the good agreement within the ranges of parameters studied herein. [ABSTRACT FROM AUTHOR]

In this research article, we have analyzed the effect of thermal stratification of shear layers due to mixed convection heat transfer past a pair of side-by-side square cylinders in a confined domain, an extended part of our recent study [A. Sanyal and A. Dhiman, “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)]. Investigations from the studies of instantaneous and time-averaged isotherms revealed the actual stretches of the temperature gradient in streamwise and transverse extents at Re = 1–40, Ri = 0–1, s/d = 0.7–10, and Pr = 50. The effects of “baroclinic production,” embedded in the transport of vorticity, were rigorously analyzed through the determination of local period-averaged vorticity flux at a certain cross section in the near-field downstream. The study also revealed the underlying flow physics pertaining to the variations in period-averaged wall vorticity and the local Nusselt number. The transport of vorticity has been explained in terms of the vortex structure formulations, and because of the absence of any such similar studies for multiple bluff-body arrangements, the study has been thoroughly correlated from the cases of single bluff-body flow. In an attempt to control several flow regimes by slightly changing the flow and thermal parameters, it is found that chaotic flow cannot exist beyond a certain value of s/d. However, an abnormality was noted in terms of the flow bifurcations at s/d = 1.5 at the juncture of flow transition from unseparated to a separated steady flow for the first time and this is solely attributed to the effect of thermal buoyancy in the flow field. [ABSTRACT FROM AUTHOR]

This paper focuses on the effects of wall confinements (or blockage ratios) on the flow and heat transfer characteristics around a long equilateral triangular bluff body placed in a horizontal channel for Reynolds number (Re) range 1 to 80 and blockage ratio range 0.1 to 0.5 for air as the working fluid. The governing continuity, Navier-Stokes and energy equations along with appropriate boundary conditions are solved by using a finite volume method-based commercial solver Ansys Fluent. The total drag coefficient decreases with an increasing value of Re for a fixed value of the blockage ratio; however, it increases with an increasing value of the blockage ratio for a fixed value of Re due to the fact that the channel walls exert an extra retardation force on the obstacle. The onset of flow separation is delayed as the value of the blockage ratio increases. The critical Re (i.e., the transition to a time-periodic regime) exists between 45 and 46, 46 and 47, 58 and 59, and 79 and 80 for the blockage ratios of 0.1, 0.125, 0.25, and 0.5, respectively. The simple correlations for wake length, total drag coefficient, and average obstacle Nusselt number are obtained for the range of conditions covered. [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]

The effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady forG = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed forG = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasingGand/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% atG = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value atG = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained. [ABSTRACT FROM AUTHOR]

This study involves the numerical solution of the laminar heat transfer in a separating and reattaching flow by simulating the flow and heat transfer downstream of a backward-facing step. The in-house finite volume code has been implemented employing a hybrid differencing scheme and the SIMPLE algorithm for the pressure-velocity coupling. Three principal parameters governing heat transfer in this geometry, that is channel expansion ratio (ER), Reynolds number (Re), and Prandtl number (Pr), are systematically varied in the range ER = 1.111 to 2, Re = 1 to 200, and Pr = 0.71 to 100, and the simple correlations between these parameters have been elucidated. A series of important findings have been established by analyzing the results some of which are: (1) there is an associated shifting of the point of maximum heat transfer with respect to the flow-reattachment point with gradually decreasing the values of ER and (2) the heat transfer enhancement increases with the increase in Pr number as a result of the compression of the thermal boundary layer and the maximum Nusselt number varies as [ABSTRACT FROM AUTHOR]

The influence of opposing-buoyancy mixed convection from a square cylinder in a vertical channel has been studied at Reynolds numbers (Re) = 1–100, Richardson numbers (Ri) = 0 to −1, and blockage ratios (β) = 10–50% for air as a working fluid. The onset of a steady to a time-periodic regime is found for Ri = 0 (at Re = 35, 65, 74, and 62), Ri = −0.5 (at Re = 12, 39, 48, and 54), and Ri = −1 (at Re = 9, 30, 39, and 50) forβ = 10%, 25%, 30%, and 50%, respectively. The initiation of flow separation is also determined. Finally, the correlations of Strouhal number, drag coefficient, and the Colburn heat transfer factor were obtained. [ABSTRACT FROM AUTHOR]

Extensive numerical computations for the confined flow and heat transfer of shear-thinning fluids over two long tandem triangular bluff bodies are performed for Reynolds number (Re) = 1–40, power-law index (n) = 0.2–1, and gap ratio (S/B) = 1–4 for a fixed blockage ratio and Prandtl number of 25% and 50, respectively. The values of critical Re are obtained for each of the two triangular cylinders for allS/Bandn. Augmentation in heat transfer for the two tandem triangular cylinders is calculated with respect to bothS/Bandn. [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]

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 increasingRe. However, the average Nusselt number shows a soft response toward increasingRi. The criticalRefor 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, andRi. [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]

Effects of cross-buoyancy mixed convection on flow and heat transfer characteristics of a long semi-circular cylinder (long in neutral direction) in a confined channel have been investigated in the laminar regime. The numerical results have been presented and discussed for the range of conditions as Reynolds number (Re) = 1–40, Richardson number (Ri) = 0–4, Prandtl number (Pr) = 0.71–50 and blockage ratio (β) = 16.67%–50%. The drag coefficient increases with increasing Richardson number and/or blockage ratio. The average Nusselt number is showing a maximum relative enhancement of approximately 45% for Ri = 4 with respect to corresponding forced convection value (Ri = 0). The average Nusselt number increases with increase in Prandtl number and shows a maximum relative enhancement of approximately 1136% for Pr = 50 with respect to corresponding value at Pr = 0.71. On the other hand, the maximum relative variation of the total drag coefficient is found to be approximately 55% for Ri = 4 with respect to corresponding value at Ri = 0. Finally, the simple heat transfer correlation is obtained for the proceeding range of control parameters. [ABSTRACT FROM AUTHOR]

Mixed-convectionflow and heat transfer of non-Newtonian power-law fluids over a pairof side-by-side circular cylinders in aiding buoyancy are investigatednumerically. The calculations are performed in an unconfined domainfor the following range of physical control parameters: Reynolds number(Re) = 1–40, Richardson number (Ri) = 0–1, and power-law index (n) = 0.2–1for a transverse gap ratio of 1.5 at a constant Prandtl number (Pr) of 50. Extensive numerical results are presented, suchas viscous, pressure, and total drag coefficients, average Nusseltnumber, and transition from a steady to a time-periodic regime. Theoverall drag coefficient and its components decrease with the Reynoldsnumber and increase with the Richardson number for all values of thepower-law index considered. The average Nusselt number increases withan increase in both the Reynolds and Richardson numbers but decreaseswith an increase in the power-law index. It is observed that aidingbuoyancy and shear-thinning tendency augment heat-transfer characteristics.The maximum enhancement in heat transfer is found to be approximately85% for Re= 40, n= 0.2, and Ri= 1. However, the maximum enhancement in the value ofthe average Nusselt number for Ri= 0 and 0.5 isfound to be approximately 70% and 81%, respectively. Finally, a simpleheat-transfer correlation is obtained for the values of Re, n, and Ricovered in this study. [ABSTRACT FROM AUTHOR]

ABSTRACT Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluff body are investigated for the range Re = 1 to 150 (thereby covering both steady and unsteady periodic regimes) and Pr = 0.7 (air). A number of engineering parameters, e.g. drag and lift coefficients, Strouhal and Nusselt numbers, and others, is calculated for the above range of conditions. No flow separation occurs from the surface of the trapezoidal cylinder for the range Re ≤ 5; however, flow starts to separate from the rear surface of the cylinder at Re = 6. Therefore, the onset of flow separation exits between Re = 5 and 6. The critical value of the Reynolds number (i.e. transition from steady to unsteady) exists between Re = 46 and 47. The drag coefficient decreases with increasing Reynolds number in the steady regime; however, the drag increases with Reynolds number in the unsteady regime. The Strouhal number and the average Nusselt number increase with increasing value of the Reynolds number. Finally, the simple correlation for the average Nusselt number is obtained in the steady flow regime. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Steady and unsteady forced convection flow and heat transfer past a long expanded trapezoidal bluff body are investigated for the air as working fluid for Re=1–150. The wake length increases as the Reynolds number increases in the steady flow regime (1⩽Re⩽47). The transition from steady regime to unsteady regime occurs between Re=47 and 48. The total drag coefficient decreases with the increasing value of the Reynolds number up to Re=90 and thereafter it increases with Reynolds number. However, heat transfer as well as Strouhal number increase with the increasing value of the Reynolds number. The maximum augmentation in heat transfer for the expanded trapezoidal cylinder with respect to the tapered trapezoidal cylinder is found to be approximately 146%. On the other hand, pressure drop shows an enhancement of approximately 97% for the expanded trapezoidal cylinder when compared with the tapered one. Simple correlations of wake length, drag, average Nusselt number and Strouhal number with Reynolds number have also been established. [Copyright &y& Elsevier]

Abstract: In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re =1–40 and Richardson number, Ri =0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re =1–2, between Re =2–3 and between Re =3–4 for Ri =0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work. [Copyright &y& Elsevier]

Abstract: The current study investigates the augmentation in the laminar forced convection characteristics of the backward-facing step flow in a two-dimensional channel by means of introducing an adiabatic circular cylinder in the domain. The effects of various cross-stream positions (i.e., yc  = 0–1.5) of the circular cylinder on the flow and heat transfer characteristics of the backward-facing step flow has been numerically explored for the Reynolds number range 1–200 and Prandtl number of 0.71 (air). The governing continuity, Navier–Stokes and energy equations along with appropriate boundary conditions are solved by using FLUENT. The flow and thermal fields have been explained by streamline and isotherm profiles, respectively; however, no temperature dependency effects are considered for the flow viscosity and thermal conductivity. The engineering parameters like wake/recirculation length, total drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions. The present results show an enhancement in the peak Nusselt value of up to 155% using a circular cylinder as compared to the unobstructed case (i.e., without cylinder). Finally, simple correlations for total drag coefficient and peak Nusselt number are obtained for the above range of conditions. [Copyright &y& Elsevier]

Effects of Reynolds number on the heat transfer characteristics of a long (heated) equilateral triangular cylinder are investigated for the range of conditions Re = 50-150 (in the steps of 10) and Prandtl number = 0.71 (air) in the unconfined unsteady cross-flow regime. In order to simulate the present situation, the computational grid is created by using commercial grid generator GAMBIT and the numerical computations are carried out by using FLUENT (6.3). The SIMPLEmethod is used to solve continuity, Navier-Stokes and energy equations along with the appropriate boundary conditions. The second order upwind scheme is used to discretize the convective terms, while the central difference scheme is used to discretize the diffusive terms in the governing equations. The present results are in an excellent agreement with the literature values. The temperature isotherms and temporal history of Nusselt number are presented in detail. The local as well as time-averaged Nusselt numbers are calculated. The time- averaged Nusselt number increases with increasing Reynolds number for the fixed value of the Prandtl number. Finally, the present numerical results are used to develop the simple heat transfer correlation for the range of conditions covered here. [ABSTRACT FROM AUTHOR]