Effect of blockage on heat transfer from a cylinder to power law liquids

Bharti, Ram P.; Chhabra, R.P.; Eswaran, V.

doi:10.1016/j.ces.2007.06.002

Cited by 65 publications

(9 citation statements)

References 22 publications

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“…Broadly speaking, the shear-thinning fluid behavior (powerlaw index less than unity) facilitates heat transfer, and indeed it is possible to augment the value of the Nusselt number by up to 70-80% under appropriate operating conditions. This inference is in line with that reported for a sphere [7][8][9] and numerous two-dimensional objects of various shapes, including circular cylinders [10][11][12], square bars [13][14][15], elliptic cylinders [16], semicircular cylinders [17,18], and triangular cross-section bars [19]. The bulk of this information has been reviewed recently [20].…”

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confidence: 74%

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Sasmal

Chhabra

2014

Journal of Thermophysics and Heat Transfer

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Extensive results are presented on the laminar free convection heat transfer in power-law fluids from a heated hemisphere in two orientations, namely, its flat base oriented upward (inverted) or downward (upright). The coupled field equations have been numerically solved over wide ranges of conditions as follows: Grashof number (10 ≤ Gr ≤ 10 5 ), Prandtl number (0.72 ≤ Pr ≤ 100) and power-law index (0.3 ≤ n ≤ 1.5). Detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the results are analyzed in terms of the total drag coefficient and local Nusselt number variation along the surface of the hemisphere, together with its surface averaged value. The average Nusselt number increases with both the Grashof and Prandtl numbers. Furthermore, for fixed values of the Grashof and Prandtl numbers, and for a given orientation, shear-thinning behavior (n < 1) enhances the rate of heat transfer whereas shear-thickening (n > 1) impedes it with reference to that in Newtonian fluids, especially when there is a reasonable degree of advection. Finally, the present numerical results of drag coefficient and Nusselt number have been correlated using a general composite parameter, which is essentially a modified Rayleigh number. The use of such a Rayleigh number also emphasizes the varying nature of dependence of the average Nusselt number on the Grashof and Prandtl numbers governed by the type of fluid behavior, i.e., shear-thinning (n < 1) or shear-thickening (n > 1). Nomenclatureof the hemisphere, m D ∞ = diameter of the outer domain, m F D = total drag force, N F DF = frictional component of drag force, N F DP = pressure component of drag force, N Gr= Grashof number, dimensionless g = acceleration due to gravity, m · s −2 h = heat transfer coefficient, W · m −2 · K −1 I 2 = second invariant of the rate of the strain tensor, s −2 k = thermal conductivity of fluid, W · m −1 · K −1 m = power-law consistency index, Pa · s n n = power-law index, dimensionless n s = unit normal vector Nu = average Nusselt number, dimensionless Nu l = local Nusselt number, dimensionless P = pressure, dimensionless Pr = Prandtl number, dimensionless R = radius of hemisphere, m Ra = Rayleigh number GrPr, dimensionless S = surface area, m 2 T = temperature of fluid, dimensionless T w = hemisphere surface temperature, K T ∞ = ambient fluid temperature, K ΔT = temperature difference T w − T ∞ , K U = velocity vector, ms −1 U c = characteristic or reference velocity, m · s −1 X, Y = Cartesian coordinates, dimensionless β = coefficient of volume expansion, K −1 ε = components of the rate of the strain tensor, s −1 η = viscosity, Pa · s θ = nondimensional temperature, dimensionless ρ = density of the fluid, kg · m −3 τ = extra stress tensor, Pa

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confidence: 74%

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Sasmal

Chhabra

2014

Journal of Thermophysics and Heat Transfer

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“…where the kinematic viscosity is simply defined as ν = µ/ρ just like Newtonian fluid, which does not lose the generality even for such non-Newtonian fluids. The stream function, ψ is defined as, satisfying Equation (11),…”

Section: Flow Uniformitymentioning

confidence: 99%

“…Owing to their high viscosity levels, this material is generally regarded to be processed in the laminar flow conditions in the moderate flow speed. Various non-Newtonian fluids such as polymeric systems display viscoelastic behaviors, but so far only a few available literatures have been published either for the creeping flow past a single cylinder or over a periodic transverse array of cylinders across the main flow, which implies that the viscoelastic effects have not been well investigated as they are regarded as minor in the present flow configuration [2], but so far the researches on numerical analyses have been much published in the category of rheology using the index of power law [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Some of them manifested various physics related with flow such as drag coefficient, vortex shedding, heat transfer, etc., around single shape or many figures of circular or elliptic cylinders [18,19].…”

Section: Introductionmentioning

confidence: 99%

Characterization and Control for the Laminar Flow of Liquid Polyurethane System in a Wide Angle Diffuser with Transversely Arrayed Obstacles

2020

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In the manufacturing process of hard-board poly-urethane foams, the uniformity is a very important issue for the raw compound of the liquid poly-urethane system flow for the quality control of such products. One of the universal methods to generate more uniform flow is that some obstacles are located inside the diffuser at the end of injector. For the regime of non-Newtonian laminar flow, better flow uniformity can be achieved with the enhancement of mixing in the wake after the resistive obstacles. In this research, the parametric study is made for the gap interval between adjacent obstacle components as well as the cross-sectional shape with a computational fluid dynamics (CFD) technique. The flow fields around circular and elliptic cylinders are visualized for flow velocity and vorticity with the comparison of root-mean-square (RMS) error for the deviation of velocity at the outlet as a lumped parameter to estimate flow uniformity and mixing. When the blockage ratio is fixed 0.3 for the pipe of Reynolds number 58.5 based on its diameter, eliminating the effect of wall boundary ratio with the classical Blasius velocity profile, the RMS error is reduced 77% to 92% from the baseline case in the case of 60%-diameter gaps for the figure of circles and 2:1 longitudinal ellipse, respectively. The flow is visualized around obstacle components with vorticity as well as flow velocity where the three-dimensional components of vorticity vector are also elucidated in physics for the evolution of complex multi-dimensional flow wake.

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“…The available information on the flow of power-law fluids across an isolated cylinder is less extensive than that of Newtonian fluids. Indeed, during the past two decades, numerical works have appeared in the literature on the dynamic characteristics (Bharti et al , 2007a, 2006; Chhabra et al , 2004; D’Alessio and Pascal, 1996; Whitney and Rodin, 2001) and on heat transfer in both forced (Bharti et al , 2007b, 2007c; Soares et al , 2005) and mixed (Bouaziz et al , 2010; Soares et al , 2009; Srinivas et al , 2009) convection regimes. In general, all the results corresponding to the power-law fluids are in good agreement between them.…”

Section: Introductionmentioning

confidence: 99%

A numerical study of two-dimensional laminar flow of power-law fluids around three circular cylinders in side-by-side arrangement

Benamor

Abidi-Saad

Mebrouk

et al. 2022

WJE

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Purpose This study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders. Design/methodology/approach The numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail. Findings It is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index. Originality/value The flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

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Effect of blockage on heat transfer from a cylinder to power law liquids

Cited by 65 publications

References 22 publications

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Characterization and Control for the Laminar Flow of Liquid Polyurethane System in a Wide Angle Diffuser with Transversely Arrayed Obstacles

A numerical study of two-dimensional laminar flow of power-law fluids around three circular cylinders in side-by-side arrangement

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