Effect of Blockage on Heat Transfer from a Sphere in Power-Law Fluids

Song, Daoyun; Gupta, Rakesh; Chhabra, R.P.

doi:10.1021/ie901524h

Cited by 41 publications

(30 citation statements)

References 37 publications

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“…Suffice it to add here that the present average Nusselt number values are within ±1.5% of that reported in ref . In addition, a comparison between the present average Nusselt number values and that of refs and for a sphere ( e = 1) is presented in Table S4 and the present numerical results were seen to be within ±4%. Finally, the present values of the recirculation lengths in Newtonian fluids were found to be within 2–2.5% of that reported in ref for spheroidal particles.…”

Section: Results and Discussionsupporting

confidence: 81%

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Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Gupta

Chhabra

2014

Ind. Eng. Chem. Res.

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In the present work, the forced convection momentum and heat transfer aspects of isothermal spheroidal particles (both prolates and oblates) in Bingham plastic fluids have been numerically investigated in the steady axisymmetric flow regime. Extensive results on the detailed structures of the flow and temperature fields are presented and analyzed in terms of the streamline and isotherm contours, and the yield surfaces as well as their dependence on the pertinent influencing parameters, namely, Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), and Bingham number (0 ≤ Bn ≤ 100) are delineated. Five values of aspect ratio, e = 0.2 and 0.5 (oblates) and e = 2 and 5 (prolates), and the limiting case of a sphere, i.e., e = 1, are considered here to elucidate the effect of shape on both drag and Nusselt number values. Broadly, for a given shape (value of e), drag shows the classic inverse dependence on the Reynolds number and a positive correlation with the Bingham number. Similarly, the mean Nusselt number bears a positive dependence on each of these parameters, Re, Pr, and Bn, due to the sharpening of the temperature gradient in the thin thermal boundary layer. The present drag results have been correlated via the use of a modified Reynolds number whereas the heat transfer results have been consolidated in terms of the Colburn j H factor, thereby enabling their prediction in a new application.

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Section: Results and Discussionsupporting

confidence: 81%

“…On the other hand, in the forced convection regime, shear-thinning power-law viscosity promotes the rate of heat transfer with reference to that in Newtonian fluids . Both these trends are qualitatively similar to that for a sphere in power-law fluids. − …”

Section: Introductionmentioning

confidence: 53%

Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Gupta

Chhabra

2014

Ind. Eng. Chem. Res.

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“…1 presents the comparison of the average Nusselt number of confined spherical particles at intermediate Reynolds numbers and for Pr = 7 with wall factors k = 2 and 10. The results are found to be in excellent agreement with literature values [20,21]. Therefore, based on our previous experience [4,5] and the present comparison, the results are considered to be reliable and accurate within ± 3-4 %.…”

Section: Validationsupporting

confidence: 90%

Effect of Blockage on Heat Transfer Phenomena of Spheroid Particles at Moderate Reynolds and Prandtl Numbers

Kishore

2011

Chem. Eng. Technol.

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Effects of the confining wall or blockage on the heat transfer phenomena of spheroid particles were numerically investigated. The heated spheroid particles were maintained at constant temperature and allowed to sediment in cylindrical tubes filled with Newtonian liquids. In this flow configuration, the heat transfer took place from the heated spheroid particles to the surrounding Newtonian liquid. The governing conservation equations of the mass, momentum, and energy together with appropriate boundary conditions were numerically solved using commercial software based on computational fluid dynamics. A simple correlation for the average Nusselt number of the confined spheroid particles was developed which can be applied in new applications

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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: 86%

“…Suffice it to say that the governing field equations [Eqs. (1)(2)(3)(4)(5)(6)(7)(8)] subject to the previously mentioned boundary conditions have been solved in this work using the finite volume-based commercial software ANSYS FLUENT (version 6.3.26) together with the ANSYS Workbench to mesh the computational domain. The axisymmetric, steady, laminar, and pressure-based coupled solver was used with a second order upwind scheme for discretizing the convective terms in the momentum and thermal energy equations.…”

Section: A Numerical Solution Detailsmentioning

confidence: 99%

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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Effect of Blockage on Heat Transfer from a Sphere in Power-Law Fluids

Cited by 41 publications

References 37 publications

Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

Effect of Blockage on Heat Transfer Phenomena of Spheroid Particles at Moderate Reynolds and Prandtl Numbers

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

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