Natural Convection from a Heated Elliptic Cylinder with a Different Axis Ratio in a Square Enclosure

Raman, S. Kalyana; Prakash, K. Arul; Vengadesan, S.

doi:10.1080/10407782.2012.707058

Cited by 33 publications

(6 citation statements)

References 23 publications

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“…Bararnia et al [14] have considered the walls of the enclosure to be isothermal over the range of Rayleigh number as 10 3 ≤ Ra ≤ 10 6 ; they studied three vertical positions of the elliptic cylinder of a fixed aspect ratio of 0.312 (with longer axis normal to gravity) inside the enclosure. In contrast, Kalyana Raman et al [15] have studied numerically the laminar free convection (Ra 10 4 ; 10 5 ; 10 6 ) in air from an elliptical cylinder (aspect ratio 0.2 to 1 in blunt orientation) in a square enclosure with isothermal walls. Broadly, all these results are mutually consistent with each other.…”

Section: Introductionmentioning

confidence: 90%

“…The walls of the enclosure were all isothermal at lower temperature than the cylinder. The analogous case of the laminar free convection from a stationary elliptical cylinder in a square enclosure with air as the working fluid has also been studied by Bararnia et al [14] and Kalyana Raman et al [15]. Bararnia et al [14] have considered the walls of the enclosure to be isothermal over the range of Rayleigh number as 10 3 ≤ Ra ≤ 10 6 ; they studied three vertical positions of the elliptic cylinder of a fixed aspect ratio of 0.312 (with longer axis normal to gravity) inside the enclosure.…”

Section: Introductionmentioning

confidence: 98%

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Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Patel

Chhabra

2016

Journal of Thermophysics and Heat Transfer

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Free convection from an isothermal elliptical cylinder in Bingham plastic fluids is studied numerically. This work spans a wide range of aspect ratios of the elliptical cylinder (0.1 ≤ E ≤ 10) to delineate the effect of shape on the flowfield close to the heated cylinder. The influence of the relevant parameters, namely, Rayleigh number (10 2 ≤ Ra ≤ 10 5 ), Prandtl number (10 ≤ Pr ≤ 100), and Bingham number (0.5 ≤ Bn ≤ 10 7 ), on the momentum and heat transfer characteristics is studied in terms of the yielded/unyielded regions, streamline, isotherm contours, and local Nusselt number for an elliptical cylinder of constant surface area in blunt (E > 1) and slender orientations (E < 1). The Nusselt number shows a positive dependence on the Rayleigh number, and it correlates negatively with Bingham and Prandtl numbers. The blunt orientations (E < 1) enhance heat transfer as compared to that for a circular cylinder (of equal surface area) while slender orientations (E > 1) impede it. Using the present numerical results, predictive correlations have been established in terms of the modified Rayleigh number (Ra ) and Prandtl number (Pr ), thereby enabling the prediction of Nusselt number in a new application. Nomenclature A = surface area of the cylinder, m 2 A p = projected area of the cylinder, m 2 a = semi-axis of the elliptical cylinder along the direction of flow, m Bn = τ o 2b∕μ B V c , Bingham number b = semi-axis of the elliptical cylinder normal to the direction of flow, m C = heat capacity of fluid, J∕kg ·of the outer boundary of the domain, m E = a∕b, aspect ratio of the elliptical cylinder e y = unit vector in y-direction F = total drag force per unit length of the cylinder, N∕m F DP = pressure component of drag force per unit length of the cylinder, N∕m GrGrashof number h = local heat transfer coefficient, W∕m 2 · K k = thermal conductivity of fluid, W∕m · K M = growth rate parameter in Papanastasiou model n s = unit vector normal to the surface of cylinder Nu = local Nusselt number Nu avg = average Nusselt number Nu c = Nusselt number in the conduction limit p = pressure p s = local pressure on the surface of cylinder, Pa p ∞ = reference pressure far away from the cylinder, Pa Pr = Cμ B ∕k, Prandtl number Pr = Pr1 Bn, modified Prandtl number Ra = ρ 2 ∞ CgβT w − T ∞ 2b 3 ∕μ B k, Rayleigh number Ra = Ra∕1 Bn, modified Rayleigh number T = temperature of fluid, K T w = constant wall temperature at the surface of the cylinder, K V = velocity vector V c = characteristic fluid velocity, m∕s β = −1∕ρ∂ρ∕∂Tj P , coefficient of volumetric expansion, 1∕K γ ij = components of the rate of deformation tensor δ = growth rate parameter in Bercovier and Engelman model η = effective fluid viscosity θ = position on the surface of cylinder (measured from the front stagnation point), deg μ B = Bingham plastic viscosity, Pa · s μ y = yielding viscosity, Pa · s ξ = T − T ∞ ∕T w − T ∞ , temperature of fluid ρ = fluid density, kg∕m 3 τ = extra stress tensor τ ij = components of the extra stress tensor τ 0 = Bingham yield stress, P...

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 98%

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Patel

Chhabra

2016

Journal of Thermophysics and Heat Transfer

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“…The code developed based on the above scheme was validated for fluid flow characteristics by Sudhakar and Vengadesan [27,28]. The buoyancy driven flow was also validated in Raman et al [29]. Further in this work, fluid flow over circular cylinder (AR ¼ 1.0) is simulated at Re ¼ 20, 40, 50, 100, and 150 and the value of time averaged drag coefficient (C d_av ) is compared with values available in literature [1,7,30,31].…”

Section: Problem Definition and Validationmentioning

confidence: 97%

Effect of Axis Ratio on Fluid Flow Around an Elliptic Cylinder—A Numerical Study

Raman¹,

Prakash²,

Vengadesan

2013

Journal of Fluids Engineering

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The bluff body simulations over canonical forms like circular and square cylinders are very well studied and the correlations for bulk parameters like mean drag coefficient and Strouhal numbers for the same are reported widely. In the case of elliptic cylinder, the literature is very sparse, especially for moderate Reynolds number (Re). Hence, in this work, a detailed study about fluid flow characteristics over an elliptic cylinder placed in a free stream is performed. Simulations are carried out for different Re ranging from 50 to 500 with axis ratio (AR) varied between 0.1 to 1.0 in steps of 0.1. Immersed boundary method is used for the solid boundary condition implementation which avoids the grid generation for each AR and a single Cartesian grid is used for all the simulations. The effect of AR for various Reynolds numbers is also focused on using the in-house code. The influence of AR is phenomenal for all the Re and the values of wake length, drag coefficient, and Strouhal number decrease with decreasing AR for a particular Re. The critical ARs, for vortex shedding and wake formation, are identified for various Re. Detailed correlations for wake length, critical ARs for vortex shedding and wake formation, mean drag coefficient and Strouhal number, in terms of AR, are reported in this work.

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“…The combination of the conditions of the enclosure and the internal bodies provides various reach topics. Thus, numerous studies have dealt with the natural convection for the internal bodies in the enclosure by considering the individual condition or combined conditions such as the thermal boundary [1][2][3][4][5], the shape [3,4,[6][7][8][9], 3D effect [2,[10][11][12], the size [8,9,11,[13][14][15][16][17][18][19][20][21][22], the number of the internal bodies [23], the concentric and eccentric internal body [12,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], Rayleigh number…”

Section: Introductionmentioning

confidence: 99%

Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

Yoon¹,

Shim²

2021

Energies

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The present study investigated the natural convection for a hot circular cylinder embedded in a cold square enclosure. The numerical simulations are performed to solve a two-dimensional steady natural convection for three Rayleigh numbers of 103, 104 and 105 at a fixed Prandtl number of 0.7. This study considered the wide range of the inner cylinder positions to identify the eccentric effect of the cylinder on flow and thermal structures. The present study classifies the flow structures according to the cylinder position. Finally, the present study provides the map for the flow structures at each Rayleigh number (Ra). The Ra = 103 and 104 form the four modes of the flow structures. These modes are classified by mainly the large circulation and inner vortices. When Ra = 105, one mode that existed at Ra = 103 and 104, disappears in the map of the flow structures. The new three modes appear, resulting in total six modes of flow structures at Ra = 105. New modes at Ra = 105 are characterized by the top side secondary vortices. The corresponding isotherms are presented to explain the bifurcation of the flow structure.

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Natural Convection from a Heated Elliptic Cylinder with a Different Axis Ratio in a Square Enclosure

Cited by 33 publications

References 23 publications

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Effect of Axis Ratio on Fluid Flow Around an Elliptic Cylinder—A Numerical Study

Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

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