Laminar natural convection of yield stress fluids in annular spaces between concentric cylinders

Masoumi, H.; Aghighi, Mohammad Saeid; Ammar, Amine; Nourbakhsh, Amireh

doi:10.1016/j.ijheatmasstransfer.2019.04.092

“…In recent years, developed numerical models based on the finite element method have been used for analyzing more complex flow structures and domains (Aghighi et al, 2015;Masoumi et al, 2019;Rafiei et al, 2019;Rehman et al, 2019a, b). In this study, the numerical method described in the work of Aghighi et al, 2018 has been used to solve the system of nonlinear coupled partial differential equations (Eqn (1)).…”

Section: Analysis Of Yield Stress Fluidmentioning

confidence: 99%

Natural convection of Casson fluid in a square enclosure

Aghighi

¹

,

Métivier

²

,

Masoumi

³

2020

MMMS

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PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

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“…e buoyancy effects on thermal flow characteristics of confined circular cylinder submerged laminar Poiseuille fluid are studied by Laidoudi et al [6]. Masoumi et al [7] have examined the influence of nonisothermal viscoplastic fluid flow inside the circular duck and also imposed the Galerkins Weighted Residual (GWR) scheme of FEM computation with hybrid mesh. e influence of Richardson number on flow and heat transfer topologies of an obstacle at high Reynolds number are examined by Zafar and Alam [8].…”

Section: Introductionmentioning

confidence: 99%

Topological Characteristics of Obstacles and Nonlinear Rheological Fluid Flow in Presence of Insulated Fins: A Fluid Force Reduction Study

Majeed

¹

,

Jarad

²

,

Rasheed

³

et al. 2021

Mathematical Problems in Engineering

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In this work, a comprehensive study of fluid forces and thermal analysis of two-dimensional, laminar, and incompressible complex (power law, Bingham, and Herschel–Bulkley) fluid flow over a topological cross-sectional cylinder (square, hexagon, and circle) in channel have been computationally done by using finite element technique. The characteristics of nonlinear flow for varying ranges of power law index 0.4 ≤ n ≤ 1.6 , Bingham number 0 ≤ Bn ≤ 50 , Prandtl number 0.7 ≤ Pr ≤ 10 , Reynolds number 10 ≤ Re ≤ 50 , and Grashof number 1 ≤ Gr ≤ 10 have been examined. Considerable evaluation for thermal flow field in the form of dimensionless velocity profile, isotherms, drag and lift coefficients, and average Nusselt number Nu avg is done. Also, for a range of Bn , the drag forces reduction is observed for circular and hexagonal obstacles in comparison with the square cylinder. At Bn = 0 corresponding to Newtonian fluid, maximum reduction in drag force is reported.

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“…Indeed, many experimental and numerical studies have been accomplished to analyze and determine quantitatively the rate of natural-convection heat transfer between two concentric cylinders [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Mack and Bishop [1] they performed the earlier study of natural-convection between two horizontal concentric cylinders of circular cross-sectional shape.…”

Section: Introductionmentioning

confidence: 99%

“…At the end of this paper, a correlation has been provided for Nusselt number as function of Rayleigh number and geometrical parameters which could be useful for engineering application. Masoumi et al [13] carried out a laminar natural-convection heat transfer of Bingham fluids in annular spaces of horizontal direction. The cylinders are circular cross-sectional form.…”

Section: Introductionmentioning

confidence: 99%

Natural-convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form

Laidoudi

¹

,

Helmaoui

²

,

Bouzit

³

et al. 2021

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In this paper, we performed a numerical simulation of natural convection of Newtonian fluids between two cylinders of different cross-sectional form. The inner cylinder is supposed to be hot and the outer cylinder is assumed to be cold. The diameter of inner cylinder to the diameter of outer cylinder defines the radii ratio (RR= 2.5). The governing equations describing the physical behavior of fluid flow and heat transfer are solved using finite volume method. The effects of Prandtl number (Pr = 0.71 to 100), Rayleigh number (Ra = 103 to 105) and inclination angle of inner cylinder (? = 0? to 80?) on streamlines, isotherms and dimensionless velocity are presented and discussed. Also, the mean average Nusselt number of inner cylinder is plotted versus the governing parameters. All present simulations are considered in two-dimensions for steady laminar flow regime. The obtained results showed that the flow between cylinders is more stable for the inclination angle ? = 0?. Increase in Rayleigh number increases the heat transfer rate for all values of inclination angle. Furthermore, the effect of Prandtl number on the mean average Nusselt number becomes negligible when Pr is over the value 7.01. For example at Pr = 0.71 and Ra =105, increase in inclination from 0? to 40?decreases the average Nusselt number by 5.4%. A new correlation is also provided to describe the average Nusselt number as function of Pr and Ra at ? = 0?.

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Laminar natural convection of yield stress fluids in annular spaces between concentric cylinders

Cited by 22 publications

References 19 publications

Natural convection of Casson fluid in a square enclosure

Natural convection of Casson fluid in a square enclosure

Topological Characteristics of Obstacles and Nonlinear Rheological Fluid Flow in Presence of Insulated Fins: A Fluid Force Reduction Study

Natural-convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form

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