Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls

2010 ◽  
Vol 165 (15-16) ◽  
pp. 901-913 ◽  
Author(s):  
Osman Turan ◽  
Nilanjan Chakraborty ◽  
Robert J. Poole
Keyword(s):  
Natural Convection ◽  
Bingham Fluids ◽  
Square Enclosure ◽  
Side Walls ◽  
Laminar Natural Convection

scholarly journals Lattice Boltzmann Simulation of Natural Convection in an Annulus between a Hexagonal Cylinder and a Square Enclosure

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
L. El Moutaouakil ◽  
Z. Zrikem ◽  
A. Abdelbaki
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Square Enclosure ◽  
Lattice Boltzmann Simulation ◽  
Laminar Natural Convection ◽  
Heat Transfers ◽  
Boltzmann Method ◽  
Vertical Case

Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

scholarly journals Natural convection of Casson fluid in a square enclosure

2020 ◽  
Vol 16 (5) ◽  
pp. 1245-1259
Author(s):  
Mohammad Saeid Aghighi ◽  
Christel Metivier ◽  
Hamed Masoumi
Keyword(s):  
Natural Convection ◽  
Yield Stress ◽  
Casson Fluid ◽  
Small Degree ◽  
Content Type ◽  
Square Enclosure ◽  
Casson Model ◽  
Side Walls ◽  
The Mean ◽  
Viscoplastic Models

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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