Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 12 December 2018
Issue publication date: 29 January 2019
Abstract
Purpose
This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition.
Design/methodology/approach
The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.
Findings
It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number
Originality value
Finally, the numerical findings have been used to propose a correlation for
Keywords
Citation
Yigit, S. and Chakraborty, N. (2019), "Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 1, pp. 251-279. https://doi.org/10.1108/HFF-03-2018-0101
Publisher
:Emerald Publishing Limited
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