Numerical investigation of laminar Rayleigh-Bénard convection of Bingham fluids in square cross-sectioned cylindrical enclosures

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  2. Sahin Yigit
  3. Professor Nilanjan Chakraborty
Author(s)Yigit S, Chen SQ, Quinn P, Chakraborty N
Publication type Article
JournalInternational Journal of Thermal Sciences
ISSN (print)1290-0729
ISSN (electronic)1778-4166
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Numerical simulations have been conducted under the assumption of axisymmetry to analyse steadystate laminar natural convection of yield stress fluids obeying Bingham model in square cross sectioned cylindrical annular enclosures heated from below (i.e. Rayleigh-Benard configuration). The simulations have been carried out for a representative value of nominal Prandtl number (i.e. Pr = 500) for different internal cylinder radius (0 <= r(i)/L <= 16 where r and L are the inner radius and the cylinder height respectively) for a nominal Rayleigh number range 10(3)<= Ra <= 10(5). Both constant wall temperature and constant wall heat flux boundary conditions have been imposed for differentially heated horizontal walls to analyse the effects of wall boundary condition. Although the buoyancy-driven transport strengthens with increasing Ra, the mean Nusselt number (Nu) over bar (cy) does not show a monotonic increase with increasing Ra for small values of r(i)/L because of the change in flow pattern (i.e. number of convection rolls/cells). By contrast, (Nu) over bar (cy) monotonically increases with increasing Rd, and only one cell flow pattern is obtained for large values of r(i)/L Furthermore, (Nu) over bar (cy) has been found to increase with increasing rilL but asymptotically approaches the corresponding value obtained for square enclosures (r(i)->infinity) for both CWT and CWHF boundary conditions for large values of rig. It has also been found that both the flow pattern and the mean Nusselt number (Nu) over bar (cy) are dependent on the initial conditions for Bingham fluid cases since hysteresis is evident for small values of r(i)/L. for both CWT and CWHF boundary conditions. It has been found that convection could be sustained up to a higher value of Bingham number due to stronger convection arising from higher temperature difference between horizontal walls in the case of CWT boundary condition than in the corresponding CWHF configuration. Finally, the numerical findings have been used to propose a correlation for (Nu) over bar (cy) in the range of 2 <= r(i)/L <= 16 (0.25 <= r(i)/L <= 16) and 10(3)<= Ra <= 10(5) for the CWT (CWHF) boundary condition. (C) 2016 Elsevier Masson SAS. All rights reserved.
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