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Proceedings of CHT-15. 6th International Symposium on ADVANCES IN COMPUTATIONAL HEAT TRANSFER
May, 25-29, 2015, Rutgers University, New Brunswick, NJ, USA

DOI: 10.1615/ICHMT.2015.IntSympAdvComputHeatTransf


ISBN Print: 978-1-56700-429-8

ISSN: 2578-5486

ASPECT RATIO EFFECTS ON LAMINAR RAYLEIGH-BENARD CONVECTION OF POWER-LAW FLUIDS IN RECTANGULAR ENCLOSURES: A NUMERICAL INVESTIGATION

pages 293-311
DOI: 10.1615/ICHMT.2015.IntSympAdvComputHeatTransf.260
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ABSTRACT

The effects of aspect ratio AR (height: length) on Rayleigh-Bénard convection of inelastic non-Newtonian fluids obeying the power-law model of viscosity within rectangular enclosures have been numerically analysed. The horizontal walls are subjected to constant wall temperatures with the bottom wall at higher temperature and simulations have been undertaken for 1/4 ≤ AR≤ 4. A nominal Rayleigh number range 103 ≤ Ra ≤ 105 (Ra defined based on the enclosure height) for a single representative value of nominal Prandtl number (Pr = 103) has been considered for the current analysis. It has been found that convection weakens with increasing aspect ratio and the heat transfer takes place purely due to thermal conduction for tall enclosures (i.e. AR > 1 apart from AR= 2 for Ra > 5×104 ) for all values of Ra and n considered here. It has been demonstrated using scaling arguments that the relative contribution of advection (diffusion) to overall thermal transport weakens (strengthens) with increasing AR for a given set of values of Ra, n and Pr. Additionally, the flow pattern for AR ≤ 1 has been found to be dependent not only on Ra and n but also on the choice of initial condition used for the simulation. Although viscous resistance weakens with decreasing power-law exponent for a given set of values of Ra, AR and Pr, the mean Nusselt number Nu does not exhibit a monotonic increase with decreasing n for AR ≤ 2 because of the change in flow pattern (i.e. number of convection rolls/cells) within the enclosure. Moreover, it has been found that the flow pattern and the mean Nusselt number Nu are dependent on initial conditions and it is possible to obtain different steady-state solutions for different initial conditions. This non-uniqueness of flow and isotherm patterns is prevalent for Newtonian (i.e. n = 1) and shear-thinning (i.e. n < 1) fluids for the shallow (i.e. AR < 1) enclosures. Furthermore, it is possible to obtain a steady solution for shear-thinning (i.e. n < 1) fluids only for some initial conditions, whereas other initial conditions may yield unsteady flow patterns. The simulation results have been explained based on scaling arguments and the scaling relations have been utilised to identify different regimes of natural convection of power-law fluids accounting for aspect ratio effects.

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