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DOI: 10.1615/ICHMT.2014.IntSympConvHeatMassTransf.280
pages 387-401

Sahin Yigit
School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon-Tyne, United Kingdom

Robert J. Poole
School of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK

Nilanjan Chakraborty
School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon-Tyne, NE17RU, United Kingdom


In this analysis the effects of aspect ratio AR (height: length) on natural convection of yield stress fluids obeying the Bingham model within rectangular enclosures has been investigated for 1/ 4 ≤ AR ≤ 4 . A nominal Rayleigh number range 103Ra ≤ 105 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) in a configuration with differentially heated horizontal walls subjected to constant wall temperatures with heated bottom wall has been studied. It has been found that the convective transport strengthens with increasing nominal Rayleigh number Ra for both Newtonian and Bingham fluids but the mean Nusselt number Nu for Bingham fluids remains smaller than the value obtained for Newtonian fluids for a given set of values of Ra and Pr due to augmented viscous resistance arising from yield stress in Bingham fluids. For Bingham fluids Nu decreases with increasing Bingham number Bn (non-dimensional yield stress) and thermal transport becomes principally conductiondriven for large values of Bn. The relative contribution of convection to the overall thermal transport diminishes (strengthens) with increasing (decreasing) AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids. Thus, the thermal transport takes place principally due to conduction for tall enclosures. A detailed scaling analysis has been carried out to explain the effects of AR. This scaling analysis, in turn, has been utilised here to propose a correlation, which has been demonstrated to predict Nu obtained from simulation data for 1/4 ≤ AR ≤ 4, 103Ra ≤ 105 and Pr = 500.

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