Significance of non-Oberbeck-Boussinesq effects augmented by power-law rheology in natural convection studies around fins

Abstract

The augmentation and diminution of non-Oberbeck-Boussinesq (NOB) effects due to power-law rheology cause significant changes in the results and associated implications of natural convection studies. This study focuses on the combined effect of spatial arrangement with NOB and power-law effects. Non-intuitive changes in heat transfer trends are caused by the additional effect on the shear rate distribution due to spatial arrangement of objects, represented here by an array of fins. An order of magnitude analysis was used to derive Oberbeck-Boussinesq type equations for a class of power-law fluids with all properties considered as linear functions of temperature and pressure. Significant temperature dependent properties were identified, and an explicit criterion to neglect viscous dissipation for power-law fluids in pure natural convection was derived. The identified temperature dependencies were incorporated into NOB equations and solved numerically to investigate their effect on flow field and heat transfer trends. Shear thinning significantly augmented (more than doubled) the accelerating NOB effect, while shear thickening diminished (nearly halved) it. The tendency of power-law rheology to augment or diminish NOB effects was demonstrated to considerably increase the sensitivity of results to temperature dependent properties, over and above that for the Newtonian case. Investigations to note their practical implications revealed that optimization results without NOB effects could be quite misleading for the fin array problem, due to the differing cumulative extents of augmentation. Additionally, correlation studies may be inaccurate as the nature of trends was changed fundamentally due to NOB augmentation.