A numerical investigation on laminar natural convection of non-Newtonian fluids in enclosed spaces

Abstract

Natural convection in enclosed spaces has several applications such as electronic cooling, thermal energy storage systems, solar collectors and heating and preservation of food to name a few. Although natural convection of Newtonian fluids (i.e. fluids like water, air where viscous stress is directly proportional to strain rate) in enclosures has been analysed extensively in the existing literature, relatively limited effort has been directed to the natural convection of non-Newtonian fluids where the strain rate dependence of shear stresses is non-linear in nature. For example, yield stress fluid is a special type of non-Newtonian fluid, which acts as a solid and does not flow until a threshold stress is surpassed. Materials such as mud-slurries in oil drilling, molten chocolate and anti-drip paints are common examples of yield stress fluids. It is possible to modulate the yield stress based on electrical/magnetic field in electro-rheological/magneto-rheological fluids. Thus, it is possible to eliminate (or alter the strength of) convection by applying a magnetic/electric field, which can be useful for mitigating accidental damage in the case of nuclear meltdown and storage of cryogenic materials. Additionally, shear-thinning (shear-thickening) fluids are another special type of non-Newtonian fluid, which show a decrease (increase) in viscosity with increasing shear rate. Many common man-made and biological fluids exhibit shear-thinning (e.g. ketchup and blood) and shear-thickening (e.g. mixtures of corn starch and water; so-called “bulletproof” custard) behaviour. These types of fluids can also be very useful for designing new adaptive thermal management systems (e.g. cooling of electronics, solar and nuclear power systems, etc.). Therefore, this thesis focuses on fundamental physical understanding and modelling of steady-state laminar natural convection of non-Newtonian fluids in enclosures using numerical simulations. A detailed parametric analysis has been carried out to analyse the effects of yield stress and the shear-thinning/thickening nature of viscosity on heat and momentum transport within the rectangular and cylindrical annular enclosures, for both Rayleigh-Bénard and differentially heated side wall configurations. The bi-viscosity Bingham model and power-law model of viscosity have been used to mimic yield stress (i.e. Bingham) and shearthinning/thickening fluids respectively. Accordingly, the steady-state laminar analyses have been performed to analyse the effects of nominal Rayleigh number Ra, Prandtl number P r, Bingham number Bn, power-law index n, normalized internal radius ri/L (where ri is the internal cylinder radius and L is the difference between outer and inner radii) and aspect ratio AR (AR = H/L where H is the enclosure height) on the mean Nusselt number, as Buckingham’s π theorem dilates Nu = f(Ra, P r, Bn, n, ri/L, AR) for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions. Detailed scaling analysis has been utilised to explain the effects of all the aforementioned parameters considered here. This scaling analysis, in turn, has been utilised to propose correlations for the mean Nusselt number and these correlations have been validated with respect to numerical findings. These mean Nusselt number correlations have significant practical importance and are likely to be useful for designing and improving thermal systems in many important industrial applications involving both Bingham and power-law fluids.