Numerical simulation of Rayleigh-Bénard convection in non-Newtonian phase-change-material slurries

A two-dimensional numerical study has been conducted to obtain fluid flow and heat transfer characteristics for Rayleigh-Bénard natural convection of non-Newtonian phase-change-material (PCM) slurries in a rectangular enclosure with isothermal horizontal plates and adiabatic lateral walls. Generally, with the melting of PCM, the slurry's density draws down sharply but continuously and the slurry's specific heat capacity shows a peak value. Some PCM slurries such as microemulsions can exhibit pseudoplastic non-Newtonian fluid behavior. This paper deals with the differences in natural convection and flow patterns between Newtonian and non-Newtonian fluids with or without PCM theoretically. Due to the participation of PCM in natural convection, the dependency of Rayleigh number Ra alone cannot reflect its intensity that a modified Stefan number has to be taken into account. A correlation is generalized in the form of Nu=C ·Ra^l· Ste^-m which has a mean deviation of 10.4% in agreement with the calculated data. The numerical simulation has been performed with the following parameters: a shear thinning pseudoplastic fluid for pseudoplastic index 0.8≤n≤1.0, 6×10³ ≤Ra≤2×10⁶, Prandtl number Pr=70-288, and the aspect ratio of the rectangular enclosure from 10:1 to 20:1.