Evaluation of non-Newtonian model to accurately predict high Rayleigh number natural convection characteristics using PIV experiment and CFD simulation

Non-Newtonian fluids exhibit variable viscosity particularly at relatively high Rayleigh numbers (Ra), resulting in the occurrence of a complex natural convection phenomenon. In this study, the flow and heat-transfer performances inside a square channel filled with carboxy methyl cellulose, which exhibits the shear-thinning behavior typical of non-Newtonian fluids, were investigated. A comparative study was conducted to develop a viscosity model that can accurately describe the thermal and flow performances. To achieve this objective, three different viscosity models were considered: Power-law, Cross, and Carreau models. A time-constant dependency study was conducted to determine the optimum time step since the numerical solution was highly sensitive to the selected time constant in the Carreau and Cross models. The heat-transfer performances were evaluated by analyzing the mean Nusselt number for the hot wall, whereas the flow performances were evaluated by analyzing the flow patterns obtained by numerical and experimental analyses using the nonintrusive particle image velocimetry technique (Ra = 3.20 × 10⁵, 3.09 × 10⁶, and 2.21 × 10⁷). The mean Nusselt numbers obtained by numerical analysis using the Carreau model were approximately 1.76%, 1.23%, and 0.45% higher than those obtained experimentally. Therefore, the predictions afforded by the Carreau model were in excellent agreement with those obtained experimentally. The findings of the present experimental study will provide benchmarking data for future simulations involving shear thinning or pseudoplastic non-Newtonian fluid media.