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In this study, a numerical investigation on mixed convection inside a trapezoidal cavity with a pair of rotating cylinders has been conducted. Three different power-law fluid indexes (n = 1.4, 1.0, and 0.6) have been considered to model different sets of non-Newtonian fluids. Four separate cases are considered based on the rotational orientation of the cylinders within the cavity. In the first two cases, the cylinders rotate in the same direction, i.e., both counterclockwise (CCW), and both clockwise (CW), whereas, in the other two cases, cylinders rotate in opposite directions (CW-CCW and CCW-CW). Simulations have been carried out over a broad range of Reynolds number (from 0.5 to 500) and angular speeds (a dimensionless value from 0 to 10). The average Nusselt number values at the isothermal hot inclined cavity surface are determined to evaluate heat transfer performance in various circumstances. Streamlines and isotherm contours are also plotted for a better understanding of the effects of different cases for various parameters on thermal and fluid flow fields. It is found that the Nusselt number varies nonlinearly with different angular speeds of the cylinders. The combined effect of the mixing induced by cylinder rotation and viscosity characteristics of the fluid dictates the heat transfer in the system. Predictions from the numerical investigation provide insights into the sets of key parametric configurations that have a dominant influence on the thermal performance of the lid-driven cavity with double rotating cylinders. [ABSTRACT FROM AUTHOR]

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n > 1) than the other fluids (n ⩽ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature. [ABSTRACT FROM AUTHOR]

• A comprehensive and detailed solution of double-diffusive natural convection of Casson fluids in an enclosure is obtained. • The influence of the governing parameters on fluid flow, morphology of yielded/unyielded regions, and heat and mass transfer are thoroughly examined. • The unyielded regions grow with decreasing buoyancy ratio and increasing the yield number. • The Lewis number has different effects on unyielded areas depending on the flow parameters. • Correlations for average Nusselt and Sherwood numbers are provided. This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra , yield number, Y , buoyancy ratio number, Nr , and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined. The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%. [Display omitted] [ABSTRACT FROM AUTHOR]