Correlations of mixed convection in a double lid-driven shallow rectangular cavity: The case of non-Newtonian power-law fluids

Abstract

This work provides an analytical and numerical assessment, complete with correlations, of mixed convection in a double lid-driven shallow rectangular enclosure, which confines non-Newtonian fluids of the Ostwald–de Waele type and which a uniform thermal flux heats. The finite volume method with the SIMPLER algorithm is the numerical method used to solve the governing partial differential equations along with the boundary conditions, where the parallel flow concept is the analytical approach. In the limits of the explored values of the governing parameters of this study, which are the Rayleigh number, the Peclet number, and the behavior index, the results obtained by these approaches appear to be in good harmony. On the basis of the results obtained by these approaches, we established helpful correlating relations between the governing parameters to realize the contribution of mixed convection to heat transfer. This leads to the finding that the ratio Ra/Pe²⁺ⁿ is the mixed convection parameter, which is the key to distinguishing the three convective flow modes. On the basis of this parameter, which allows the transition from one regime to another, it is possible to identify the zones that designate the predominance of natural, forced, and mixed convection. The limits of these latter depend on the behavior index, n, which is diversified from 0.6 to 1.4 to account for shear thinning (0 < n < 1, low apparent viscosity, high fluid flow, and high heat transfer rate), Newtonian (n = 1), and shear thickening (n > 1, high apparent viscosity, slow fluid flow, and low heat transfer rate) fluids. On the other hand, the study presents and interprets the influences of the steering factors on heat transfer and fluid flow.