ADI Method for Solving Convective Flow in a Square Cavity: Review of Different Empirical Models

Abstract

The growing adoption of nanofluids in research and industry highlights their improved efficiency over simple fluids. In numerical and theoretical analyses, researchers often encounter confusion when selecting formulas for calculating the thermophysical properties of nanofluids, such as conductivity and viscosity. This article reviews various theoretical models for water-based nanofluids and compares experimental correlations for the thermophysical properties of the widely used Al 2 O 3 /water nanofluid. The goal is to help researchers choose the most suitable formulas for these calculations. A comparative analysis of different theoretical models for nanofluid viscosity and conductivity is presented. These models were also tested through numerical simulations of natural convection in a square cavity filled with nanofluid, using the ADI method. We note that experimental correlations are often condition-specific, whereas theoretical formulas offer broader applicability. Our findings indicate that choosing formulas arbitrarily can lead to significant discrepancies—up to 64% for conductivity and 75% for viscosity—highlighting the importance of careful selection. Additionally, the impact on heat transfer calculations can be substantial, with differences reaching 45% in numerical results.