A rational estimation of volumetric thermal expansion coefficient of Al₂O₃-water nanofluid in thermo-fluid application

A practical approach to augment the heat transmission effectiveness of thermo-fluid systems involves the utilization of nanofluids instead of traditional fluids. The present investigation compares different models for determining nanofluids' volumetric thermal expansion coefficient with the experimental findings. A benchmark problem of free convection is chosen to assess the accuracy of the existing models. Numerical solutions of the benchmark problem are accomplished by applying the Galerkin finite element weighted residual method to unravel the two-dimensional Navier-Stokes and thermal energy expressions representing the computational model. The Rayleigh number alters between 10³ and 10⁹, while the nanoparticle volume fraction (ϕ) ranges from 0 to 4 %. The outcomes obtained by various models are contrasted with the experimental results in terms of the mean Nusselt number. Following extensive analysis, it becomes evident that the Khanafer and Vafai model exhibits the best resemblance with the experimental data for Al₂O₃-water nanofluid under specified conditions. However, for other types of nanofluid, the most commonly used model originating from the mixing rule demonstrates the best match to the experimental data compared to other available models.