An Inspection of Viscosity Models for Numerical Simulation of Natural Convection of Al2O3-Water Nanofluid with Variable Properties

Background: An innovative technique to improve the heat transfer involves dispersing the nanoscale particles in a base fluid, known as nanofluid. In earlier studies, to determine the nanofluid properties, especially the effective viscosity and thermal conductivity, basic models, namely the Brinkman model and Maxwell model have been employed. Yet these models do not take into account the dependency of the viscosity and thermal conductivity on the parameters, say, the mean diameter of the nanoparticles and the temperature. Considering this, recently, some researchers have studied nanofluid with variable properties and proposed new correlations, based on the experimental and theoretical data available in the literature, for calculating the nanofluid properties. The present paper aims to study the effects of uncertainties of different viscosity models of Al2O3-water nanofluid, namely the Brinkman, Abu-Nada, Khanafer and Vafai, and Corcione models on natural convection flow and heat transfer within a differentially heated square enclosure. Employing these models, effects of volume fraction and the mean diameter of nanoparticles, as well as the Rayleigh number, on the characteristics of flow and heat transfer are examined. Methods: The finite volume method was used in order to solve the governing equations as well as the associated boundary conditions. Also, using a second-order central difference scheme, the diffusion terms in the equations were discretized, while, to approximate the convection terms, an upwind scheme was employed. In addition, the SIMPLER algorithm was adopted to solve the coupled system of governing equations. Results: At a Rayleigh number of 105, as the volume fraction of nanoparticles increased, the average Nusselt number increased for the Brinkman model and decreased for the Khanafer and Vafai model and Corcione model, whereas an increase (at high nanoparticle volume fractions) and decrease (at low nanoparticle volume fractions) was seen for the Abu-Nada model. Also, at Ra = 106, as the volume fraction of nanoparticles increased, the average Nusselt number at first decreased and then increased for both the Khanafer and Vafai model and the Corcione model, while for the Abu-Nada model, at first it increased (at low nanoparticle volume fractions), and after that, it decreased and then increased (at high nanoparticle volume fractions). Furthermore, for all volume fractions of nanoparticles and both Rayleigh numbers of Ra = 105 and 106, the Brinkman model predicted a maximum value for the average Nusselt number. As is clear in obtained results, at both Ra = 105 and 106, as the mean diameter of the nanoparticles increased, the average Nusselt number increased for the Khanafer and Vafai model and Corcione model. However, it decreased for the Brinkman model at all volume fractions of nanoparticles. Conclusion: The maximum and minimum average Nusselt number could be obtained using the Brinkman model for Ra = 105 and 106. For Ra = 105, as the volume fraction of nanoparticles increased, the average Nusselt number decreased for the Khanafer and Vafai model and Corcione model and increased for the Brinkman model, while increasing and decreasing behavior was observed for the Abu-Nada model. For Ra = 106, as the volume fraction of nanoparticles increased, the average Nusselt number increased for the Brinkman model; however, increasing and decreasing behavior was observed for the 3 other models. For both Ra = 105 and 106, the maximum absolute value of the stream function increased for the Brinkman model, whereas increasing and decreasing behavior was noticed for the 3 other models. All 4 viscosity models employed did not significantly affect the isotherm contours.