Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

Abstract

In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or Al 2 O 3 -water mixture with nanoparticle volume fractions range of 0 ≤ φ ≤ 0.2. A system of continuity, momentum, and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids. Partial derivatives in the governing equations were approximated using the RBF method. The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations. The main goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions. To assess the accuracy of the proposed method, several test cases of natural convection in square and triangular cavities were selected. For Rayleigh numbers ranging from 10 3 to 10 5 , a validation test of natural convection of Cu-water in a square cavity was used. The numerical investigation was then extended to Rayleigh number 10 6 , as well as Al 2 O 3 -water nanofluid with a volume fraction range of 0 ≤ φ ≤ 0.2. In a second investigation, the same nanofluids were used in a triangular cavity with varying volume fractions to test the proposed meshless approach on non-rectangular geometries. The numerical results appear to be in agreement with those from earlier investigations. Furthermore, the suggested meshless method was found to be stable and accurate, demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries. KEYWORDSNatural heat convection; nanofluids; cavities; meshless method; radial basis function Abbreviations N Number of nodes Cp Specific heat, J/kg/K g Acceleration due to gravity, m/s 2 k Thermal conductivity, W /mK Nu Nusselt number Pr Prandtl number

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