Meshless Local Petrov-Galerkin Method for Natural Convection in a Square Enclosure with a Wavy Fin Utilizing Nanofluids

Heat transfer in a square enclosure with a wavy fin attached to its left side wall utilizing nanofluid is investigated numerically. The heat transfer performance of the nanofluid in the enclosure is modeled by taking into account the solid particle dispersion. The continuity and the momentum equations in terms of the stream function and the vorticity formulation together with the energy equation are solved using the meshless localPetrov-Galerkin method with unity as the test function. In this method, which is quite suitable for geometrically complex domains, a distribution of points is generated in the computational domain. Subsequently, a control volume is generated around each of the points. Substituting the moving least-squares approximation of the field variables within each control volume into the weak form of the governing equations yields a system of nonlinear algebraic equations for the unknown variables at the points. Solving the system of algebraic equations yields the values of the field variables at the points. To verify the proposed numerical scheme, different test cases are solved using the code. Subsequently, the natural convection in a square enclosure with a wavy fine attached to its side wall filled with Al2O3-water nanofluid is investigated. The results show that using nanofluid enhances the natural convection heat transfer inside the cavity at low Rayleigh numbers (Ra < 104) only. For higher Rayleighnumbers, increasing the nanoparticle concentration mitigates the natural convection heat transfer in the enclosure. It is also concluded that the length and the position of the fin have different effects on the heat transfer at different Rayleigh numbers.

کلیدواژه ها:

meshless ، natural convection ، enclosure ، nanofluid ، wavy fin