Ali Arefmanesh - Assistant professor, University of Kashan
Mehdi Nikfar - MSc student, University of Kashan
Seyed Hossein Musavi - MSc student, University of Kashan

The meshless local Petrov-Galerkin method with unity as the weighting function is applied to the solution of the natural convection in a cavity with differentiallyheated wavy side walls. The simulation performed is for incompressible and laminar flow of air in the cavity based on the stream function-vorticity formulation. To implement the method, a collection of points is selected in the domain. Subsequently, a control volume isgenerated around each of the points. The governing equations are then multiplied by the weighting function and the resulting expressions are integrated over the control volumes. The weak-form of the governing equations is obtained after integration by parts. To evaluate the integrals in the weak form of the equations by the Gassian quadrature, the field variables are approximated at each Gauss point using the moving least-squares interpolation. Substituting the interpolations into the weak form of the equations yields the discretized equations for the control volume. Assembling the control volume equations and enforcing the boundary conditions yield a system of algebraic equations for the unknown nodal values of the field variables. Using the proposed method, a parametric study is undertaken and the effects of the number of undulations and the amplitude of the wavy walls on the fluid flow and heat transfer inside the cavity is investigated. The results show that the local maxima and the local minima of the Nusselt number occur close to the crests and troughs of the wall, respectively. Moreover, the average Nusselt number drops below that of a simple square cavity as the number of undulations and the amplitude increase.

meshless, Petrov-Galerkin, naturalconvection, wavy wall, cavity