DQ Analysis of 3D Natural Convection in an Inclined Cavity Using an Velocity-Vorticity Formulation
In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331075Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1268
 H. Fasel, "Investigation of the stability of boundary layers by a finite-difference model of the Navier-Stokes equations", J. Fluid Mech., 78, 1976, 355-383.
 R. E. Bellman, B.G. Kashef, J. Casti, "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", J. Comput. Phys., 10, 1972, 40-52.
 C. Shu, Differential quadrature and its application in engineering, Springer, London, 2000.
 E. Tric, G. Labrosse, M. Betrouni, "A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions", Int. J. Heat Mass Transfer, 43 , 2000, 4043-4056.