DRBEM Solution of the Double Diffusive Mixed Convection in a Lid-Driven Square Cavity with a Square Blockage Placed at the Bottom Wall

Akgün N.

World Congrees on Engineering 2012, Londra, United Kingdom, 4 - 06 July 2012, pp.252-257, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • City: Londra
  • Country: United Kingdom
  • Page Numbers: pp.252-257
  • Van Yüzüncü Yıl University Affiliated: No

Abstract

Abstract: In this paper, the dual reciprocity boundary element method (DRBEM) is applied to solve the two-dimensional double diffusive mixed convection in a lid-driven square cavity with a square blockage placed at the bottom wall. Stream function-vorticity-temperature-concentration variables are used, and vorticity transport, energy and concentration equations are transformed to modified Helmholtz equations by utilizing forward difference with relaxation parameters for the time derivatives. The resulting modified Helmholtz equations are solved by DRBEM using the fundamental solution (1/2π)K0(x) whereas in the stream function Poisson's equation (1/2π)ln(x) is made use of. This procedure eliminates the need of another time integration scheme in vorticity transport, energy and concentration equations, and has the advantage of using large time increments. The inhomogeneities are approximated by using coordinate functions f=1+r and f=r2ln(r) in the stream function and vorticity-energy-concentration equations, respectively. Unknown vorticity boundary conditions are also obtained with the help of coordinate matrix F. The solutions are obtained for different values of Reynolds number, Richardson number and buoyancy ratio by using constant boundary elements. The solution reaches to steady-state with considerably large time increments and suitable values of relaxation parameters which occur in the argument of Bessel function K0(x).