A NUMERICAL STUDY OF THE ONSET OF CELLULAR BENARD CONVECTION IN SHEAR RATE DEPENDENT NON NEWTONIAN FLUIDS IN POROUS MEDIA - NON-DARCIAN EFFECTS

摘要

A numerical method based on the finite element method is applied to the study of onset of Benard convection in porous media. The flow is described using the so-called Darcy Brinkman model, which has close resemblance to the Navier-Stokes equations. Itis found that for Darcy numbers less than 0.0001 the results are indistinguishable from regular Darcy flows. The non-Newtonain nature of the fluid is described by the so-called power law model, of which Newtonian fluid is a special case. Numerical results are presented for n varying from 0.4 to 1.5. The critical value of Rayleigh number for onset of convection for Newtonian fluids is found to be 40 which is close to the theoretical value of 4π~2; boundary conditions on the horizontal walls have little effect in the sense that whether it is a slip or free (no shear condition) the results appear to be the same for onset of cellular motion. It is also found that the value of critical Rayleigh number increases with power law index.