Numerical simulation of thermal convection of a viscoelastic fluid in a porous square box heated from below

Thermal convection phenomena of viscoelastic fluids in a closed-top porous square box heated from below are studied numerically based on a modified Darcy's law, where two characteristic time constants lambda and epsilon are used to describe the viscoelastic properties of the fluid. Results for three set values of lambda and epsilon are obtained for a Darcy-Rayleigh number up to 400, and show very different heat transport characteristics from those of Newtonian fluids. Two types of thermal convection are shown to be possible. Oscillatory convection due to the viscoelastic properties of the fluid precedes the onset of steady convection due to thermal boundary instability. After steady convection sets in, it tends to suppress oscillatory convection. The interaction between the two types of thermal convection causes the flow patterns in the porous layer to be more complicated than those of Newtonian fluids. Furthermore, thermal convection of viscoelastic fluids in porous layers undergoes earlier bifurcations with increase of Ra than those of Newtonian fluids and the occurrence of bifurcation is earlier for larger values of lambda/epsilon in our study. Finally, our numerical results show that scaling laws exist for thermal convection of viscoelastic fluids in porous layers, and specific scaling laws were obtained by the least-squares fitting technique to describe the Nu versus Ra relationship in different regimes of Ra and for the three cases studied in this work. (C) 2007 American Institute of Physics.MechanicsPhysics, Fluids & PlasmasSCI(E)EI0ARTICLE10null1