Numerical Study of Natural Convection for Generalized Second-Grade Fluids Confined in a Square Cavity Subjected to Horizontal Heat Flux

Abstract

Two-dimensional steady laminar natural convection of a viscoelastic fluid represented by generalized second-grade fluid model in a square enclosure is studied. The cavity is submitted at its vertical sides to a uniform density of heat flux while the horizontal walls are insulated, without slipping conditions at all the solid boundaries. The governing conservation and constitutive equations with the corresponding boundary conditions are solved by finite volume method in a collocated grid system. The contributions of shear rate dependent and elastic characteristics of the viscoelastic fluid are investigated on momentum and heat transport. The effects of elastic number (E) in the range 0 - 1 on heat transfer and fluid motion are interpreted for a power-law index (n) in the range 1.4 - 0.6 and nominal values of Rayleigh number (Ra) range of 103 to 105.

Finite Volume Simulation of Natural Convection for Power-Law Fluids with Temperature-Dependent Viscosity in a Square Cavity with a Localized Heat Source

“…One of the characteristics of this heat transfer problem is that, different shapes of flows may take place within the cavity depending on different imposed thermal conditions, which may be presented by either Newmann (imposed heat flux) or Dirichlet (imposed temperature difference) types at the vertical or horizontal walls. Many studies concerning the differentially heated vertical walls case have been investigated for both Newtonian [1,2] and non-Newtonian fluids [3][4][5][6][7][8][9][10][11], where the momentum and thermal transports initiate inside the enclosure once a finite temperature difference is occurred between the side walls. When the lower wall of the enclosure is maintained at a higher temperature than the top wall while the sidewalls are adiabatic, the classical Rayleigh-Bé nard convection is observed within the cavity which starts only when a critical Rayleigh number is exceeded.…”