LAMINAR NATURAL CONVECTION OF POWER-LAW FLUIDS IN A TRAPEZOIDAL ENCLOSURE HEATED FROM THE BOTTOM

Laminar, steady-state, natural convection of power-law fluids in trapezoidal enclosures with a heated bottom wall, adiabatic top wall and cooled inclined sidewalls has been analysed based on numerical simulations for a range of different values of nominal Rayleigh numbers (i.e. 10(3) <= Ra <= 10(5)), power-law index (i.e. 0.6 <= n <= 1.8), nominal Prandtl number (i.e.. Pr = 10,10(2),10(3)) and inclination angles (i.e. 30 degrees <= phi <= 60 degrees). It has been found that the mean Nusselt number (Nu) over bar increases with increasing nominal Rayleigh number Ra and decreasing power-law index n due to the strengthening of advective transport. Moreover, an increase in the sidewall inclination angle phi leads to a decrease in (Nu) over bar due to an increase in the length of the cooled walls, leading to greater area for losing heat from the cavity. It has been found that (Nu) over bar does not vary significantly with the values of Pr considered in the current study. Furthermore, an expression for the mean Nusselt number (Nu) over bar in a trapezoidal enclosure with heated bottom wall, cooled inclined sidewalls, and an adiabatic top wall accounting for the considered range of Ra, n, Pr and phi has been identified which provides adequate approximation of the corresponding values obtained from the simulations.