Numerical investigation of steady-state laminar natural convection of power-law fluids in square cross-sectioned cylindrical annular cavity with differentially-heated vertical walls.

Purpose – Numerical simulations have been used to analyse steady-state natural convection of non-Newtonian power-law fluids in a square cross-sectioned cylindrical annular cavity for differentially heated vertical walls for a range of different values of nominal Rayleigh number, nominal Prandtl number and power-law exponent (i.e. 103 < Ra < 106, 102 < Pr < 104 and 0.6 < n < 1.8). The paper aims to discuss these issues. Design/methodology/approach – Analysis is carried out using finite-volume based numerical simulations. Findings – Under the assumption of axisymmetry, it has been shown that the mean Nusselt number on the inner periphery Nui increases with decreasing (increasing) power-law exponent (nominal Rayleigh number) due to strengthening of thermal advection. However, Nui is observed to be essentially independent of nominal Prandtl number. It has been demonstrated that Nui decreases with increasing internal cylinder radius normalised by its height ri/L before asymptotically approaching the mean Nusselt number for a two-dimensional square enclosure in the limit ri/L→infinity. By contrast, the mean Nusselt number normalised by the corresponding Nusselt number for pure conductive transport (i.e. Nui/Nucond) increases with increasing ri/L. Originality/value – A correlation for Nui has been proposed based on scaling arguments, which satisfactorily captures the mean Nusselt number obtained from the steady-state axisymmetric simulations. [ABSTRACT FROM AUTHOR]