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

• Published in: International journal of numerical methods for heat & fluid flow 2016-01, Vol.26 (1), p.85-107
• Main Authors: Yigit, Sahin, Graham, Timothy, Poole, Robert J, Chakraborty, Nilanjan
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Convection; Cylinders; Energy conservation; Engineering; Fluid flow; Fluids; Free convection; Heat transfer; Mathematical models; Mechanical engineering; Non-Newtonian fluids; Nusselt number; Power law; Prandtl number; Rayleigh number; Scaling; Simulation; Steady state; Temperature; Velocity; Viscosity; Walls
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-01-2015-0030

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 Nu i increases with decreasing (increasing) power-law exponent (nominal Rayleigh number) due to strengthening of thermal advection. However, Nu i is observed to be essentially independent of nominal Prandtl number. It has been demonstrated that Nu i decreases with increasing internal cylinder radius normalised by its height r i /L before asymptotically approaching the mean Nusselt number for a two-dimensional square enclosure in the limit r i /L→infinity. By contrast, the mean Nusselt number normalised by the corresponding Nusselt number for pure conductive transport (i.e. Nu i /Nu cond ) increases with increasing r i /L. Originality/value – A correlation for Nu i has been proposed based on scaling arguments, which satisfactorily captures the mean Nusselt number obtained from the steady-state axisymmetric simulations.