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

Sahin Yigit (School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon Tyne, UK)
Timothy Graham (School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon Tyne, UK)
Robert J Poole (School of Engineering, University of Liverpool, Liverpool, UK)
Nilanjan Chakraborty (School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon Tyne, UK)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 4 January 2016

219

Abstract

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.

Keywords

Citation

Yigit, S., Graham, T., Poole, R.J. and Chakraborty, N. (2016), "Numerical investigation of steady-state laminar natural convection of power-law fluids in square cross-sectioned cylindrical annular cavity with differentially-heated vertical walls", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 1, pp. 85-107. https://doi.org/10.1108/HFF-01-2015-0030

Publisher

:

Emerald Group Publishing Limited

Copyright © 2016, Emerald Group Publishing Limited

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