NATURAL CONVECTION OF POWER-LAW FLUIDS IN RECTANGULAR CROSSSECTIONAL CYLINDRICAL ANNULAR ENCLOSURES WITH DIFFERENTIALLY HEATED VERTICAL WALLS

2017 ◽  
Author(s):  
Sahin Yigit ◽  
Osman Turan ◽  
Nilanjan Chakraborty
Keyword(s):  
Natural Convection ◽  
Power Law ◽  
Power Law Fluids ◽  
Vertical Walls

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

2016 ◽  
Vol 26 (1) ◽  
pp. 85-107 ◽  
Author(s):  
Sahin Yigit ◽  
Timothy Graham ◽  
Robert J Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Power Law ◽  
Content Type ◽  
Power Law Fluids ◽  
Power Law Exponent ◽  
Vertical Walls ◽  
The Mean

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.

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