Laminar Natural Convection of Power-Law Fluids in a Square Enclosure With Differentially Heated Sidewalls Subjected to Constant Wall Heat Flux

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Osman Turan ◽  
Anuj Sachdeva ◽  
Robert J. Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Power Law ◽  
Newtonian Fluids ◽  
Wall Heat Flux ◽  
Power Law Fluids ◽  
Constant Wall Heat Flux ◽  
Laminar Natural Convection ◽  
The Mean

Two-dimensional steady-state laminar natural convection of inelastic power-law non-Newtonian fluids in square enclosures with differentially heated sidewalls subjected to constant wall heat flux (CHWF) are studied numerically. To complement the simulations, a scaling analysis is also performed to elucidate the anticipated effects of Rayleigh number (Ra), Prandtl number (Pr) and power-law index (n) on the Nusselt number. The effects of n in the range 0.6 ≤ n ≤ 1.8 on heat and momentum transport are investigated for nominal values Ra in the range 103–106 and a Pr range of 10–105. In addition the results are compared with the constant wall temperature (CWT) configuration. It is found that the mean Nusselt number Nu¯ increases with increasing values of Ra for both Newtonian and power-law fluids in both configurations. However, the Nu¯ values for the vertical walls subjected to CWHF are smaller than the corresponding values in the same configuration with CWT (for identical values of nominal Ra, Pr and n). The Nu¯ values obtained for power-law fluids with n<1 (n>1) are greater (smaller) than that obtained in the case of Newtonian fluids with the same nominal value of Ra due to strengthening (weakening) of convective transport. With increasing shear-thickening (i.e., n > 1) the mean Nusselt number Nu¯ settles to unity (Nu¯=1.0) as heat transfer takes place principally due to thermal conduction. The effects of Pr are shown to be essentially negligible in the range 10–105. New correlations are proposed for the mean Nusselt number Nu¯ for both Newtonian and power-law fluids.

Laminar Natural Convection Between a Vertical Surface With Uniform Heat Flux and Pseudoplastic and Dilatant Fluids

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Massimo Capobianchi ◽  
A. Aziz
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Shear Rate ◽  
Power Law ◽  
Average Nusselt Number ◽  
Vertical Surface ◽  
Flux Boundary Condition ◽  
Shear Rates ◽  
Laminar Natural Convection

This paper reports the average Nusselt number for steady, laminar natural convection between a vertical surface and otherwise quiescent pseudoplastic and dilatant fluids under a constant and uniform surface heat flux boundary condition. Models for the fluids' apparent viscosity were utilized that are valid in all five regions of the flow curve. The results are thus applicable for whatever shear rates may exist within the flow field and a dimensionless shear rate parameter was identified that quantifies the shear rate region where the given system is operating. The data indicate that the average Nusselt numbers approach the corresponding Newtonian values when the shear rates are predominantly in either the zero or the infinite shear rate Newtonian regions. However, power law values are approached only when both of the following two conditions are met: (1) the shear rates are principally in the power law region and (2) the fluid's limiting zero and infinite shear rate Newtonian viscosities differ sufficiently, by approximately 4 orders of magnitude or more. For all other cases, the average Nusselt number was found to reside between the Newtonian and the power law asymptotes. Results are provided in both graphical and tabular form over a broad range of system parameters.

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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