Author:
Aghighi Mohammad Saeid,Ammar Amine
Abstract
Purpose
The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model.
Design/methodology/approach
In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 103 < Ra < 105), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10).
Findings
Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects.
Originality/value
This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.
Subject
Computational Theory and Mathematics,Computer Science Applications,General Engineering,Software
Reference23 articles.
1. Parametric solution of the Rayleigh-Benard convection model by using the PGD application to nanofluids;International Journal of Numerical Methods for Heat & Fluid Flow,2015
2. Non-incremental transient solution of the Rayleigh-Bénard convection model by using the PGD;Journal of Non-Newtonian Fluid Mechanics,2013
3. Les tourbillons cellulaires dans une nappe liquide;Revue Generale Des Sciences Pures Et Appliquees,1900
4. Non-linear properties of thermal convection;Reports on Progress in Physics,1978
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