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ISSN Online: 2377-424X

ISBN Print: 978-1-56700-474-8

ISBN Online: 978-1-56700-473-1

International Heat Transfer Conference 16
August, 10-15, 2018, Beijing, China

INFLUENCE OF WALL RADIATION IN 2D CAVITIES HEATED FROM BELOW

Get access (open in a dialog) DOI: 10.1615/IHTC16.cov.023541
pages 3377-3384

Аннотация

This study investigates numerically the effects of wall radiation on Benard cells in cavities heated from below using Chebyshev spectral methods. Bifurcation theory is also used to describe and analyse the cellular flow solutions obtained in a square and a rectangle cavities filled with air.
As wall radiation modifies the flow via the adiabatic vertical wall condition, the motionless and thermally stratified solution no longer exists at low Rayleigh numbers and is replaced by a very weak 2 × 2 cellular solution. This 4-cell weak flow undergoes pitchfork bifurcations at higher Rayleigh numbers: both perfect and imperfect pitchfork bifurcations are observed in the presence of wall radiation. Bifurcations to cellular flows with a reflection symmetry become imperfect because the cellular flows with the opposite rotating directions are no more equivalent. Therefore the resulting convective and radiative Nusselt numbers of the two bifurcated branches are no longer the same on the top or bottom wall. Note also that Nusselt numbers (either convective or radiative) of any bifurcated branch at one Rayleigh number are different on the bottom and top walls with wall radiation. Results obtained are analysed and some recommendations are given to describe Benard flows with wall radiation.