Abstract

Linear and weakly nonlinear stability analyses of Rayleigh-Benard convection (RBC) in a radiating Newtonian fluid are studied in the paper. The optical properties of the Newtonian fluid are considered to be independent of the wavelength of radiation. A grey medium thus assumed allows us to consider two asymptotic cases: a) optically thin fluid medium (transparent) and b) optically thick fluid medium (opaque). Using the solution of a truncated Fourier series representation we arrive at the analytical expression for the Rayleigh number and examine the thermal radiation properties. A modified Lorenz model which has in it the influence of the radiation parameters is derived. The analytically intractable three-dimensional Lorenz model is then projected into the one-dimensional Stuart-Landau equation. The analytical solution of the Stuart-Landau equation is used to quantify the heat transport. It is shown that the radiation inhibits primary instability of convection in both transparent and opaque media. However, the delay of convection is more in the opaque medium compared to that in the transparent medium. Inclusion of a transparent medium is to create a "heat-sink-like situation" whereas, the opaque medium leads to an "enhanced-thermal-diffusivity situation". Both these situations result in diminished heat transport in RBC. The analytical expression of the Hopf-Rayleigh number by linearizing the modified Lorenz model around one of its post-onset critical points provides information about the commencement of chaos in the dynamical system. The impact of radiation effect is to delay the appearance of chaos.

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