KEYWORDS: Radiation interaction; Convective Nusselt number; Radiative Nusselt number; Stability analysis; Finite volume method; spectral collocation method; Gray and non-gray participating gas mixtures.

The present thesis provides numerical investigation of radiation interaction with conduction and/or natural convection heat transfer in the presence of gray and non-gray participating media. Such heat transfer interactions are seen in solar collectors, furnaces, combustion systems etc. The governing equations of mass,
momentum and energy are solved by the finite volume method. The radiative source term in the energy equation is governed by the radiative transfer equation which is solved by the finite volume based discrete ordinates method and/or the traditional discrete ordinates method. The radiation intensity depends on frequency, spatial
distance, direction of travel, and on time for unsteady problems. These factors increase the complexity of total energy transfer calculations in the domain.
A mixture of carbon dioxide, water vapor, nitrogen is considered in the present study which is radiatively active. The radiation intensity passing through such a medium possesses non-gray emission and absorption characteristics i.e. emission and absorption
depend on wavelength. The absorption coefficient which is the fundamental quantity in the radiative transfer equation is modeled by the methods of weighted sum of gray gases and spectral line weighted sum of gray gases as well as equivalent gray approximations available in literature.
Rigorous numerical study has been carried out to shed a light on (i)
conduction-radiation interaction (ii) convection-radiation interaction (iii) onset of Rayleigh-Benard convective instability with radiation interaction happening with conduction in a gray and non-gray participating medium. Initial studies on pure radiation and conduction-radiation heat transfer are reported first, in which the effects of various parameters such as wall emissivity, gas composition and conduction to radiation parameter are systematically studied. On
observing the results carefully, it is found that the non-gray gas models, such as weighted sum of gray gases/spectral line weighted sum of gray gases, can be represented fairly accurately by an equivalent temperature dependent gray absorption
coefficient model. This model is tested on various operating cases and a good agreement is found with the results of weighted sum of gray gases and spectral line weighted sum of gray gas models. The same model is extended to study natural convection and radiation heat transfer in a differentially heated square cavity of CO2,
H2O, and N2 mixture, in varying proportions. The radiation and flow parameters influence the temperature and velocity distributions in the cavity. In turn, the convective and radiative heat transfer rates in the system are modified. Finally, the study has been extended to analyze the onset of convective instability in the presence of gray and non-gray participating media, using linear stability theory in conjunction
with spectral collocation method. Radiation phenomena are strongly affected by the operating temperature of the medium. Hence, the onset of convective instability is marked by critical parameter values (Rayleigh number and wavenumber) which are substantially changed due to change in the temperature gradient at the walls. The study
has been conducted for individual and mixture of gases in varying proportions. The sensitivity of critical Rayleigh number (Rac) and wavenumber (kc) to flow and radiation parameters has been addressed in detail. The study is focused on gray and
non-gray behavior of radiatively active gases and gas mixtures. Also, the physics associated with the conduction, convection and radiation heat transfer interactions in radiatively participating gases, is brought out.