Many applications that demand attenuation of heat flux through an intervening medium very commonly encounter coupled effects of conduction and radiation. The presence of participating media always introduces challenges due to geometry changes, temperature and wavelength dependant properties of the medium. The mathematical model boils down to solution of integro-differential equation subject to appropriate boundary conditions and may always not easily lend themselves to quick solutions. The current work looks at one dimensional formulation and solution of coupled conduction and radiation through insulating gray medium. The numerical solution has been implemented using two-flux (Schuster-Schwarzschild approximation) for isotropic scattering. As a simple extension to a near realistic situation, numerical solution using exponential kernel approximation for linear anisotropic scattering has also been presented. Even this simple model is quite handy as quick sizing tool and proves to be very useful in evaluating different possible options for heat flux attenuation. The paper discusses sizing for two diverse applications and systematically presents some interesting deductions. The current work demonstrates effectiveness of different fibrous insulations for assumed temperature boundary conditions for inconel honeycomb panels. Overall heat flux evaluations shows the efficacy of fibrous insulation as function of core thickness. Sizing for another diverse application of heat flux attenuation through double walled glass windows of air conditioned compartments is also presented using the linear anisotropic scattering based model. Results shows an interesting feature of heat flux reduction by more than 25 % for wall spacings greater than 5 mm with silica fibre filling in spacing. This could considerable reduce the running cost of air-conditioning units.