Combined Conductive and Radiative Heat Transfer in an Absorbing and Scattering Infinite Slab

Simultaneous radiation and conduction heat transfer results are presented for an absorbing and isotropically scattering medium having negligible emission. The radiatively participating medium is assumed to be one-dimensional and bounded by an opaque substrate and by a semi-transparent top interface. The boundary interfaces are assumed to reflect and transmit radiation in accordance with Fresnel’s equations and Snell’s law, respectively. A diffuse radiative flux, along with a conductive flux, is assumed incident upon the participating medium at the top interface. The Chandrasekhar solution to the transport equation is employed, then the solution of the governing energy equation is formulated for the radiatively participating medium. Heat transfer to the substrate is presented as a function of the governing parameters: albedo, optical thickness, and substrate and medium refractive indices. Finally, dimensionless temperature profiles are shown. Solutions for a convective boundary condition are also derived.