A formal averaging procedure for radiation heat transfer in particulate media

Radiative heat transfer in participating particulate media is modeled using a formal volume averaging procedure. The multiphase medium is composed of emitting–absorbing–scattering phases, i.e., a gas phase and several particle phases. Each particle phase contains large, opaque, gray, diffuse, and spherical particles having locally the same geometrical, thermophysical, and radiative properties. The resulting multiphase radiative transfer equation (MRTE) is solved using the discrete ordinates method. The present computed results are found to be in good agreement with those obtained using the Monte-Carlo theory and with the available experimental results. The coupling effect of the MRTE with the averaged energy equations in a three-dimensional cavity which is differentially heated or which contains a volumetric heat source is studied. A parametric study is performed for particle-phase and gas properties, and wall emissivity.