Natural element method analysis for coupled radiative and conductive heat transfer in semitransparent medium with irregular geometries

• Natural element model is developed for coupled radiative–conductive heat transfer.
• Irregular geometries are considered.
• Complex optical boundary conditions are considered.
• Convective heating (cooling) and external irradiation are considered at the surface.

This paper analyzes the radiative heat transfer problem coupled with conduction in an absorbing, emitting and isotropically scattering medium with the irregular geometries using the natural element method (NEM). Two kinds of optical boundary conditions are considered: semitransparent boundary with diffuse reflection and transmission of radiation and opaque gray boundary. The boundary is kept at constant temperature or subjected to the convective heating (cooling) and irradiation of black surroundings. The NEM as a meshless method is a relative new numerical scheme in the field of computational mechanics. It has been employed to solve the radiative heat transfer recently. In this paper, we first validate the natural element solutions in dealing with the coupled heat transfer problem with the semitransparent surface considering mixed boundary conditions by comparison with those reported in the literature. Afterward, we study the steady state and transient heat transfer problems coupled with radiation and conduction in the semicircular enclosure with an inner circle. For the steady state coupled heat transfer, only one surface with convective heating and irradiation of black environment is considered semitransparent, while other surfaces are opaque and subjected to constant wall temperature. For transient coupled heat transfer, the conditions of convective heating and environment irradiation are set on two surfaces that are semitransparent and opaque, respectively. Effects of various parameters such as the conduction–radiation parameter, refractive index of the medium, extinction coefficient, scattering albedo, convective heat transfer coefficient and the temperature of the black surrounding are analyzed on the temperature distributions in the medium.