Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Abstract

Purpose This paper aims to develop a numerical model to investigate coupled conduction radiation heat transfer in a multilayer semi-transparent polymeric foam. Design/methodology/approach The model uses a multi-phase approach in which the radiative transfer is determined by solving the radiative transfer equation explicitly in the whole medium incorporating an interface condition valid in the geometric optics rgime. This is executed by using a combination of ray splitting and a discrete curved ray tracing technique. Both partial photon reflection and total internal reflection at the interface are considered in the present investigation. Findings The directional distribution of intensity within the whole medium can be determined, which is used to obtain the detailed temperature profile inside the domain. The performance of the proposed methodology has been tested by simulating the modelled foam at ambient conditions. The results obtained from the simulations are in good agreement with the published results and shows that there is a global non-linearity in the temperature profile in problems where conduction to radiation parameter is small. Originality/value Specular nature of radiative transfer at the interface is accounted for in the present analysis. Instead of working with direction integrated quantities (as in the case of P1 approximation), each bundle of rays is treated separately within the whole medium. This model serves as a starting point for a detailed spatially three dimensional study of heat transfer in foams and the mathematical nature of the formulation is such that it may result in an implementation to three-dimensions.