Finite difference solution for radiative–conductive heat transfer of a semitransparent polycarbonate layer

Abstract

Thermal radiation greatly affects the transient thermal response of translucent materials in many practical applications, such as radiative heat shields and ignition and flame spreads for translucent plastics. However, because of the complexities that transients impose, less work has been done on the transient analysis of combined radiation-conduction heat transfer than on steady-state analysis. In this study, the transient heat transfer analysis of a polycarbonate (PC) layer was done with the use of the two-flux method and implicit finite difference formulations. The radiative and conductive properties of PC available in the literature, together with computer implementation prepared on the basis of the two-flux method and implicit finite difference formulations, were used to obtain the transient thermal response of a PC layer. On the basis of these results, we show that, compared to the conduction-alone case, the PC layer responded faster when radiation effects were considered. It is also shown that the internal reflectivity of boundaries had a great effect on the thermal response of the layer, whereas the thermal conductivity had a minor influence.

Solving nonlinear heat transfer problems using variation of parameters

“…The method of variation of parameters is used to find the particular solution to Equation (15). The details of this solution are omitted here for brevity, but are provided in [29].…”

“…Equations (18) and (19) are substituted into Equation (17) which is, in turn, substituted into Equation (15). The method of variation of parameters is used to find the particular solution to Equation (15).…”

“…These problems are encountered in the analysis of combustion chambers, rocket nozzles, high-temperature heat exchangers, translucent glass or ceramic coatings, porous insulation, heat treatment of glass plates, and the drawing of optical fibers. The combined conduction-radiation problem has been solved using an integral transformation method [10,11], the finite element method [12,13], the finite difference method [14,15], the finite volume method [16,17], the lattice Boltzmann method [18e20], and finite strip theory [21].…”