We derive the closed-form fundamental solutions (Green's functions) of a linearized two-temperature model that captures heat transfer in rarefied polyatomic gases by treating translational and internal energy modes separately. These solutions exhibit both diffusive and wave-like behavior and include exponential terms that give rise to a nonequilibrium thermal layer near heat sources—analogous to the Knudsen layer in momentum transport. Unlike classical heat conduction, this layer reflects the localized mismatch between translational and internal temperatures arising from finite-rate energy exchange. To demonstrate their utility, we apply the derived solutions within the method of fundamental solutions, a meshless boundary method, to solve benchmark two- and three-dimensional problems. Numerical results show excellent agreement with analytical solutions and kinetic theory, validating both the model and the fundamental solutions. The work offers a physically consistent and computationally efficient framework for modeling heat transfer in rarefied polyatomic gases, with direct relevance to microscale thermal systems where nonequilibrium effects are prominent.
Farkya et al. (Sun,) studied this question.