Investigation of transient coupled conduction and radiation heat transfer in the linearly anisotropic scattering cylindrical medium by spectral collocation method

In this paper, a spectral collocation method (SCM) is developed to solve transient conduction and radiation heat transfer problems in infinitely long annular cylinders with participating medium. The participating medium is an absorbing, emitting and linearly anisotropic scattering medium. To avoid the complex calculation of ray tracing, the radiative transfer equation and the transient heat conduction equation are expressed in eulerian coordinates. In the solving process, for the radiative transfer equation, both spatial and angular domains are discretized by the SCM; for the transient heat conduction equation, the spatial domain is discretized by the SCM, and the time domain is discretized by the fully implicit Euler scheme. The spatial derivative term, angular derivative term and scattering source integral term are approximated by the high order spectral collocation scheme. Compared with available data in references, the SCM can achieve very good accuracy even using few nodes. Thus, the SCM is a very effective method to achieve high order accuracy for transient coupled conduction and radiation heat transfer in an anisotropic scattering cylindrical medium. Moreover, the effects of conduction-radiation parameter, optical thickness, and wall emissivity on the transient temperature distribution and energy flow rate have also been comprehensively investigated.