An iteration method is extended to analyze the influences of the turbulent fluctuation on the reconstruction of Reynolds time-averaged temperature in turbulent axisymmetric free flames when the temperature profiles are retrieved by the low time-resolution data of outgoing emission and transmission radiation intensities. A simplified probability density function is used to simulate the turbulent fluctuation of temperature and absorption coefficient. The effects of turbulent fluctuating intensities on the estimation of the Reynolds time-averaged temperature and absorption coefficient are examined. The results show that the effects of turbulent fluctuation on the reconstruction of time-averaged absorption coefficient are not significant. In the case of weak turbulent fluctuation, the influences of turbulent fluctuation on the estimation of time-averaged temperature profiles are small. But in the case of strong turbulent fluctuation, the influences of turbulent fluctuation on the estimation of time-averaged temperature profiles are significant.

The internal distribution of radiative absorption in one-dimensional semitransparent slab exposed to collimated irradiation is determined by the ray tracing method, and the detailed computation formulae for the distribution of radiative absorption are deduced. It is found that the ray will be polarized by specular reflection of slab boundaries even if the collimated irradiation is unpolarized, and the extent of polarization increases with the internal reflection times. The effects of polarization on the radiative absorption are analyzed and the radiative absorption distributions are compared with those obtained from the case in which the effects of polarization are omitted. The results show that the large differences between re6ectances of perpendicular and parallel polarized components are the main causes resulting in errors of radiative absorption distribution. The polarization of incident beam has significant influences on the radiative absorption. Even for an unpolarized beam irradiated near Brewster's angle, omitting the effects of polarization will result in large errors, and the errors increase with the refractive index.

A Monte Carlo curved ray-tracing method is used to analyze the radiative heat transfer in one-dimensional absorbing-emitting-scattering semitransparent slab with variable spatial refractive index. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example in this paper. The predicted temperature distributions are determined by the proposed method and compared with the data in references. The results show that influences of refractive index gradient are important and the influences increase with the refractive index gradient, the temperature distribution approaches to the one obtained for a constant refractive index when the slab optical thickness is far greater than 1.0, and the effect of the scattering phase function is similar to that in the medium with constant refractive index.

The transient temperature responses in a one-dimensional semitransparent slab with variable refractive index caused by a pulse irradiation are studied. The processes of the transient coupled radiative-conductive heat transfer in the semitransparent slab are analyzed numerically. An implicit central-difference scheme is employed for handling the energy equation, while a discrete curved ray-tracing method is used to solve the radiative transfer equation. The transient temperature responses in the case of constant refractive index are compared with those in the case of variable spatial refractive index. The results show that the spatial variation of refractive index has significant influences on the transient temperature responses of semitransparent slab. Omitting the spatial variation of refractive index may result in errors of transient temperature responses within semitransparent slab to some extent. The effects of optical thickness and refractive index gradient on the transient temperature responses are significant. Increasing the slab optical thickness, the effects of refractive index gradient on the transient temperature responses increase, especially for the non-incident surface.

A radiative transfer model for a linearly or nonlinearly anisotropic scattering medium is developed by the ray tracing method. Under specular reflection, the radiative transfer coefficients of absorbing and anisotropic scattering layer with opaque boundaries are deduced. Coupled radiative and conductive heat transfer is solved. The advantage of the method is that it only needs to disperse spatial position, but not solid angle. A comparison of the present results with the previous results shows that the radiative transfer coefficients of an anisotropic scattering slab are correct. The influence of optical thickness, surface emissivity, spectrum characteristics, albedo, and boundary conditions on the transient temperature and the heat flux distribution are analyzed. According to analyzed results of linear scattering and nonlinear scattering, it is found that the ratio of two-dimensionless heat fluxes with two different scattering phase functions is a monotone function of optical thickness. It can be used as a benchmark to verify the results.