Radiative heat transfer inside a cylindrical tube is modeled using a statistical method called the discrete probability function (DPF) method. The DPF method involves solution of the equation of radiative heat transfer using Lagrangian simulations of representative photon trajectories on a discrete spatial grid. The DPF method is different from the Markov Chain method in terms of associating a probability with each state of the photon rather than a transition from one state to another. The advantages and disadvantages of the DPF method in comparison to the Markov Chain method are demonstrated in this paper using two practical applications of the cylindrical tube radiative heat transfer problem. The cylindrical tube has a hot source at one end and a detector at the other end. The cylindrical wall absorbs and reflects (both diffusely and specularly) the radiation incident on it. The present calculations have applications in: (1) intrusive pyrometry with collimating light guides, and (2) measurement of the spectral absorption and reflection coefficients of coatings using two, coated cylindrical tubes as specimen. The results show that: (1) the effect of light guide surface properties on errors in pyrometry must be carefully assessed, and (2) the method can be used for a convenient evaluation of radiative properties of coatings.
Effects of Surface Properties on Radiative Transfer in a Cylindrical Tube With a Nonparticipating Medium
Sivathanu, Y. R., and Gore, J. P. (August 1, 1997). "Effects of Surface Properties on Radiative Transfer in a Cylindrical Tube With a Nonparticipating Medium." ASME. J. Heat Transfer. August 1997; 119(3): 495–501. https://doi.org/10.1115/1.2824123
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