Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.

[1]  P. Waterman,et al.  Matrix-exponential description of radiative transfer , 1981 .

[2]  Graeme L. Stephens,et al.  On the fundamental solution of the radiative transfer equation , 1988 .

[3]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[4]  James R. Wait.  Electromagnetic radiation from cylindrical structures , 1959 .

[5]  J. Grzesik,et al.  Effect of particle size in composite materials on radiative properties , 1993 .

[6]  T. W. Tong,et al.  Radiative Heat Transfer in Fibrous Insulations—Part I: Analytical Study , 1983 .

[7]  S. Lee.  Radiative transfer through a fibrous medium: Allowance for fiber orientation , 1986 .

[8]  Milton Kerker,et al.  The Scattering of Light and Other Electromagnetic Radiation ~Academic , 1969 .

[9]  G. Mie.  Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen , 1908 .

[10]  C. Tropea,et al.  Light Scattering from Small Particles , 2003 .

[11]  J. Roche,et al.  A finite difference solution of non‐linear systems of radiative–conductive heat transfer equations , 2002 .

[12]  J. Mayo Greenberg,et al.  Electromagnetic Scattering by Obliquely Oriented Cylinders , 1966 .

[13]  M. N. Özişik.  Radiative Transfer And Interactions With Conduction And Convection , 1985 .

[14]  C. Tien,et al.  Radiative Heat Transfer in Fibrous Insulations—Part II: Experimental Study , 1983 .

[15]  G. Jeandel,et al.  Model of radiative transfer in fibrous media : matrix method , 1993 .