A space-fractional model of thermo-electromagnetic wave propagation in anisotropic media

A theoretical study of the propagation of electromagnetic waves through anisotropic media is presented. A Euclidean nonlinear model that couples Maxwell's and heat transfer equations is generalized considering Stillinger's formalism in terms of a spatial fractal dimension α. The numerical results reveal a significant influence of α on current density and temperature distributions along the radial direction of a cylindrical conductor. When α increases approaching unity, the anisotropy of the medium becomes increasingly weak; thus the wave penetrates deeper into the medium and the skin effect is weakened. Interestingly, the steady state temperature at any location along the radial direction reaches a maximum at α = 1/2. Beyond this maximum, the temperature decreases with increasing α, reaching a finite value at the Euclidean limit α = 1. The generalized model presented here not only simplifies the analysis of electromagnetic transmission through complex structures such as porous media but also provides a quantitative measure of the anisotropy along the radial direction of the conductive medium by a fractional dimension.