SELF-SIMILAR SOLUTIONS OF THE NONLINEAR DIFFUSION EQUATION AND APPLICATION TO NEAR-CRITICAL FLUIDS

We use analytic self-similar solutions of both the linear and non-line ar diffusion equation to determine the behavior of a heat conducting s ystem experiencing a time-dependent energy production. Supposing a pow er law evolution of the system parameters, we calculate the correspond ing exponents to describe the temporal behavior of the system. in the non-linear case, we are able to introduce a variation of both the coef ficient of diffusion and the amplitude of the heat source. The analyti c solutions are checked numerically. These results can be considered, for example, as the basis for further developments on the non-linear b ehavior of supercritical fluids in a microgravity environment, e.g. th e ''Piston Effect'' (M. Bonetti et al., Phys. Rev. E 49 (1994) 4779) o r the ''Jet Instability'' (D. Beysens et al., Near-critical Fluids in Space, in: Lectures on Thermodynamics and Statistical Mechanics, M, Co stas et al., eds. (World Scientific, Singapore, 1994) p. 88).