Abstract:

The lecture presents the physical basis and the mathematical approach to solve nonlinear diffusion of heat and mass in new materials exhibition nonlinear transport properties by integral-0balance technique. The special cases discussed are: 1) Transient nonlinear heat (mass) diffusion equation with power-law nonlinearity of the thermal (mass) diffusivity; 2) Transient heat conduction with linearly temperature-dependent thermal diffusivity; 3) Transient diffusion with exponentially dependent on the concentration diffusivity emerging in polymers and concretes. 4) Thermal grooving of metals; 5; Heat radiation diffusion models, etc. The integral-balance method leads to closed form solutions based on the single and double-integration technique and a new approach to the nonlinear spatial derivative avoiding the commonly used linearization by the Kirchhoff transformation.

Jordan Hristov is a professor of Chemical Engineering at the University of Chemical Technology and Metallurgy, Sofia, Bulgaria. He was graduated in 1979 as Electrical Engineer (MS equivalent) at the Technical University, Sofia, Bulgaria. His PhD thesis on the magnetically assisted fluidization was awarded by the University of Chemical Technology and Metallurgy in 1995. Prof. Hristov’s research interests cover the areas of particulate solids mechanics, fluidisation, heat and mass transfer with special emphasis on scaling and approximate solutions of nonlinear problems. Relevant information is available at http://hristov.com/jordan