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SPECIALIZED SCHOOL - LECTURE

APPROXIMATE SOLUTIONS TO NONLINEAR HEAT AND MASS DIFFUSION EQUATIONS:

Application of improved integral-balance approach

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. 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.

Keywords: nonlinear heat conduction, nonlinear diffusion, temperature-dependent thermal diffusivity, concentration-dependent diffusion coefficient, approximate solutions 

Biography: Professor Jordan Yankov Hristov was born in Dupnitza town on 7th September 1954. He has graduated from Electrical Engineering (Measurements), Technical University- Sofia in 1979. He is working at the Department of Chemical Engineering, University of Chemical Technology and Metallurgy from Sofia. Starting from a position of a technician, even though he was a graduated engineer, he was promoted in the next 3 years to a research fellow. He has obtained his Ph. D degree in 1994 in Chemical Engineering. He was promoted in 1998 to the associate professor position and in January 2014 as a professor of Chemical Engineering. The main research area developed more than 30 years was the fluidization, especially, external field effects (magnetic or electric) for controlling the bed hydrodynamics and consequently the performed heat and mass transfer operations. Professor Hristov supervised 6 PhD theses and more than 25 M.Sc. theses. He obtained a NATO fellowship at the Center for Studies on Risk Technologies (CERTEC), University Politecnica de Catalunya, Barcelona. He published more than 135 papers and he obtained more than 700 citations. Since 2009, Professor Jordan Yankov Hristov is the Editor-in Chief of the International Review of Chemical Engineering-Rapid Communications and since 2012 he become the Editor in Chief of the International Journal on Advanced Materials and Technologies.