Prof. Peter Guba
Department of Applied Mathematics and Statistics, Comenius University
Wednesday, November 15, 2017, 15:30 - 16:30
Building 101, Lecture Room C
Wednesday, November 15, 2017, 13:30 - 14:30
Host: Dan Anderson
Abstract: During the solidification of multicomponent alloys, the regions referred to as mushy layers commonly form. A mushy layer is a porous region of solid and liquid phases in thermodynamic equilibrium, forming between the completely solid and completely liquid regions of a solidifying system composed of two or more components. Such layers are significant in a number of industrial and environmental contexts, including alloy castings in metallurgy, semiconductor industry and large-scale environmental settings. In this talk, we present an account of the development of mathematical models for binary and ternary mushy layers, with an emphasis on the intrinsic interactions between solidification, and both diffusive and convective transport of heat and solutes. Such models provide a number of analytically tractable bifurcation problems, allowing for a theoretical understanding of these coupled transport processes. We discuss particular physical effects that lead to novel types of convective behaviour, distinguishing the binary and ternary mushy layer systems from the classical single-diffusive and double-diffusive non-reactive porous medium systems respectively. We discuss the results from these models and compare the predictions with the available experimental observations.
Bio: Peter Guba studied Mathematics and Physics at the Comenius University (Bratislava, Slovakia) and gained a PhD in Geophysics. He was a Royal Society Research Fellow at the University of Cambridge (United Kingdom) and a Research Fellow at the University of Nottingham (United Kingdom), before finally returning to the Comenius University in 2007, where he is an Associate Professor of Applied Mathematics. Within the Department of Applied Mathematics and Statistics, his research encompasses applied and computational mathematics to model and understand fluid dynamics phenomena in nature and engineering.