Plenary Lecture

Modeling Nonlinear Flow during Alloy Solidification

Professor Daniel N. Riahi
Professor Emeritus of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign,
Professor of Mathematics at the University of Texas-Pan American, U.S.A.
Department of Mathematics, 1201 West University Drive,
University of Texas-Pan American,
Edinburg, Texas78539-2999 U.S.A.
E-mail: driahi@utpa.edu
 

Abstract: We consider the problem of nonlinear buoyant convection in horizontal mushy layers during the solidification of binary alloys. We present and validate a new model to understand such flow that can be used, in particular, for flow control purposes to reduce tendency for chimney formation within the mushy layers. The chimneys produce undesirable freckles in the final form of the solidified alloys, which are imperfections that reduce the quality of the material. Methods of control aiming at eliminating the convective flow in the chimneys also serve to eliminate the presence of chimneys thereby result in producing higher quality crystals. For the new model, no assumption is made on the thickness of the mushy layer, and a number of simplifying assumptions made in previous theoretical investigations of the problem are relaxed here in order to study the problem based on a more realistic model. Using both analytical and numerical methods, we determine the solutions for the nonlinear problem in a range of the Rayleigh number R near its critical value. We found that depending on the range of values of the parameters, bifurcation to convective flow can be either supercritical or subcritical. However, among all the computed solutions in particular range of values of the parameters that are mostly relevant to those of experiments and in contrast to all the previous studies, only particular form of the convective flow, which has been observed in the experiments, was found realizable, in the sense that its amplitude increases with R.

Brief Biography of the Speaker:
Daniel N. Riahi joined Dept of Theoretical and Applied Mechanics (TAM) of The University of Illinois at Urbana-Champaign (UIUC) in 1980 and later affiliated with Dept of Mechanical and Industrial Eng (MIE) at UIUC. He served as Full Professor at UIUC from 1995 to 2005 and as Professor Emeritus at UIUC since 2005 with the Home Dept of Mechanical Science and Eng (MechSE) after joining MIE & TAM as a combined MechSE Dept at UIUC in 2006. Professor Riahi also was appointed as Full Professor in the Dept of Math at University of Texas-Pan American since 2006. Dr. Riahi was a Cambridge Univ. (U.K.)-Visiting Scholar in 1986. Earlier than 1980, Dr. Riahi worked at UCLA, Winthrop Univ. and a three-year Post-Doctoral position at the Florida State Univ. (FSU). His academic degrees are Ph.D. in Applied Math (Fluid Mech.) from FSU in1974, M.S. in Math from FSU in 1970 and B.S. in Math from Tehran Univ. in 1966.
Dr. Riahi’s research work & interest in the last four decades include studies in convection, flow instabilities & turbulence, flow during solidification & crystal growth, and math modeling and theoretical developments with applications to eng and physical sciences. Professor Riahi received UIUC-MechSE &UIUC-TAM Service Appreciation Letters in 2006, a UIUC Service Recognition Certificate in 2006, a UIUC Honorific Title Award in 2005, a UIUC-TAM Recognition Award in 2005. He was included in a UIUC List of Teachers Rank as Excellent by their Students. He is member of over seven professional societies and a Fellow of Wessex Institute of Great Britain. He is author of Chapters in a book on Centrifugal Processing that won the Best Basic Science Book-Award by International Academy of Aeronautics in 1997. Dr. Riahi also received a UIUC-COE Research Award in 1994 and an Outstanding UIUC Service Recognition Certificate in 1987. He is author of over 310 publications mostly published in rigorously referred journals, including books, invited articles and chapters of books. Dr. Riahi’s Professional Activities include Chairman of Applied Math at Winthrop Univ. (1977-78), and UIUC Eng Mech Coordinator and Chief Advisor (1985-86). He was awarded NSF Grants and supervised NASA Sponsored Res. Projects. He also received several UIUC-RB Research Grants and NCSA Awards. He is ABI’s Research Board Advisor, Member of the Program Committee of the 4th Int. Workshop on Materials Processing in High Gravity, Member of the Int. Scientific Committees of the 5th and 6th Int. Conferences on Advances in Fluid Mechanics and Member of Int. Scientific Advisory Board of Advances in Fluid Mech. He is Editor & Editorial Board Member of over 15 Technical Journals and Book Series.

Research Accomplishment of Daniel N. Riahi:
Dr. Riahi’s research accomplishments include new theories, such as those for flow in mushy layers, shear flow over wavy walls, rough turbulence and convective flow in the presence of imperfections, uncovering new types of flow patterns for simple- or mixed-modes and multi-modal cases, and a number of discoveries in fundamental areas of convective and shear flows, some of which were already confirmed by the experimental studies. These include, in particular, flow structure during alloy solidification, roughness roles in turbulent shear flow, flow patterns in layers with finite conducting boundaries and non-monotonic dependence of the heat flux with respect to the rotation rate.

Complete Affiliation:

(a) Professor Emeritus, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, U.S.A. (http://www.mechse.uiuc.edu/)

(b) Professor, Department of Mathematics, University of Texas-Pan American, U.S.A. (http://www.math.panam.edu/driahi.html)

Mailing address: Department of Mathematics, THE UNIVERSITY OF TEXAS-PAN AMERICAN, #1201 West University Drive, Edinburg, Texas 78541-2999; Telephone: 956-316-7063 (E-mail: driahi@utpa.edu ) (http://myprofile.cos.com/riahi).