This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.
Antonio Barletta, at the beginning of his academic career, pursued research on theoretical physics under a grant from the Italian National Institute of Nuclear Physics. At that time, his main research interests were quantum field theory and general relativity. He is currently a Full Professor of Technical Physics at the School of Engineering and Architecture at Alma Mater Studiorum Università di Bologna in Italy, where his research focuses on convection dynamics and heat transfer of Newtonian and non-Newtonian fluids, as well as of fluid-saturated porous media. He has published more than 170 peer-reviewed papers in international journals and he is currently an Associate Editor of the ASME Journal of Heat Transfer and of the International Journal of Applied and Computational Mathematics.
Preface.- Fourier Transform and Wavepackets.- Flow Solutions and Their Stability.- Models of Convection in Porous Media.- Rayleigh-Benard Instability, Thermal Instabilities and Dynamics of Normal Modes.- Transition from Convective to Absolute Instability.- Numerical Methods.- Bibliography.