This unique book provides a unified and systematic account of internal, external and unsteady slow viscous flows, including the latest advances of the last decade, some of which are due to the author. The book shows how the method of eigenfunctions, in conjunction with least squares, can be used to solve problems of low Reynolds number flows, including three-dimensional internal and unsteady flows, which until recently were considered intractable. Although the methods used are quantitative, much stress is laid on understanding the qualitative nature of these intriguing flows. A secondary purpose of the book is to explain how the complex eigenfunction method can be used to solve problems in science and engineering.Although primarily aimed at graduate students, academics and research engineers in the areas of fluid mechanics and applied mathematics, care has been taken, through the use of numerous diagrams and much discussion, to explain to the non-specialist the qualitative features of these complex flows.
Physical Background; Least Squares and Eigenfunction Expansions; The Lid Driven Container (LDC); Similarity Solutions, Streamlines and Eddies in Planar Flows; The New Embedding Method for Complex Geometries; The Singular LDC Problem and Its Resolution; Stokes Flows in Special Geometries; Planar Thermal, Mixed and Thermocapillary (Marangoni) Convection; General Features of Three-Dimensional (3D) Flows; 3D Flow in a Cylinder and in a Liquid Bridge; 3D Corner Eddies; 3D Flow in Rectangular Container; 3D Thermal Convection in a Cylinder; Eddy Structure in an Oscillating LDC; Applications to Mixing in LDCs and Viscous Attenuation; The Oseen Equations for External Flows; Flows Past Bluff Bodies and Arbitrary Streamlined Bodies.