Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Book Details

• Publisher: Birkhäuser

• Author: Hamid Bellout

• Language: English

• Edition: 2014 Edition

• ISBN: 9783319008905

• Pages: 569

• Cover: Hardcover

• Release Date: 04-12-2013

• Part Number: 16 black & white illustrations, biographies

• Package Dimensions: 9.3 x 6.4 x 1.5 inches

About the Book

The Theory of Incompressible Multipolar Viscous Fluids offers an advanced and rigorous exploration of non-Newtonian fluid models, specifically the theory of multipolar viscous fluids. These fluids, unlike Newtonian fluids, incorporate nonlinear viscosity and higher-order velocity gradients, offering a more generalized approach compared to the traditional Navier-Stokes model.

This book challenges the standard Navier-Stokes framework by relaxing the constraints of the Stokes hypothesis, leading to a more comprehensive model of fluid dynamics. The theory is grounded in first principles, adhering to fundamental thermodynamical processes and the principle of material frame indifference. This makes the multipolar viscous fluid theory a more general and rigorous alternative to many existing models that rely on ad hoc assumptions regarding the stress tensor and velocity relationships.

One of the key features of this work is the formulation of higher-order boundary conditions, which result from the principle of virtual work. These conditions offer a stark contrast to artificial viscosity approaches often employed in other non-Newtonian fluid studies.

Research groups across the United States, Germany, Eastern Europe, and China have made significant contributions to this field, exploring specific geometries, solution existence, and dynamical systems related to multipolar viscous fluids. This book draws on those efforts and contributes new insights, making it an invaluable resource for mathematicians, applied mathematicians, fluid dynamicists, and mechanical engineers interested in the mathematical and practical aspects of fluid mechanics.

With its detailed treatment of multipolar viscous fluid models and their applications, this book will be a critical reference for anyone working in advanced fluid dynamics or nonlinear partial differential equations.