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hello sir
please can you help me ? what is definition of micropolar fluids? thanks.
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Micro-polar Fluid Theory
Equations of motion, constitutive equations and boundary conditions are derived for a class of fluids called micro-polar fluids. These fluids respond to the micro-rotation movements and the inertia of the rotation and therefore can withstand the stress of the couple and distributed couples of the body. The thermodynamic constraints are studied in detail and field equations for density, velocity vector and micro-rotation vector are obtained. The system is solved for a channel flow that exhibits certain interesting phenomena.
Micro-polar fluids are micro-structured fluids. They belong to a class of fluids with a non-symmetrical tensor that we will call polar fluids and include, as a special case, the well-established Navier-Stokes model of classical fluids that we will call ordinary fluids. Physically, micro-polar fluids can represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of the fluid particles is ignored. It is worth studying the model of micro-polar fluids introduced by C. A. Eringen as very balanced. First, it is a well-founded and significant generalization of the classic Navier-Stokes model, which encompasses, in theory and in applications, many more phenomena than the classic one. On the other hand, it is elegant and not too complicated, in other words, man susceptible of age for both mathematicians who study his theory and the physicists and engineers who apply it. The main objective of this book is to present the theory of micro-polar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micro-polar fluids, one in lubrication theory and the other in porous media theory, as well as several exact solutions to particular problems and a numerical method. We strive to make the presentation clear and uniform.
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