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This Book is intended to generate mathematical formulation using nonlinear partial differential equations that reflect the physics of flow dynamics, in order to investigate how molecules, move in micropolar and nanofluids when subjected to various constraints. These fluids demonstrate the effects of local rotary inertia and thermal conductivity that make appropriate non-Newtonian fluid models. The models developed in this work, in fact, take into account the Brownian motion and thermophoretic effects that replicate how nanoparticles move through the molecules of a base fluid and occasionally...