**Preface VII**



Preface

 

 

 

 

*"A teacher can never truly teach unless he is still learning himself. A lamp can never light another lamp unless it continues to burn its own flame. The teacher who has come to the end of his subject, who has no living traffic with his knowledge but merely repeats his lessons to his students, can only*

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that de‐ scribes the flow of fluids, liquids, and gases. It has several subdisciplines, including aerody‐ namics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modeling fis‐ sion weapon detonation. In this book, we provide readers with the fundamentals of fluid flow problems. Specifically, Newtonian, non-Newtonian and nanofluids are discussed. Sev‐ eral methods exist to investigate such flow problems. This book introduces the applications of new, exact, numerical and semianalytical methods for such problems. The book also dis‐

**Chapter 1** is an introductory chapter, providing a brief discussion of fluid flow problems

**Chapter 2** is a brief description of existing viscoelastic models, starting with the classical differential and integral models, and then focusing on new models that take advantage of the enhanced properties of the Mittag–Leffler function (a generalization of the exponential function). The generalized models considered in this work are the fractional Kaye–Bern‐ stein, Kearsley, Zapas integral model and the differential generalized exponential Phan-Thien and Tanner (PTT) model. The integral model makes use of the relaxation function obtained from a step-strain applied to the fractional Maxwell model, and the differential model generalizes the familiar exponential PTT constitutive equation by substituting the ex‐

In **Chapter 3**, a magnetohydrodynamic flow of a viscous and conducting fluid confined be‐ tween two parallel differentially moving boundaries is considered. The whole system is in a strong magnetic field chosen in such a way that the Hartmann boundary layers that form in this problem become singular at the points where the magnetic field becomes tangent to the boundary. Two geometries are taken into account: plane and spherical. Within the class of such configurations the velocity field of the fluid and the influence of the conductivity of the

ponential function of the trace of the stress tensor by the Mittag–Leffler function.

cusses different models for the simulation of fluid flow.

boundaries on the fluid's motion are reviewed here.

and their application in society.

*load their minds; he cannot quicken them."*

—Rabindranath Tagore
