Some Flow Problems in Differential Type Fluids

Non-Newtonian flows arise in many processes in
engineering, science and biology for example, in
polymer processing, coating, ink-jet printing,
microfluidics, geological flows in the earth mantle,
homodynamic and many others. Modeling non-Newtonian
flows is important for understanding and predicting
the behaviour of processes and thus for designing
optimal flow configurations. Several models based on
empirical observations have been suggested for these
fluids. A constitutive equation of the non-Newtonian
fluids is in general have their order higher than
those describing the motion of the Newtonian fluids,
but apparently there is no corresponding increase in
the number of boundary conditions. Applied
mathematicians and computer scientists are thus
forced with the so-called ill-posed boundary value
problems which, in theory have a family of infinitely
many solutions. The task them becomes of selecting
one of them under some plausible assumption. The main
objective of this book is to consider the problems in
one class of non-Newtonian fluids namely the fluids
of differential type and to develop analytic
solutions using the homotopy analysis method (HAM).