Mathematical Modellingof Non-Newtonian Thin Film Flows on Vertical Surfaces: Exactand ApproximateSolutions

In this dissertation an attempt is made to present a theoretical and computational study of the thin ?lm of viscoelastic non-Newtonian ?uids in laminar motion on vertical surfaces. In this thesis two types of problems have been discussed: (i)Whenaverticalmovingbelt(cylinder)isliftverticallyupwardwithaconstant velocity from a bath of viscoelastic non-Newtonian liquid. (ii) When a non-Newtonian ?uid ?ows down a stationary in?nite vertical wall, plane or cylinder under the in?uence of gravity.Inbothphenomenaathincoatingofuniformthicknessadherestothesurface of the wall in the form of a continuous thin layer. The non-Newtonian viscoelastic pseudo-plastic and Johnson-Segalman ?uid models are considered to study the thin ?lm layer for the lifting (withdrawal) and drainage problems. Starting with the equations of ?uid motion, the momentum equation, mass and suitable boundary conditions, a general theory for the thin ?lm ?ow is presented under the assumption of one dimensional ?ow. Exact, numerical and asymptotic methods are applied for the solution of the non-linear differential equations arising from the mathematical modelling of the above stated problems.</br> Expressions for velocity pro?le, volumetric ?ow rate, average velocity, shear and normal stresses and the condition for the possibility of net upward ?ow (for lifting) are reported. The well-known Newtonian solution is retrieved for each ?ow problem. In both problems the effect of the Weissenberg number, Stokes number, the magnetohydrodynamic effect and the non-Newtonian ?uid parameter ? are investigated. The series solutions are compared with their corresponding numerical solutions for different values of ?uid parameters