Mathematical Analysis of non-Newtonian Fluid Flows Over a Stretchable Surfaces

Abstract

Flow behavior of several complex fluids is characterized by viscosity dependency on the rate of deformation. The viscosity dependency is the basic criteria of the non-Newtonian fluids rather than Newtonian fluids. The non-Newtonian (rate type) fluids with elastic and viscous forces exhibits the phenomena, which are known as relaxation and creep. The flow of viscoelastic materials in the nature has the application in polymers process, paints manufacturing, chemical and biological liquid production. The researchers developed several constitutive models to predict the rheological properties of non-Newtonian fluids model. The non-Newtonian fluid models under discussion in this study are consisting of Maxwell, Burger’s, Oldroyd-B, and Casson fluid models. These models deliberate the relaxation and retardation aspect of fluids consequently. The main contribution of this thesis is to present the mathematical formulation of steady and unsteady, 2D and 3D, incompressible boundary layer flow of non-Newtonian fluid models with microorganisms over a stretchable surface. Further, the heat energy and mass transport in non-Newtonian fluid with various effects are examined in this thesis. The modelled partial differential equations of the flow problem are transformed into system of coupled ordinary differential equations by using similarity transformation. The whole computational work is carried out with the help of well-known numerical approaches built-in MATLAB solver (Bvp4c) and Richardson extrapolation (Bvp traprich) built-in MAPLE. A meaningful physical interpretation in the form of computational analysis is observed to characterize the behavior of velocity, temperature, concentration, and microorganism density of non-Newtonian fluid. It is interesting to observe that increment in the stress relaxation phenomenon, the fluid velocity declines, while fluid velocity is improved in the case of retardation phenomenon. Further, it is noted that higher trend of thermal and mass relaxation time (which are the results of Cattaneo Christov theory), decreases the energy and mass transport in the fluid over a stretching surface. The comparison tables are presented for the validation of results.