An Investigation of Stokes' Second Problem for Non-Newtonian Fluids

ABSTRACT

Stokes flow produced by an oscillatory motion of a wall is analyzed in the presence of a non-Newtonian fluid. A total of eight non-Newtonian models are considered. A mass balance approach is introduced to solve the governing Equations. The velocity and temperature profiles for these models are obtained and compared to those of Newtonian fluids. For the power law model, correlations for the velocity distribution and the time required to reach the steady periodic flow are developed and discussed. Furthermore, the effects of the dimensionless parameters on the flow are studied. For the temperature distribution, an analytical solution for Newtonian fluid is developed as a comparative source. To simulate the rheological behavior of blood at unsteady state, three non-Newtonian constitutive relationships are used to study the wall shear stress. It is found that in the case of unsteady stokes flow, although the patterns of velocity and wall shear stress is consistent across all models, the magnitude is affected by the model utilized.