A mathematical study of peristaltic transport of a casson fluid

In this paper, the peristaltic flow of rheologically complex physiological fluids when modelled by a non-Newtonian Casson fluid in a two-dimensional channel is considered. A perturbation series method of solution of the stream function for zeroth and first order in amplitude ratio is sought. Of interest is the difference between peristaltic transport of Newtonian and non-Newtonian fluids. It is found that Newtonian fluid is an important subclass of non-Newtonian fluids that may adequately represent some physiological phenomena. Analytical and numerical solutions are found for the zeroth and first order in stream function and compared to well-documented research in the literature. It is shown that for a Casson fluid, when certain approximations are made in the most generalized form of constitutive equation, the fluid may be adequately represented as an improvement of a Newtonian fluid.