(237q) Numerical and Recursion Solution of the Shear Stress of Biological Fluids in Rectangular and Cylindrical Capillary Vessels

Mathias A. Oyanader and Mario A. Oyanader,

Chemical Engineering Department, California Baptist University, 8432 Magnolia Ave. Riverside, CA 92504, E-mail: moyanader@calbaptist.edu

The accurate prediction of velocity profiles is key factor on the study of advective processes where the fluid rheology affect not only the velocity field but also the concentration and temperature profile in the bulk of the system. Biological fluids are well known by for their deviation from the typical Newtonian behavior and therefore from a fundamental analysis approach it is more challenging to study them. Indeed, the momentum balance equation can be solved for this fluids if an ad-doc model is used to represent the shear rate. The power law model, Ostwald-de Waele equation, usually is the chosen model for the task. To simplify the complexity of the resulting differential equation different approaches have been proposed including Taylor series expansion but not without issues.

This contribution focuses on the development of a new approach that completely departure from the application of the Taylor's expansion series as a strategic solution of the power law momentum transport model. This new approach is based on the principle of recursion performed in a mathematical function. Furthermore, this study concentrates on the comparison of the numerical solution and the recursion solution to validate the accuracy of this last method predictions. A few different geometries have been chosen to further validate the approach and highlight its simplicity. Potential uses in describing biological fluids behavior will be also presented.