In this talk I will present an application to fluid mechanics of the fractional continuum mechanics model developed recently by Drapaca and Sivaloganathan. The constitutive law of an incompressible non-Newtonian fluid linearly relates the Cauchy stress tensor and a Caputo fractional strain rate tensor. Analytic solutions for the Poiseuille flows in a circular pipe and between infinite parallel plates will be presented and compared with those corresponding to an incompressible Newtonian fluid and an incompressible power law non-Newtonian fluid. Possible applications to hemodynamics and studies of aneurysms and strokes will be discussed.

Bio: Dr. Corina Drapaca is a Professor in the Department of Engineering Science & Mechanics at Pennsylvania State University. She completed her PhD in Applied Mathematics at the University of Waterloo and has held visiting positions at the Mayo Clinic, at the University of California at San Francisco and at the University of Waterloo.