A mathematical model of pulsatile flows of microstretch fluids in circular tubes

Pulsatile flows of micropolar fluids with stretch whose microelements can undergo expansions and contractions besides translations and rotations in straight circular tubes are considered. The governing field equations for such flows of linear microstretch fluids turn out to be a nonlinear coupled partial differential system. Solutions are sought for this system starting with a reasonable initial approximation for microinertia and the consequent linearization of the field equations. One of the coupled equations governing the microstretch and microinertia is solved approximately by the method of Laplace transforms taken with respect to the time variable. Making use of this approximate solution, the other coupled equation is solved leading to explicit higher order approximation solutions for microinertia, microstretch and micropressure. Next, the coupled equations governing the velocity and the microrotation fields are solved by employing the finite Hankel transform operators on a space variable and their inversions, and higher order approximation solutions are determined. All the above-mentioned explicit solutions are obtained in computationally suitable forms. These solutions have the promise of application to many practically important physical situations such as flows of polymeric fluids with deformable springy suspensions and flows of biological fluids including blood with deformable cell suspensions in small arteries.