https://doi.org/10.1140/epjp/i2014-14252-6
Regular Article
Self-similar flow due to the stretching of a deformable fiber
1
Department of Mechanical and Aerospace Engineering, North Carolina State University, 27695, Raleigh, NC, USA
2
Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, 12211, Giza, Egypt
* e-mail: tfang2@ncsu.edu
Received:
6
August
2014
Revised:
17
October
2014
Accepted:
27
October
2014
Published online:
25
November
2014
The boundary layer flow over a stretching fiber in a stationary fluid is investigated by including the coupling of the flow and fiber dynamics. This approach is quite different from the literature on flows over a stretching fiber, which has prescribed fiber kinematics. The flow problem is formulated by using a curvilinear coordinate system, and self-similarity is invoked. The similarity transformations convert the governing partial differential equations of the flow into ordinary differential equations, involving parameters determined by considering the fiber dynamics. The similarity equations are solved numerically using a shooting method. Two kinds of fibers are considered including an elastic one and a viscous one. It is found that the fluid velocity over both kinds decays algebraically to the ambient, though with different rates. Self-similarity imposes restrictions on the parameters of the problem. Nonetheless, practically feasible parameters can be chosen and solutions thereof are presented. The solution can offer more accurate estimations of fiber dynamics and fluid flow for practical applications in fiber stretching.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014
