Study of magnetic and heat transfer on the peristaltic transport of a fractional second grade fluid in a vertical tube

This study is concerned with the peristaltic flow of the fractional second grade fluid confined in a cylindrical tube. The effects of magnetic field in the presence of heat transfer are taken into account. Mathematical modeling is based upon continuity, momentum and energy equations. This analysis is carried out under the constraints of long wavelength (0<Hartmann number M, heat source/sink parameter b, Grashof number Gr, material constant l1, pressure rise DP and friction force F alone with Reynolds number Re and Prandtl number Pr are discussed through graphs. It is found that an increase in constant of fractional second grade fluid results in the decrease of velocity profile for the case of fractional second grade fluid whereas the velocity remains unchanged for the case of second grade fluid. It is also observed that the absolute value of heat transfer coefficient increases with an increase in b and aspect ratio 4. It is due to the fact that the nature of heat transfer is oscillatory which is accordance with the physical expectation due to oscillatory nature of the tube wall. It is perceived that with an increase in Hartmann number, the velocity decreases. A suitable comparison has been made with the prior results in the literature as a limiting case of the considered problem, for instance, fractional second grade fluid model reduces to second grade models for a1 ¼1 and classical Naiver Stokes fluid model can be deduced from this as a special case by taking l1 ¼ 0. Copyright © 2015, The Authors. Production and hosting by Elsevier B.V. on behalf of Karabuk University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by