Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5409125 | Journal of Molecular Liquids | 2017 | 25 Pages |
Abstract
Natural convection flow of differential type fluid with non-integer order Caputo-fractional derivatives is investigated in this study. The non-dimensional temperature, concentration, and velocity fields are solved by using the Laplace transform method. There is no such result regarding second grade fluid with non-integer order Caputo fractional derivatives established. The obtained solutions are expressed in terms of G-function, Mittage-Leffler function, Robotnov-Hartley and Wright's function. Some known solutions from literature are recovered as a limiting case. Expression for Nusselt and Sherwood numbers with non-integer and integer order, respectively, are also determined. Numerical computations and graphical discussion were made to observe influence of Caputo-time fractional parameter α and second grade parameter α2 on the fluid flow. A comparison for second grade and viscous fluid for non-integer and integer order is also depicted. It is also observed that ordinary fluids have greater velocities than fractional fluids. This shows that how non-integer order fractional parameter affects the fluid flow.
Keywords
Related Topics
Physical Sciences and Engineering
Chemistry
Physical and Theoretical Chemistry
Authors
M.A. Imran, I. Khan, M. Ahmad, N.A. Shah, M. Nazar,