Decay of Potential Vortex and Diffusion of Temperature in a Generalized Oldroyd-B Fluid through a Porous Medium

Xiaoyi Guo
2014 Mathematical Problems in Engineering  
Based on a modified Darcy law, the decay of potential vortex and diffusion of temperature in a generalized Oldroyd-B fluid with fractional derivatives through a porous medium is studied. Exact solutions of the velocity and temperature fields are obtained in terms of the generalized Mittag-Leffler function by using the Hankel transform and discrete Laplace transform of the sequential fractional derivatives. One of the solutions is the sum of the Newtonian solutions and the non-Newtonian
more » ... -Newtonian contributions. As limiting cases of the present solutions, the corresponding solutions of the fractional Maxwell fluid and classical Maxwell fluids are given. The influences of the fractional parameters, material parameters, and the porous space on the decay of the vortex are interpreted by graphical results.
doi:10.1155/2014/719464 fatcat:kd5d3eynmzc7tl3hhscdsn4age