An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations

In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating direction implicit (ADI) spectral method is developed based on Legendre spectral approximation in space and finite difference discretization in time. Numerical stability and convergence of the schemes are proved, the optimal error is $O(N^{-r}+\tau^2)$, where $N, \tau, r$ are the polynomial degree, time step size and the regularity of the exact solution, respectively. We also consider the non-smooth solution case by adding some correction terms. Numerical experiments are presented to confirm our theoretical analysis. These techniques can be used to model diffusion and transport of viscoelastic non-Newtonian fluids

Effects of Heat Transfer and an Endoscope on Peristaltic Flow of a Fractional Maxwell Fluid in a Vertical Tube

We investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Maxwell model through two coaxial vertical tubes. This analysis has been carried under low Reynolds number and long wavelength approximations. Analytical solution of the problem is obtained by using a fractional calculus approach. The effects of Grashof number, heat parameter, relaxation time, fractional time derivative parameter, amplitude ratio, and the radius ratio on the pressure gradient, pressure rise, and the friction forces on the inner and outer tubes are graphically presented and discussed

UNSTEADY MHD THREE DIMENSIONAL FLOW OF MAXWELL FLUID THROUGH POROUS MEDIUM IN A PARALLEL PLATE CHANNEL UNDER THE INFLUENCE OF INCLINED MAGNETIC FIELD

In this paper, we discuss the unsteady hydro magnetic flow of an electrically conducting Maxwell fluid in a parallel plate channel bounded by porous medium under the influence of a uniform magnetic field of strength Ho inclined at an angle of inclination with the normal to the boundaries. The perturbations are created by a constant pressure gradient along the plates. The time required for the transient state to decay and the ultimate steady state solution are discussed in detail. The exact solutions for the velocity of the Maxwell fluid consists of steady state are analytically derived, its behaviour computationally discussed with reference to the various governing parameters with the help of graphs. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed in detail