Stress Fluid In Channel Research Articles

Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium

Fractal-fractional derivative is a new class of fractional derivative with power Law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional derivatives with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper new concept of fractal-fractional derivative for the modeling of couple stress fluid (CSF) with the combined effect of heat and mass transfer have been used. The magnetohydrodynamics (MHD) flow of CSF is taken in channel with porous media in the presence of external pressure. The constant motion of the left plate generates the CSF motion while the right plate is kept stationary. The non-dimensional fractal-fractional model of couple stress fluid in Riemann–Liouville sense with power law is solved numerically by using the implicit finite difference method. The obtained solutions for the present problem have been shown through graphs. The effects of various parameters are shown through graphs on velocity, temperature and concentration fields. The velocity, temperature and concentration profiles of the MHD CSF in channel with porous media decreases for the greater values of both fractional parameter alpha and fractal parameter beta respectively. From the graphical results it can be noticed that the fractal-fractional solutions are more general as compared to classical and fractional solutions of CSF motion in channel. Furthermore, the fractal-fractional model of CSF explains good memory effect on the dynamics of couple stress fluid in channel as compared to fractional model of CSF. Finally, the skin friction, Nusselt number and Sherwood number are evaluated and presented in tabular form.

Chemical reaction in peristaltic motion of MHD couple stress fluid in channel with Soret and Dufour effects

Abstract This paper looks at the peristaltic motion of MHD couple stress fluid in an inclined asymmetric channel. Simultaneous effects of heat and mass transfer are considered. Soret and Dufour features lead to the coupled differential systems. Channel walls satisfy the convective conditions of heat and mass transfer. Exact solutions for the stream function and pressure gradient are derived. Temperature and concentration are obtained numerically. Graphical illustrations for axial velocity, temperature, concentration and streamline patterns are developed. Physical interpretation of obtained results has been presented. It can be seen that both Soret and Dufour numbers reduce the concentration field while reverse effect is seen towards temperature for both numbers. It is also observed that concentration reduces towards destructive chemical reaction and enhances for constructive chemical reaction. The heat transfer Biot number gives rise to fluid temperature. Further more the mass transfer Biot number decreases the concentration.