Thermophoresis and concentration effects in a fourth grade peristaltic flow with convective walls

Abstract

In this investigation, we have studied the peristaltic fluid flow in an asymmetric channel with convective walls. Fourth grade fluid model has been utilized in view of the fact that the results of all other differential type models can be deduced as the special case. Combined effects of heat and mass transfer are considered. The thermophoresis effects occur in the energy equation. Convective heat and mass boundary conditions have been given special attention. Long wave length and low Reynolds number approximations are utilized for the simplifications. Approximate analytic solutions for the velocity, temperature and concentration profiles are calculated using perturbation technique and elaborated in the form of graphical observations for various physical quantities.

Keywords

fourth grade fluid / convective boundary conditions / pumping and trapping / peristalsis

References

[1] HayatT, MamboungouH M, MahmoodF M. A note on some solutions for the flow of a fourth grade fluid in a porous space [J]. Nonlinear Analysis: Real World Applications, 2009, 10(1): 368-374

[2] NadeemS, AliM. Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel’s models of viscosities [J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(5): 2073-2090

[3] MarincaV, HerisanuN, BotaC, MarincaB. An optimal homotopyanymptotic method applied to the steady flow of a fourth grade fluid past a porous plate [J]. Applied Mathematics Letters, 2009, 22(2): 245-251

[4] AzizT, MahmoodF M. Reductions and solutions for the unsteady flow of a fourth grade fluid on a porous plate [J]. Applied Mathematics Computations, 2013, 219(17): 9187-9195

[5] AbdallaA M, AbodahabS M, ElshahranyH D. Effects of rotation and initial stress on peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field [J]. Journal of Magnetism and Magnetic Materials, 2014, 349: 268-280

[6] EbrahimpourM, GanjiD D, ForoughniaH. Steady state flow for inside porous flat channel with using analytical solution to fourth grade fluid [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(2): 525-531

[7] AzizT, MaganA B, MahmoodF M. Invarient solutions for the unsteady magnetohydrodynamics (MHD) flow of a fourth grade fluid induced due to the impulsive motion of a flat plate [J]. Brazilian Journal of Physics, 2015, 45: 120-131

[8] NazR, AlsaediA, HayatT. Flow of fourth grade fluid in a porous medium [J]. Applied and Computational Mathematics, 2015, 14(2): 125-140