Impact of an inclined magnetic field, heat generation/absorption and radiation on the peristaltic flow of a Micropolar fluid through a porous non-uniform channel with slip velocity

Abstract

Incompressible peristaltic flow of a micro-polar fluid through a permeable non-uniform channel in the vicinity of an inclined magnetic field with heat and mass transfer is investigated in the present study. Effects of heat generation, radiation and spin velocity on the fluid are also studied. Presumptions of long wavelength and low Reynolds number approximations are utilized. Mathematical expressions for axial velocity, micro-rotation speed, pressure gradient, volumetric stream rate, temperature and concentration are described in the physical area. The impact of different applicable physical parameters is dissected hypothetically and figured numerically. The outcomes got are delineated and showed graphically. The outcomes determine that the impact of Magnetic  field, coupling number, micropolar parameter, slip parameter, inclination of magnetic field parameter, porosity parameter, heat  generation and thermal radiation parameter is extremely protuberant in the phenomena.

Keywords

• Micropolar fluid,inclined magnetic field,non-uniform channel,heat generation

Kaynakça

1. T. W. Latham, Fluid Motion in a Peristaltic Pump, MIT, Cambridge, MA, 1966.
2. A. H. Shapiro, M. Y. Jaffrin, S. L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number, J. Fluid Mech. 37(1969) 799-825.
3. O. Eytan , A. J. Jaffa , D. Elad, Peristaltic flow in a tapered channel: Application to embryo transport within the uterine cavity. Med. Eng. Phys. 23 (2001) 473-482.
4. M. Elshahed, M. H. Haroun, Peristaltic transport of JohnsonSegalman fluid under effect of a magnetic field, Math. Problems Eng. 6 (2005) 663-667.
5. T. Hayat, Y. Wang, A. M. Siddiqui, K. Hutter, S. Asghar, Peristaltic transport of a third order fluid in a circular cylindrical tube, Math. Models Methods Appl. Sci. 12 (2002) 1691-1706.
6. Kh. S. Mekheimer, Peristaltic transport of blood under effect of a magnetic field in a non-uniform channels, Appl. Math. Comput. 153 (2004) 763-777.
7. E. F. El Shehawey, Kh. S. Mekheimer, Couple-stresses in peristaltic transport of fluids, J. Phys. D Appl. Phys. 27 (1994) 1163-1170.
8. Y. Wang, T. Hayat, K. Hutter, Peristaltic flow of a JohnsonSegalman fluid through a deformable tube, Theor. Comput. Fluid Dyn. 21 (2007) 369-380.

9. Kh. S. Mekheimer, Nonlinear peristaltic transport through a porous medium in an inclined planar channel, J. Porous Media 6(2003) 189-201.
10. M. Kotkandapani, S. Srinivas, Nonlinear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium, Phys. Lett. A 372 (2008) 1265-1276.
11. M. kothandapani, S. Srinivas, Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel, Int. J. Non-Linear Mech. 43 (2008) 915-924.
12. D. Tripathi, S.K. Pandey, S. Das, Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel, Appl. Math. Comput. 215 (2010) 3645-3654.
13. A. Ebaid, A new numerical solution for the MHD peristaltic flow of a biofluid with variable viscosity in circular cylindrical tube via adomian decomposition method, Phys. Lett. A 372 (2008) 5321-5328.
14. P. Hariharan, V. Seshadri, R. K. Banerjee, Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms, Math. Comput. Model. 48 (2008) 998-1017.
15. M. H. Haroun, Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel, Commun. Nonlinear Sci. Numer. Simul.12 (2007) 1464-1480.
16. A. C. Eringen, Theory of micropolar fluids, J Math Mech 16 (1966) 1-16.
17. T. Ariman, M.A. Turk, N.D. Sylvester, Review article applications of microcontinuum fluid mechanics, Int. J. Eng. Sci. 12 (1974) 273-293.
18. G. Lukaszewicz, Micropolar Fluids-Theory and Applications, Birkhauser, 1999.
19. T. Hayat, N. Ali, Effects of an endoscope on the peristaltic flow of a micropolar fluid, Math. Comput. Model. 48 (2008) 721-733.
20. R. S. Agarwal, C. Dhanapal, Numerical solution of free convection micropolar fluid flow between two parallel porous vertical plates. Int J Eng Sci., 26 (1988) 1247-1255.
21. M. Sheikholeslami, M. Hatami, D. D. Ganji, Micropolar fluid flow and heat transfer in a permeable channel using analytical method. J. Mol. Liq. 194 (2014) 30-36.
22. R. Bhargava, L. Kumar, H.S. Takhar, Finite element solution of mixed convection microploar fluid driven by a porous stretching sheet, Int. J. Eng. Sci. 41 (2003) 2161-2178.
23. M. A. A. Mahmood, S. E. Waheed, MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation(absorption) and slip velocity, J. Egypt. Math. Soc. 20 (1) (2012) 20-27.
24. M. M. Rahman, M.A. Sattar, Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving porous plate in the presence of heat generation/absorption. ASME J. Heat Trans. 128 (2006) 142-152.
25. N. A. Yacos, A. Ishak, I. Pop, Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid, Comput. Fluids 47 (1) (2011) 16-21.
26. H. Rosali, A. Ishak, I. Pop, Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction, Int. Commun. Heat Mass Transf. 39 (6) (2012) 826-829.
27. J. C. Umavathi, J. Sultana, Mixed convective flow of a micropolar fluid mixture in a vertical channel with boundary conditions of the third kind. J. Eng Phys Thermophys 85 (2012) 895-908.
28. S. S. Motsa, S. Shateyi , The effects of chemical reaction, Hall, and ion-slip currents on MHD micropolar fluid flow with thermal diffusivity using a novel numerical technique. J Appl Math 2012 (2012) 1-30.
29. B. Mohanty, S. R. Mishra, H.B. Pattanayak, Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet through porous media, Alexandria Engineering Journal 54 (2015) 223-232.
30. M. A. El-Aziz, Mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation, J. Egypt. Math. Soc. 21 (3) (2013) 385-394.
31. E. A. Ashmawy, Fully developed natural convective micropolar fluid flow in a vertical channel with slip, Journal of the Egyptian Mathematical Society 23 (2015) 563-567
32. R. Ellahi, S. U. Rahman, S. Nadeem, Noreen Sher Akbar, Influence of heat and mass transfer on micropolar fluid of blood flow through a tapered stenosed arteries with permeable walls. J Comput Theor Nanosci. 11 (2014) 1156-1163.
33. B. I. Olajuwon, J. I. Oahimire, M. Ferdow, Effect of thermal radiation and Hall current on heat and mass transfer of unsteady MHD flow of a viscoelastic micropolar fluid through a porous medium, Engineering Science and Technology, an International Journal 17 (2014) 185-193.