Library Subscription: Guest
ESCI SJR: 0.277 SNIP: 0.52 CiteScore™: 1.3

ISSN Print: 2151-4798
ISSN Online: 2151-562X

# Special Topics & Reviews in Porous Media: An International Journal

DOI: 10.1615/SpecialTopicsRevPorousMedia.2019028609
pages 245-258

## MHD PERISTALTIC ROTATING FLOW OF A COUPLE STRESS FLUID THROUGH A POROUS MEDIUM WITHWALL AND SLIP EFFECTS

M. Veera Krishna
Dept of Mathematics, Rayalaseema University, Kurnool, Andhra Pradesh, India - 518007
A J Chamkha
KCST

### ABSTRACT

We have discussed the systematic solution of time-dependent mean velocity on MHD peristaltic rotating flow of an electrically conducting couple stress fluid in a uniform elastic porous channel. The consequence of slip condition has been studied. The precise model is formulated assuming a small Reynolds number and long-wavelength approximations. Various aspects such as magnetic parameter, Darcy number, slip parameter, and couple stress parameter are discussed through graphs under the existence and nonexistence of both stiffness and viscous damping forces. It is noticed that the time-dependent mean velocity decreases with increase in the magnetic parameter in the presence of elastic parameters and flow reversal occurs at the center line of the channel. It reduces with growth in nonzero elastic parameters.

### REFERENCES

1. Abu Arqub, O., Fitted Reproducing Kernel Hilbert Space Method for the Solutions of Some Certain Classes of Time-Fractional Partial Differential Equations Subject to Initial and Neumann Boundary Conditions, Comput. Math. Appl., vol. 73, pp. 1243-1261,2017.

2. Abu Arqub, O., Numerical Solutions for the Robin Time-Fractional Partial Differential Equations of Heat and Fluid Flows based on the Reproducing Kernel Algorithm, Int. J. Numer. Methods Heat Fluid Flow, vol. 28, pp. 828-856, 2018a.

3. Abu Arqub, O., Numerical Algorithm for Solving Time-Fractional Partial Integrodifferential Equations Subject to Initial and Dirichlet Boundary Conditions, Numer. Methods Partial Differ. Equations, vol. 34, pp. 1577-1597, 2018b.

4. Abu Arqub, O., Solutions of Time-Fractional Tricomi and Keldysh Equations of Dirichlet Functions Types in Hilbert Space, Numer. Methods Partial Differ. Equations, vol. 34, no. 5, pp. 1759-1780, 2018c.

5. Akbar, N., Raza, M., and Ellahi, R., Influence of Induced Magnetic Field and Heat Flux with the Suspension of Carbon Nanotubes for the Peristaltic Flow in a Permeable Channel, J. Magn. Magn. Mater., vol. 381, pp. 405-415, 2015.

6. Beavers, J., Boundary Conditions at aNaturally Permeable Wall, J. FluidMech., vol. 30, no. 1, pp. 197-207,1967.

7. Bhatti, M.M., Zeeshan, A., and Ijaz, N., Slip Effects and Endoscopy Analysis on Blood Flow of Particle-Fluid Suspension Induced by Peristaltic Wave, J. Mol. Liq., vol. 218, pp. 240-245, 2016a.

8. Bhatti, M.M., Ali Abbas, M., and Rashid, M.M., Combine Effects of Magnetohydrodynamics (MHD) and Partial Slip on Peristaltic Blood Flow of Ree-Eyring Fluid with Wall Properties, Eng. Sci. Technol., vol. 19, no. 3, pp. 1497-1502, 2016b.

9. Ellahi, R., Effect of the Slip Boundary Condition on Non-Newtonian Flows in a Channel, Commun. Nonlinear Sci. Numer. Simul., vol. 14, no. 4, pp. 1377-1384,2009.

10. Ellahi, R. and Hussain, F., Simultaneous Effects of MHD and Partial Slip on Peristaltic Flow of Jeffery Fluid in a Rectangular Duct, J. Magn. Magn. Mater., vol. 393, pp. 284-292,2015.

11. Hayat, T., Nisar, Z., Ahmad, B., and Yasmin, H., Simultaneous Effects of Slip and Wall Properties on MHD Peristaltic Motion of Nanofluid with Joule Heating, J. Magn. Magn. Mater., vol. 395, pp. 48-58, 2015.

12. Hina, S., Mustafa, M., and Hayat, T., On the Exact Solution for Peristaltic Flow of Couple Stress Fluid with Wall Properties, Bull. Chem. Commun., vol. 47, pp. 30-37,2015.

13. Hummady, L. and Abdulhadi, A., Influence of MHD on Peristaltic Flow of Couple Stress Fluid through a Porous Medium with Slip Effect, Adv. Phys. Theor. Appl., vol. 30, pp. 34-44, 2014.

14. Hussanan, A., Ismail, Z., Khan, I., Hussein, A., and Shafie, S., Unsteady Boundary Layer MHD Free Convection Flow in a Porous Medium with Constant Mass Diffusion and Newtonian Heating, Eur. Phys. J. Plus, vol. 129, pp. 1-16, 2014.

15. Hussanan, A., Salleh, M.Z., Khan, I., Tahar, R.M., and Ismail, Z., Soret Effects on Unsteady MHD Mixed Convective Heat and Mass Transfer Flow in a Porous Medium with Newtonian Heating, Maejo Int. J. Sci. Technol., vol. 9, no. 2, pp. 224-245,2015.

16. Hussanan, A., Khan, I., Salleha, M.Z., and Shafie, S., Slip Effects on Unsteady Free Convective Heat and Mass Transfer Flow with Newtonian Heating, Therm. Sci., vol. 20, no. 6, pp. 1939-1952,2016a.

17. Hussanan, A., Khan, I., Hashim, H., Mohamed, M.K.A., Ishak, N., Sarif, N.M., and Salleh, M.Z., Unsteady MHD Flow of Some Nanofluids past an Accelerated Vertical Plate Embedded in a Porous Medium, J. Teknol., vol. 78, no. 2, pp. 121-126,2016b.

18. Kill, F., The Function of the Urethra and the Renal Pelvis, Philadelphia: Saunders, 1957.

19. Kothandapani, M. and Srinivas, S., On the Influence of Wall Properties in the MHD Peristaltic Transport with Heat Transfer and Porous Medium, Phys. Lett. A, vol. 372, no. 25, pp. 4586-4591, 2008.

20. Maiti, S. and Misra, J.C., Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics, J. Mech. Med. Biol., vol. 12, no. 3, p. 1250048,2012.

21. Mekheimer, Kh.S., Effect of the Induced Magnetic Field on the Peristaltic Flow of a Couple Stress Fluid, Phys. Lett. A, vol. 372, pp. 4271-4278,2008.

22. Mishra, M. and Rao, A.R., Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel, ZAMP, vol. 54, pp. 532-550, 2003.

23. Misra, J.C. and Pandey, S.K., Peristaltic Transport of Blood in Small Vessels: Study of Mathematical Model, Comput. Math. Appl., vol 43, pp. 1183-1193,2002.

24. Mittra, T.K. and Prasad, S.N., On the Influence of Wall Properties and Poiseuille Flow in Peristalsis, J. Biomech., vol. 6, pp. 681-693, 1973.

25. Raju,K.L. andDevananthan, R., Peristaltic Motion of a Non-Newtonian Fluid, PartI, Rheol. Acta, vol. 11, pp. 170-178, 1972.

26. Riaz, A., Ellahi, R., and Nadeem, S., Peristaltic Transport of a Carreau Fluid in a Compliant Rectangular Duct, Alexandria Eng. J, vol. 53, no. 2, pp. 475-484, 2014.

27. Sankad, G.C. andNagathan, P.S., Unsteady MHD Peristaltic Flow of a Couple Stress Fluid through Porous Medium with Wall and Slip Effects, Alexandria Eng. J., vol. 55, pp. 2099-2105, 2016.

28. Sankad, G.C. and Radhakrishnamacharya, G., Effects of Magnetic Field on the Peristaltic Transport of Couple Stress Fluid in a Channel with Wall Properties, Int. J. Biomath, vol. 4, no. 3, pp. 365-378,2011.

29. Shapiro, H., Jaffrin, M.Y., and Weinberg, S.L., Peristaltic Pumping with Long Wavelengths at Low Reynolds Number, J. Fluid Mech., vol. 37, pp. 799-825, 1969.

30. Shit, G.C. and Roy, M., Hydromagnetic Effect on Inclined Peristaltic Flow of a Couple Stress Fluid, Alexandria Eng. J., vol. 53, pp. 949-958, 2014.

31. Shukla, J.B., Chandra, P, Sharma, R., and Radhkrishnamacharya, G., Effects of Peristaltic and Longitudinal Wave Motion of the Channel Wall on Movement of Micro-Organisms: Application to Spermatozoa Transport, J. Biomech., vol. 21, no. 11, pp. 947-954, 1988.

32. Srinivasacharya, D., Mishra, M., and Rao, A.R., Peristaltic Pumping of a Micropolar Fluid in a Tube, Acta Mech., vol. 161, pp. 165-178,2003.

33. Stokes, V.K., Couple Stresses in Fluids, Phys. Fluids, vol. 9, pp. 1709-1715, 1966.

34. Sud, V.K., Sekhon, G.S., and Mishra, R.K., Pumping Action on Blood by a Magnetic Field, Bull. Math. Biol., vol. 39, no. 3, pp. 385-390, 1977.

35. Tripathi, D., Beg, O.A., Pandey, V.S., and Singh, A.K., A Study of Creeping Sinusoidal Flow of Bio-Rheological Fluids through a Two Dimensional High Permeability Medium Channel, J. Adv. Biotechnol. Bioeng., vol. 1, pp. 52-61, 2013.

36. Vafai, K., Khan, A., Sajjad, S., and Ellahi, R., The Study of Peristaltic Motion of Third Grade Fluid under the Effects of Hall Current and Heat Transfer, Z. Naturforsch., A: Phys. Sci., vol. 70, no. 4, pp. 281-293, 2015.

37. Vajravelu, K., Radhakrishnamacharya, G., and Radhakrishnamurthy, V, Peristaltic Flow and Heat Transfer in a Vertical Porous Annulus with Long Wave Approximation, Int. J. Non-Linear Mech., vol. 42, pp. 754-759, 2007.

38. Veera Krishna, M. and Chamkha, A.J., Hall Effects on Unsteady MHD Flow of Second Grade Fluid through Porous Medium with Ramped Wall Temperature and Ramped Surface Concentration, Phys. Fluids, vol. 30, p. 053101, 2018.

39. Veera Krishna, M. and Jyothi, K., Heat and Mass Transfer on MHD Rotating Flow of a Visco-Elastic Fluid through Porous Medium with Time Dependent Oscillatory Permeability, J. Anal., vol. 25, no. 2, pp. 1-19, 2018.

40. Veera Krishna, M. and Subba Reddy, G., Unsteady MHD Reactive Flow of Second Grade Fluid through Porous Medium in a Rotating Parallel Plate Channel, J. Anal., vol. 25, no. 2, pp. 1-19, 2018.

41. Veera Krishna, M., Subba Reddy, G., and Chamkha, A.J., Hall Effects on Unsteady MHD Oscillatory Free Convective Flow of Second Grade Fluid through Porous Medium between Two Vertical Plates, Phys. Fluids, vol. 30, p. 023106, 2018a.

42. Veera Krishna, M., Swarnalathamma, B.V., and Prakash, J., Heat and Mass Transfer on Unsteady MHD Oscillatory Flow of Blood through Porous Arteriole, Appl. Fluid Dyn., vol. 22, pp. 207-224, 2018b.

43. Veera Krishna, M., Jyothi, K., and Chamkha, A.J., Heat and Mass Transfer on Unsteady, Magnetohydrodynamic, Oscillatory Flow of Second-Grade Fluid through a Porous Medium between Two Vertical Plates, under the Influence of Fluctuating Heat Source/Sink, and Chemical Reaction, Int. J. Fluid Mech. Res., vol. 45, no. 5, pp. 459-477, 2018c.

44. Veera Krishna, M., Swarnalathamma, B.V., and Chamkha, A.J., Heat and Mass Transfer on Magnetohydrodynamic Chemically Reacting Flow of Micropolar Fluid through a Porous Medium with Hall Effects, Spec. Top. Rev. Porous Media, vol. 9, no. 4, pp. 347-364, 2018d.

45. Veera Krishna, M., Gangadhara Reddy, M., and Chamkha, A.J., Heat and Mass Transfer on MHD Free Convective Flow over an.

46. Infinite Non-Conducting Vertical Flat Porous Plate, Int. J. FluidMech. Res, vol. 46, no. 1, pp. 1-25, 2019a.

47. Veera Krishna, M., Anand, P.V.S., and Chamkha, A.J., Heat and Mass Transfer on Free Convective Flow of a Micro-Polar Fluid through a Porous Surface with Inclined Magnetic Field and Hall Effects, Spec. Top. Rev. Porous Media, vol. 10, no. 2, 2019b. DOI: 10.1615/SpecialTopicsRevPorousMedia.2018026943.

### Articles with similar content:

EFFECT OF POROSITY AND FLR CORRECTIONS ON JEANS INSTABILITY OF SELF-GRAVITATING RADIATIVE THERMALLY CONDUCTING VISCOUS PLASMA
Journal of Porous Media, Vol.16, 2013, issue 8
Sachin Kaothekar, Rajendra K. Chhajlani
HALL CURRENT EFFECTS ON HYDROMAGNETIC FLOW THROUGH UNIFORM CHANNEL BOUNDED BY POROUS MEDIA
International Journal of Fluid Mechanics Research, Vol.45, 2018, issue 5
K. Ramakrishnan
MHD NATURAL CONVECTION FLOW IN A VERTICAL POROUS MICROCHANNEL FORMED BY NONCONDUCTING AND CONDUCTING PLATES IN THE PRESENCE OF INDUCED MAGNETIC FIELD
Heat Transfer Research, Vol.48, 2017, issue 18
BABATUNDE AINA, Basant K. Jha
UNSTEADY CONVECTION HEAT AND MASS TRANSFER OF A FRACTIONAL OLDROYD-B FLUID WITH CHEMICAL REACTION AND HEAT SOURCE/SINK EFFECT
Heat Transfer Research, Vol.49, 2018, issue 13
Xinxin Zhang, Liancun Zheng, Fawang Liu, Jinhu Zhao
A Mathematical Model of Peristalsis in Tubes through a Porous Medium
Journal of Porous Media, Vol.9, 2006, issue 1
Saleem Ashgar, Abdul Majeed Siddiqui, Masood Khan