Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T16:36:51.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady MHD Natural Convective Flow of a Rotating Walters’-B Fluid Over an Oscillating Plate with Fluctuating Wall Temperature and Concentration

Published online by Cambridge University Press:  10 April 2017

J. K. Singh ,
N. Joshi  and
P. Rohidas
J. K. Singh*
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
N. Joshi
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
P. Rohidas
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
*
*Corresponding author (s.jitendrak@yahoo.com)
Get access

Abstract

In the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

Keywords

Walters’-B fluidNatural convectiveRotationHall and ion-slip effects
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 519 - 532
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Abo-Eldahab, E. M. and Aziz, M. A. E., “Hall and Ion-Slip Effects on MHD Free Convective Heat Generating Flow past a Semi-Infinite Vertical Flat Plate,” Physica Scripta, 61, pp. 344–348 (2000).Google Scholar
2. Ibrahim, F. S., Hassanien, I. A. and Bakr, A. A., “Unsteady Magnetohydrodynamic Micropolar Fluid Flow and Heat Transfer over a Vertical Porous Plate through a Porous Medium in the Presence of Thermal and Mass Diffusion with a Constant Heat Source,” Canadian Journal of Physics, 82, pp. 775–790 (2004).Google Scholar
3. Chaudhary, R. C. and Jain, A., “Combined Heat and Mass Transfer Effects on MHD Free Convection Flow past an Oscillating Plate Embedded in Porous Medium,” Romanian Journal Physics, 52, pp. 505–524 (2007).Google Scholar
4. Postelnicu, A., “Influence of Chemical Reaction on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects,” Heat and Mass Transfer, 43, pp. 595–602 (2007).Google Scholar
5. Mbeledogu, I. U. and Ogulu, A., “Heat and Mass Transfer of an Unsteady MHD Natural Convection Flow of a Rotating Fluid past a Vertical Porous Flat Plate in the Presence of Radiative Heat Transfer,” International Journal of Heat and Mass Transfer, 50, pp. 1902–1908 (2007).Google Scholar
6. Beg, O. A., Bakier, A. Y. and Prasad, V. R., “Numerical Study of Free Convection Magnetohydrodynamic Heat and Mass Transfer from a Stretching Surface to a Saturated Porous Medium with Soret and Dufour Effects,” Computational Materials Science, 46, pp. 57–65 (2009).Google Scholar
7. Ghosh, S. K., Beg, O. A. and Zueco, J., “Hydromagnetic Free Convection Flow with Induced Magnetic Field Effects,” Meccanica, 45, pp. 175–185 (2010).Google Scholar
8. Makinde, O. D., “Similarity Solution of Hydromagnetic Heat and Mass Transfer over a Vertical Plate with a Convective Surface Boundary Condition,” International Journal of Physical Sciences, 5, pp. 700–710 (2010).Google Scholar
9. Rahman, M. M. and Salahuddin, K. M., “Study of Hydromagnetic Heat and Mass Transfer Flow over an Inclined Heated Surface with Variable Viscosity and Electric Conductivity,” Communications in Non-Linear Science and Numerical Simulation, 15, pp. 2073–2085 (2010).Google Scholar
10. Chamkha, A. J. and Aly, A. M., “MHD Free Convection Flow of a Nanofluid past a Vertical Plate in the Presence of Heat Generation or Absorption Effects,” Chemical Engineering Communications, 198, pp. 425–441 (2010).Google Scholar
11. Seth, G. S., Ansari, Md. S. and Nandkeolyar, R., “MHD Natural Convection Flow with Radiative Heat Transfer past an Impulsively Moving Plate with Ramped Wall Temperature,” Heat and Mass Transfer, 47, pp. 551–561 (2011).Google Scholar
12. Das, K., “Effect of Chemical Reaction and Thermal Radiation on Heat and Mass Transfer Flow of MHD Micropolar Fluid in a Rotating Frame of Reference,” International Journal of Heat and Mass Transfer, 54, pp. 3505–3513 (2011).Google Scholar
13. Khan, I., Fakhar, K. and Shafie, S., “Magnetohydrodynamic Free Convection Flow past an Oscillating Plate Embedded in a Porous Medium,” Journal of Physical Society of Japan, 80, 104401 (2011).Google Scholar
14. Prasad, V. R., Vasu, B. and Beg, O. A., “Thermo-Diffusion and DiffusionThermo Effects on MHD Free Convection Flow past a Vertical Porous Plate Embedded in a Non-Darcian Porous Medium,” Chemical Engineering Journal, 173, pp. 598–606 (2011).Google Scholar
15. Narahari, M. and Debnath, L., “Unsteady Magnetohydrodynamic Free Convection Flow past an Accelerated Vertical Plate with Constant Heat Flux and Heat Generation or Absorption,” Journal of Applied Mathematics and Mechanics (ZAMM), 93, pp. 38–49 (2013).Google Scholar
16. Deka, R. K., Paul, A. and Chaliha, A., “Transient Free Convection Flow past an Accelerated Vertical Cylinder in a Rotating Fluid,” Ain Shams Engineering Journal, 5, pp. 505–513 (2014).Google Scholar
17. Hossain, Md. D., Samad, Md. A. and Alam, Md. M., “MHD Free Convection and Mass Transfer Flow through a Vertical Oscillatory Porous Plate with Hall, Ion-Slip Currents and Heat Source in a Rotating System,” Procedia Engtneering, 105, pp. 56–63 (2015).Google Scholar
18. Balamurugan, K. S., Ramaprasad, J. L. and Varma, S. V. K., “Unsteady MHD Free Convective Flow past a Moving Vertical Plate with Time Dependent Suction and Chemical Reaction in a Slip Flow Regime,” Procedia Engineering, 127, pp. 516–523 (2015).Google Scholar
19. Seth, G. S. and Sarkar, S., “Hydromagnetic Natural Convection Flow with Induced Magnetic Field and nth Order Chemical Reaction of a Heat Absorbing Fluid past an Impulsively Moving Vertical Plate with Ramped Temperature,” Bulgarian Chemical Commucations, 47, pp. 66–79 (2015).Google Scholar
20. Butt, A. S. and Ali, A., “Entropy Generation Effects in a Hydromagnetic Free Convection Flow past a Vertical Oscillating Plate,” Journal of Applied Mechanics and Technical Physics, 57, pp. 27–37 (2016).Google Scholar
21. Cramer, K. R. and Pai, S. I., Magnetofluid-Dynamics for Engineers and Applied Physicists, McGraw-Hill, New York, (1973).Google Scholar
22. Raptis, A. and Singh, A. K., “Rotation Effects on MHD Free-Convection Flow past an Accelerated Vertical Plate,” Mechanics Research Communications, 12, pp. 31–40 (1985).Google Scholar
23. Kythe, P. K. and Puri, P., “Unsteady MHD Free Convection Flows on a Porous Plate with Time-Dependent Heating in a Rotating Medium,” Astrophysics Space Science, 143, pp. 51–62 (1988).Google Scholar
24. Tokis, J. N., “Free Convection and Mass Transfer Effects on the Magnetohydrodynamic Flows Near a Moving Plate in a Rotating Medium,” Astrophysics Space Science, 144, pp. 291–301 (1988).Google Scholar
25. Nanousis, N., “Thermal Diffusion Effects on MHD Free Convective and Mass Transfer Flow past a Moving Infinite Vertical Plate in a Rotating Fluid,” Astrophysics Space Science, 191, pp. 313–322 (1992).Google Scholar
26. Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, New York, (1988).Google Scholar
27. Beard, D. W. and Walters, K., “Elastico-Viscous Boundary-Layer Flows. I. Two-Dimensional Flow Near a Stagnation Point,” Mathematical Proceedings of the Cambridge Philosophical Society, 60, pp. 667–674 (1964).Google Scholar
28. Nandeppanavar, M. M., Abel, M. S. and Tawade, J., “Heat Transfer in a Walter's Liquid B Fluid over an Impermeable Stretching Sheet with Non-Uniform Heat Source/Sink and Elastic Deformation,” Communications in Non-linear Science and Numerical Simulation, 15, pp. 1791–1802 (2010).Google Scholar
29. Chang, T. B. et al., “Numerical Study of Transient Free Convective Mass Transfer in a Walters-B Viscoelastic Flow with Wall Suction,” Communications in Non-linear Science and Numerical Simulation, 16, pp. 216–225 (2011).Google Scholar
30. Khan, I., Ali, F., Shafie, S. and Qasim, M., “Unsteady Free Convective Flow in a Walters’-B Fluid and Heat Transfer Analysis,” Bulletin of the Malaysian Mathematical Sciences Society, 37, pp. 437–448 (2014).Google Scholar
31. Uwanta, I. J., Isah B. Y. and Ibrahim, M. O., “Viscoelastic Fluid Flow past an Infinite Vertical Plate with Heat Dissipation,” International Journal of Computer Applications, 36, pp. 17–24 (2011).Google Scholar
32. Hayat, T., Asad, S., Mustafa, M. and Alsulami, H. H., “Heat Transfer Analysis in the Flow of Walters’B Fluid with a Convective Boundary Condition,” Chinese Physics B, 23, 084701 (2014).Google Scholar
33. Hayat, T., Hutter, K., Nadeem, S. and Asghar, S., “Unsteady Hydromagnetic Flow of a Conducting Second Grade Fluid,” Journal of Applied Mathematics and Physics (ZAMP), 55, pp. 626–641 (2004).Google Scholar
34. Siddheshwar, P. G. and Mahabaleshwar, U. S., “Effects of Radiation and Heat Source on MHD Flow of a Viscoelastic Liquid and Heat Transfer over a Stretching Sheet,” International Journal of Non-Linear Mechanics, 40, pp. 807–820 (2005).Google Scholar
35. Ghasemi, E., Bayat, M. and Bayat, M., “Viscoelastic MHD Flow of Walters Liquid B Fluid and Heat Transfer over a Non-Isothermal Stretching Sheet,” International Journal of Physical Sciences, 6, pp. 5022–5039 (2011).Google Scholar
36. Prakash, O., Kumar, D. and Dwivedi, Y. K., “Heat Transfer in MHD Flow of Dusty Viscoelastic (Walters’ Liquid Model-B) Stratified Fluid in Porous Medium under Variable Viscosity,” Pramana-Journal of Physics, 79, pp. 1457–1470 (2012).Google Scholar
37. Khan, I., Fakhar, K. and Anwar, M. I., “Hydromagnetic Rotating Flows of an Oldroyd-B Fluid in a Porous Medium,” Special Topics and Review in Porous Media, 3, pp. 89–95 (2012).Google Scholar
38. Garg, B., Singh, K. D. and Bansal, A., “Hall Current Effect on Viscoelastic (Walter's Liquid Model-B) MHD Oscillatory Convective Channel Flow through a Porous Medium with Heat Radiation,” Kragujevac Journal of Science, 36, pp. 19–32 (2014).Google Scholar
39. Singh, K. D., Garg, B. and Bansal, A., “Hall Current Effect on Visco-Elastic MHD Oscillatory Convective Flow through a Porous Medium in a Vertical Channel with Heat Radiation,” Proceedings of Indian National Science Academy, 80, pp. 333–343 (2014).Google Scholar
40. Ramesh, K. and Devakar, M., “Effect of Heat Transfer on the Peristaltic Flow of Walters B Fluid in a Vertical Channel with an External Magnetic Field,” Journal of Aerospace Engineering, 29, 04015050 (2016).Google Scholar
41. Veera Krishna, M. and Gangadhar Reddy, M., “MHD Convective Rotating Flow past an Oscillating Porous Plate with Chemical Reaction and Hall Effects,” IOP Conference Series: Materials Science and Engineering, 149, 012217 (2016).Google Scholar
42. Abdel-Rahman Rashed, G. M. and El-fayez, F. M. N., “Studying Fadiation and Reaction Effects on Unsteady MHD Non-Newtonian (Walters’B) Fluid in Porous Medium,” Abstract and Applied Analysis, 2016, 9262518 (2016).Google Scholar
43. Ali, F., Sheikh, N. A., Saqib, M. and Khan, A., “Hidden Phenomena of an MHD Unsteady Flow in Porous Medium with Heat Transfer,” Nonlinear Science Letters A, 8, pp. 101–116 (2017).Google Scholar
44. Sutton, G. and Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill, New York, 1965.Google Scholar
45. Meyer, R. C., “On Reducing Aerodynamic Heat-Transfer Rates by Magnetohydrodynamic Technique”, Journal of Aerospace Sciences, 25, pp. 561–566 (1958).Google Scholar