MHD forced convection ow and heat transfer of ferro fluids over a moving at plate with uniform heat flux and second-order slip effects

Document Type : Article


1 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

2 Faculty of Mathematics and Computer Science, Babes-Bolyai University, 400084 Cluj-Napoca, Romania


In this study, the problem of two-dimensional forced convection MHD flow and heat transfer of ferro fluids over a moving  at plate with the influence of uniform heat flux and secondorder slip eff ects is considered. By applying the similarity transformation, the governing equations are reconstructed into the similarity equations and the resulting equations are solved via shooting technique. Then, we implement a stability analysis in order to verify which solutions are stable and physically realizable. The e ects of the magnetic parameter,
moving parameter, mass transfer parameter, rst-order surface slip parameter, second-order surface slip parameter and volume fraction of solid ferroparticles on the dimensionless velocity, temperature, skin friction and Nusselt numbers are discussed in the form of tabular and graphical presentation. For this present study, we consider the results based on three preferred ferroparticles, namely magnetite, cobalt ferrite and Mn-Zn ferrite in water- and kerosene-based fluids. The results display the existence of dual solutions for a plate moving towards the origin in which the rst solution is stable and physically realizable, while the second solution is not. Moreover, it is demonstrated that the magnetic, moving, mass transfer and slip eff ects together with the volume fraction of ferro fluids delay the boundary layer separation.


Main Subjects

1. Choi, S.U.S. \Enhancing thermal conductivity of
with nanoparticles", Dev. Appl. Non-Newtonian
Flows, 231, pp. 99-105 (1995).
2. Xuan, Y. and Li, Q. \Heat transfer enhancement of
uids", Int. J. Heat Fluid Flow, 21, pp. 58-64
3. Tiwari, R. and Das, M. \Heat transfer augmentation in
a two-sided lid-driven di erentially heated square cavity
utilizing nano
uids", Int. J. Heat Mass Transfer,
50, pp. 2002-2018 (2007).
4. Ahmad, S., Rohni, A., and Pop, I. \Blasius and
Sakiadis problems in nano
uids", Acta Mech, 218, pp.
195-204 (2011).
5. Tangthieng, C., Finlayson, B., Maulbetsch, J., and
Cader, T. \Heat transfer enhancement in ferro
subjected to steady magnetic elds", J. Magn. Magn.
Mater, 201, pp. 252-255 (1999).
6. Kuncser, V., Schinteie, G., Sahoo, B., Keune, W.,
Bica, D., Vekas, L., and Filoti, G. \Magnetic interactions
in water based ferro
uids studied by Mossbauer
spectroscopy", J. Phys.: Condens. Matter, 19(1), pp.
016205-016221 (2007).
7. Li, M., Shi, H., and Zhu, L. \Boundary layer velocity
distribution of two special ferromagnetic
uid", Proc.
Eng., 31, pp. 166-169 (2012).
8. Khan, W.A., Khan, Z.H., and Haq, R.U. \Flow and
heat transfer of ferro
uids over a
at plate with
uniform heat
ux", Eur. Phys. J. Plus, 130(86), 10
pages (2015).
9. Sheremet, M.A., Pop, I., and Rosca, N.C. \Magnetic
eld e ect on the unsteady natural convection in a
wavy-walled cavity lled with a nano
uid: Buongiorno's
mathematical model", J. Taiwan Institute
Chemical Engineers, 61, pp. 211-222 (2016).
10. Bondareva, N.S., Sheremet, M.A., and Pop, I. \Magnetic
eld e ect on the unsteady natural convection in
a right-angle trapezoidal cavity lled with a nano
Buongiorno's mathematical model", Int. J. Numerical
Methods Heat Fluid Flow, 25, pp. 1924-1946 (2015).
11. Rosca, A.V. and Pop, I. \Flow and heat transfer over
a vertical permeable stretching/shrinking sheet with a
second order slip", Int. J. Heat Mass Transfer, 60, pp.
355-364 (2013).
N. Ramli et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2186{2197 2197
12. Weidman, P.D., Kubitschek, D.G., and Davis, A.M.J.
\The e ect of transpiration on self-similar boundary
ow over moving surfaces", Int. J. Engng. Sci.,
44, pp. 730-737 (2006).
13. Harris, S.D., Ingham, D.B., and Pop, I. \Mixed convection
ow near the stagnation point on a
vertical surface in a porous medium: Brinkman model
with slip", Transport Porous Media, 77, pp. 267-285
14. Cortell, R. \Numerical solutions of the classical Blasius

at-plate problem", Appl. Math. Comput., 170, pp.
706-710 (2005).
15. Yazdi, M., Abdullah, S., Hashim, I., and Sopian,
K. \E ects of viscous dissipation on the slip MHD

ow and heat transfer past a permeable surface with
convective boundary conditions", Energies, 4, pp.
2273-2294 (2011).