Document Type : Article

**Authors**

Department of Physics, University of Isfahan, Isfahan, Iran

**Abstract**

In the present study, the mixed convection Flow of nano Fluid in a lid-driven parallelogramic porous enclosure subjected to a magnetic Field is investigated numerically. Induced magnetic Field is also considered, in terms of the magnetic potential, in solving the magnetohydrodynamic (MHD) Flow and temperature equations. The Darcy-Brinkman-Forchheimer model with the Boussinesq approximation is adopted and the Finite volume method based on SIMPLE algorithm is utilized to solve the governing equations with the appropriate boundary conditions in an orthogonal computational domain. The governing equations in a non-orthogonal physical domain are transformed into a computational domain in an orthogonal co-ordinate by co-ordinate transformations. It has been shown that the Flow Field and heat transfer are sensible greatly to the skew angle variation. Magnetic potential circulates through the parallelogramic porous enclosure with either high either magnetic Reynolds number or magnetic permeability of the nano Fluid. Results also indicate that the influence of external magnetic Field on Fluid characteristics and heat transfer manifests variety fashions mainly depends on the effective area of the parallelogramic enclosure. Besides, the variation in rates of heat transfer while adding nanoparticles or applying magnetic Field are affected to some extent by porous medium permeability and Richardson number.

**Keywords**

- Parallelogramic enclosure
- MHD mixed convection
- porous media
- Nano Fluid
- Heat Transfer
- Magnetic potential

**Main Subjects**

1. Nield, D.A. and Bejan, A., Convection in Porous

Media, 4th Edition, New York, Springer (2013).

2. Sahoo, S.N., Panda, J.P., and Dash, G.C. The MHD

mixed convection stagnation point

ow and heat transfer

in a porous medium", In Proceedings of National

Academy Sciences, India, Section A Physical Sciences,

83, pp. 371-381 (2013).

3. Shermet, M.A. and Pop, I. Thermo-Bi convection in

a square porous cavity lled by oxytactic microorganisms",

Trans. Porous Media, 103, pp. 191-205 (2014).

4. Ghalambaz, M., Moattar, F., Shermet, M.A., and

Pop, I. Triple-diusive natural convection in a square

porous cavity", Trans. Porous Media, 111, pp. 59-79

(2016).

5. Mahmoud, A., Mejri, I., Abbasi, M.A., and Omri, A.

Analysis of MHD natural convection in a nano

uid-

lled open cavity with non-uniform boundary condition

in the presence of uniform heat generation/

absorption", Powder Technol., 269, pp. 275-289

(2015).

6. Sheikholeslami, M., Hatami, M., and Ganji, D.D.

Analytical investigation of MHD nano

uid

ow in a

semi-porous channel", Powder Technol., 246, pp. 327-

336 (2013).

7. Servati, A.A., Javaherdeh, K., and Ashorynejad, H.R.

Magnetic eld eects on force convection

ow of a

nano

uid in a channel partially lled with porous

media using lattice Boltzmann method", Adv. Powder

Technol., 25, pp. 666-675 (2014).

8. Choi, S.U.S. Enhancing thermal conductivity of

uid

with nanoparticles", ASME Fluid Eng. Div., 23, pp.

99-105 (1995).

9. Fersadou, I., Kahalerras, H., and El Ganaoui, M.

MHD mixed convection and entropy generation of a

nano

uid in a vertical porous channel", Computers and

Fluids, 121, pp. 164-179 (2015).

10. Ziaei-Rad, M., Saeedan, M., and Afshari, E. Simulation

and prediction of MHD dissipative nano

uid

ow

on a permeable stretching surface using articial neural

network", Appl. Thermal Eng., 99, pp. 373-382 (2016).

11. Ziaei-Rad, M., Kasaeipoor, A., Rashidi, M.M., and

Lorenzini, G. A similarity solution for mixedconvection

boundary layer nano

uid

ow permeable

surface", J. Thermal Sci. Eng. Appl., 9, p. 021015

(2017).

12. Zeeshan, A., Ellahi, R., and Hasan, M. Magnetohydrodynamic

ow of water/ethylene glycol based

nano

uids with natural convection through a porous

medium", The European Physical Journal Plus, 129,

pp. 261-271 (2014).

13. Murthy, P.V.S.N., Reddy C., Chamkha, A.J., and

Rashad. A.M. Magnetic eect on thermally stratied

nano

uid saturated non-Darcy porous medium under

convective boundary condition", Int. Comm. Heat

Mass Transfer, 47, pp. 41-48 (2013).

14. Pekmen, B. and Tezer-Sezgin, M. DRBEM solution

of free convection in porous enclosure under the eect

of a magnetic eld", Int. J. Heat Mass Transfer, 56,

pp. 454-468 (2013).

15. Shermet, M.A., Grosan, T., and Pop, I. Free convection

in a square cavity lled with a porous medium

saturated by nano

uid using Tiwari and Das nano

uid

model", Trans. Porous Media, 106, pp. 595-610

(2015).

16. Mabood, F., Shateyi, S., Rashidi, M.M., Momoniat,

E., and Freidoonimehr, N. MHD stagnation point

ow

heat and mass transfer of nano

uids in porous medium

with radiation, viscous dissipation and chemical reaction",

Adv. Powder Technol., 27, pp. 742-749 (2016).

17. Sarris, I.E., Zikos, G.K., Grecos, A.P., and Vlachos,

N.S. On the limits of validity of the low magnetic

Reynolds number approximation in MHD naturalconvection

heat transfer", Num. Heat Transfer, Part

B: Fundamentals: An International Journal of Computation

and Methodology, 50, pp. 157-180 (2006).

18. Bari, A., Zarco-Pernia, E., and Garcia de Maria, J.-

M. A review of natural convection in enclosures for

1806 O. Ghaarpasand and D. Fazeli/Scientia Iranica, Transactions F: Nanotechnology 25 (2018) 1789{1807

engineering applications: The particular case of the

parallelogrammic diode cavity", Appl. Ther. Eng., 63,

pp. 304-322 (2014).

19. Singh, R.K., Singh, A.K., Sacheti, N.C., and Chandran,

P. On hydromagnetic free convection in the

presence of induced magnetic eld", Heat Mass Transfer,

46, pp. 523-529 (2010).

20. Costa, V.A.F., Sousa, A.C.M., and Vasseur, P. Natural

convection in square enclosures lled with

uidsaturated

porous media under the in

uence of the

magnetic eld induced by two parallel vertical electric

currents", Int. J. Heat Mass Transfer, 55, pp. 7321-

7329 (2012).

21. Kumar, A. and Singh, A.K. Unsteady MHD free

convective

ow past a semi-innite vertical wall with

induced magnetic eld", Appl. Math. Comput., 222,

pp. 462-471 (2013).

22. Akbar, N.S., Raza, M., and Ellahi, R. Interaction of

nanoparticles for the peristaltic

ow in an asymmetric

channel with the induced magnetic eld", The European

Physical Journal Plus, 129, pp. 155-167 (2014).

23. Akbar, N.S., Raza, M., and Ellahi, R. In

uence

of heat generation and heat

ux on peristaltic

ow

with interacting nanoparticles", The European Physical

Journal Plus, 129, pp. 185-190 (2014).

24. Pekmen, B. and Tezer-Sezgin, M. MHD

ow and heat

transfer in a lid driven porous enclosure", Computers

and Fluids, 89, pp. 191-199 (2014).

25. Seth, G.S. and Sarkar, S. Hydromagnetic natural

convection

ow with induced magnetic eld and nth

order chemical reaction of a heat absorbing

uid past

an impulsively moving vertical plate with ramped

temperature", Bul. Chem. Commun., 47, pp. 66-79

(2015).

26. Kumar, V.A. Numerical study of eect of induced

magnetic eld on transient natural convection over a

vertical cone", Alexandria Eng. J., 55 pp. 1211-1223

(2016).

27. Demirdzic, I., Lilek, Z., and Peric, M. Fluid

ow and

heat transfer test problems for non-orthogonal grids:

bench-mark solutions", Int. J. Num. Meth. Fluids, 15,

pp. 329-354 (1992).

28. Roychowdhury, D.G., Das, S.K., and Sundarsrajan,

T. An ecient solution method for incompressible

Navier-Stokes equations using non-orthogonal collected

grid", Int. J. Num. Methods Eng., 45, pp. 741-

763 (1999).

29. Wang, Y. and Komori, S. On the improvement of

the SIMPLE-Like method for

ows with complex

geometry", Heat Mass Transfer, 36, pp. 71-78 (2000).

30. Qu, Z.G., Tao, W.Q., and Hw, Y.L. An improved

numerical scheme for the SIMPLER method on

nonorthogonal curvilinear coordinates: SIMPLER",

Num. Heat Transfer Part B: Fundamentals, 51, pp.

43-66 (2007).

31. Costa, V.A.F. Double-diusive natural convection

in parallelogrammic enclosure", Int. J. Heat Mass

Transfer, 47, pp. 2913-2926 (2006).

32. Al-Farhany, K. and Turan, A. Numerical study of

double diusive natural convective heat and mass

transfer in an inclined rectangular cavity lled with

porous medium", Int. Commun. Heat Mass Transfer,

39, pp. 174-181 (2012).

33. Chamkha, A.J., Hussain, S.H., and Ali, F.H.

Conduction-combined forced and natural convection

in a lid-driven parallelogram-shaped enclosure divided

by a solid partition", Progress in Comput. Fluid Dyn.,

12, pp. 309-321 (2012).

34. Jagadeesha, R.D., Prasanna, B.M.R., and Sarkar, M.

Double diusive convection in an inclined parallelogrammic

porous enclosure", Procedia Engineering,

127, pp. 1346-1353 (2015).

35. Le Dez, V. and Sadat, H. Radiation heat transfer in

a parallelogram shaped cavity", Int. Commun. Heat

Mass Transfer, 68, pp. 137-149 (2015).

36. Hussein, S.H. and Hussain, A.K. Natural convection

heat transfer enhancement in a dierentially

heated parallegramic enclosure lled with copperwater

nano

uid", ASME J. Heat Transfer, 136, pp.

82502-82508 (2014).

37. Nayak, R.K., Bhattacharyya, S., and Pop, I. Numerical

study on mixed convection and entropy generation

of Cu-water nano

uid in a dierentially heated skewed

enclosure", Int. J. Heat Mass Transfer, 85, pp. 620-634

(2015).

38. Ghaarpasand, O. Conjugate eect of Joule heating

and unsteady MHD natural convection in a dierentially

heated skewed porous cavity saturated by Cuwater

nano

uid", J. Appl. Fluid Mech., 9, pp. 2823-

2836 (2016).

39. Tiwari, R.K. and Das. M.K. Heat transfer augmentation

in a two-sided lid-driven dierentially heated

square cavity utilizing nano

uids", Int. J. Heat Mass

Transfer, 50, pp. 2002-2018 (2007).

40. Hamilton, R.I. and Crosser, O.K. Thermal conductivity

of heterogeneous two-component systems", Ind.

Eng. Chem. Fund., 1, pp. 187-191 (1962).

41. Abu-Nada, E. and Chamkha, A.J. Mixed convection

ow of a nano

uid in a lid-driven cavity with wavy

wall", Int. Commun. Heat Mass Transfer, 57, pp. 36-

47 (2014).

42. Mahmoud, A., Mejri, I., Abbasi, M.A., and Omri, A.

Analysis of MHD natural convection in a nano

uid-

lled open cavity with non-uniform boundary condition

in the presence of uniform heat generation/

absorption", Powder Technol., 269, pp. 275-289

(2015).

43. Mehrez, Z., Cafsi, A.E., Belghith, A., Quere, P.Le.

MHD eects and entropy generation of nano

fluid

flow

in an open cavity", J. Mag. Mag. Mat., 374, pp. 214-

224 (2015).

Transactions on Nanotechnology (F)

May and June 2018Pages 1789-1807