Document Type : Article

**Authors**

Mechanical Engineering Department, University of Kashan, Kashan, Iran

**Abstract**

Forced convection fluid flow and heat transfer is investigated in a porous channel with expanding or contracting walls with which is filled Al_{2}O_{3}-Cu/water micropolar hybrid nanofluid in the presence of magnetic field. In order to solve the governing equations analytically, the least square method is employed. The hot bottom wall is cooled by the coolant fluid which is injected into the channel from the top wall. The range of nanoparticles volume fraction (90% Al_{2}O_{3} and 10% Cu by volume) is between 0% and 2%. The effects of consequential parameters such as Reynolds number, Hartmann number, micro rotation factor and nanoparticles volume fraction on velocity and temperature profiles are examined. The results show that with increasing Reynolds number, the values of temperature and micro rotation profiles decrease. Furthermore, when the hybrid nanofluid is used compared to common nanofluid, the heat transfer coefficient will increase significantly. It is also observed that when the Hartmann number increases, Nusselt number increases, too.

**Keywords**

**Main Subjects**

References

1. Aziz, A. and Bouaziz, M.N. \A least square method for a longitudinal n with tempreture dependent internal M. Mollamahdi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 208{220 219 heat generation and thermal conductivity", Energy

Convers. Manage., 52(8-9), pp. 2876-2882 (2011).

1. Aziz, A. and Bouaziz, M.N. \A least square method for a longitudinal n with tempreture dependent internal M. Mollamahdi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 208{220 219 heat generation and thermal conductivity", Energy

Convers. Manage., 52(8-9), pp. 2876-2882 (2011).

2. Hatami, M. and Ganji, D.D. \Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu-water nano fl uid using porous media approach and least square method", Energy Convers. Manage., 78, pp. 347-358 (2014).

3. Hatami, M. and Ganji, D.D. \Natural convection of

sodium alginate (SA) non-Newtonian nanofluid flow between two vertical at plates by analytical and

numerical methods", Case Studies in Thermal Engineering,

2, pp. 14-22 (2014).

4. Ghasemi, S.E., Hatami, M., Mehdizadeh Ahangar,

GH.R. and Ganji, D.D. \Electrohydrodynamic

ow

analysis in a circular cylindrical conduit using least

square method", Journal of Electrostatics, 72, pp. 47-

52 (2014).

5. Hatami, M., Sheikholeslami, M., Hosseini, M.

and Ganji, D.D. \Analytical investigation of MHD

nano

uid

ow in non-parallel walls", J. Mol. Liq., 194,

pp. 251-259 (2014).

6. Fakour, M., Ganji, D.D. and Abbasi, M. \Scrutiny of

underdeveloped nano

uid MHD

ow and heat conduction

in a channel with porous walls", Case Studies in

Thermal Engineering, 4, pp. 202-214 (2014).

7. Fakour, M., Vahabzadeh, A. and Ganji, D.D. \Study

of heat transfer and

ow of nano

uid in permeable

channel in the presence of magnetic eld", Propulsion

and Power Research, 4, pp. 50-62 (2015).

8. Darzi, M., Vatani, M., Ghasemi, S.E. and Ganji

D.D. \Eect of thermal radiation on velocity and

temperature elds of a thin liquid lm over a stretching

sheet in a porous medium", Phys. J. Plus, 130(5), pp.

89-100 (2015).

9. Abbaszadeh, M., Ababaei, A., Abbasian Arani, A.A.

and Abbasi Sharifabadi, A. \MHD forced convection

and entropy generation of CuO-water nano

uid in a

microchannel considering slip velocity and temperature

jump", J. Braz. Soc. Mech. Sci. Eng., 36(9), pp.

775-790 (2016).

10. Sheikhzadeh, G., Aghaei, A., Ehteram, H. and Abbaszadeh,

M. \Analytical study of parameters aecting

entropy generation of nano

uid turbulent

ow in

channel and micro-channel", Thermal Sci., 20(6), pp.

2037-2050 (2016).

11. Sheikhzadeh, G., Ghasemi, H. and Abbaszadeh,

M. \Investigation of natural convection boundary

layer heat and mass transfer of MHD water-AL2O3

nano

uid in a porous medium", International Journal

of Nano Studies & Technology (IJNST), 5, pp. 110-122

(2016).

12. Rahmati, A., Roknabadi, A.R. and Abbaszadeh, M.

\Numerical simulation of mixed convection heat transfer

of nano

uid in a double lid-driven cavity using

lattice Boltzmann method", Alexandria Engineering

Journal, 55(4), pp. 3101-3114 (2016).

13. Wang, X., Xu, X. and Choi, S. \Thermal conductivity

of nanoparticle-

uid mixture", J. Thermophys Heat

Transfer., 13, pp. 474-480 (1999).

14. Selvakumar, P. and Suresh, S. \Use of Al2O3-Cu/water

hybrid nano

uid in an electronic heat sink, components",

Packaging and Manufacturing Technology, 2,

pp. 1600-1607 (2012).

15. Madhesh, D., Parameshwaran, R. and Kalaiselvam, S.

\Experimental investigation on convective heat transfer

and rheological characteristics of Cu-TiO2 hybrid

nano

uids", Exp. Therm Fluid Sci., 52, pp. 104-115

(2014).

16. Esfe, M.H., Abbasian Arani, A.A., Rezaie, M., Yan,

W. and Karimipour, A. \Experimental determination

of thermal conductivity and dynamic viscosity of Ag-

MgO/water hybrid nano

uid", International Communications

in Heat and Mass Transfer, 66, pp. 189-195

(2015).

17. Ho, C.J., Huang, J.B., Tsai, P.S. and Yang, Y.M.

\Preparation and properties of hybrid water-based suspension

of Al2O3 nanoparticles and MEPCM particles

as functional forced convection

uid", International

Communications in Heat and Mass Transfer, 37, pp.

490-494 (2010).

18. Suresh, S., Venkitaraj, K.P., Selvakumar, P. and Chandrasekar,

M. \Synthesis of Al2O3-Cu/water hybrid

nano

uids using two step method and its thermo

physical properties", Colloids and Surfaces A: Physicochemical

and Engineering Aspects, 388, pp. 41-48

(2011).

19. Suresh, S., Venkitaraj, K.P., Selvakumar, P. and

Chandrasekar, M. \Eect of Al2O3-Cu/water hybrid

nano

uid in heat transfer", Exp. Therm Fluid Sci., 38,

pp. 54-60 (2012).

20. Abbasia, S.M., Rashidib, A., Nematia, A. and Arzania,

K. \The eect of functionalisation method on the

stability and the thermal conductivity of nano

uid hybrids

of carbon nanotubes/gamma alumina", Ceram.

Int., 39, pp. 3885-3891 (2013).

21. Balla, H., Abdullah, S., MohdFaizal, W., Zulki

i, R.

and Sopian, K. \Numerical study of the enhancement

of heat transfer for hybrid CuO-Cu nano

uids

owing

in a circular pipe", Journal of Oleo Science, 62, pp.

533-539 (2013).

22. Takabi, B. and Salehi, S. \Augmentation of the heat

transfer performance of a sinusoidal corrugated enclosure

by employing hybrid nano

uid", Advances in

Mechanical Engineering, 6, pp. 1459-1470 (2014).

23. Moghadassi, A., Ghomi, E. and Parvazian, F. \A

numerical study of water based Al2O3 and Al2O3-

Cu hybrid nano

uid eect on forced convective heat

transfer", Int. J. Therm. Sci., 92, pp. 50-57 (2015).

24. Mollamahdi, M., Abbaszadeh, M. and Sheikhzadeh,

G.A. \Flow eld and heat transfer in a channel with a

permeable wall lled with Al2O3-Cu/water micropolar

hybrid nano

uid, eects of chemical reaction and

magnetic eld", Journal of Heat and Mass Transfer

Research, 3(2), pp. 101-114 (2016).

220 M. Mollamahdi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 208{220

25. Eringen, A.C., Journal of Mathematical Analysis and

Applications, 16, pp. 1-18 (1966).

26. Nadeem, S., Rehman, A., Vajravelu, K., Lee, J. and

Lee, C. \Axisymmetric stagnation

ow of a micropolar

nano

uid in a moving cylinder", Hindawi Publishing

Corporation, Mathematical Problems in Engineering

(2012).

27. Si, X., Zheng, L., Lin, P., Zhang, X. and Zhang, Y.

\Flow and heat transfer of a micropolar

uid in a

porous channel with expanding or contracting walls",

Int. J. Heat. Mass. Tran., 67, pp. 885-895 (2013).

28. Bourantas, G.C. and Loukopoulos, V.C. \Modeling the

natural convective

ow of micropolar nano

uids", Int.

J. Heat. Mass. Tran., 68, pp. 35-41(2014).

29. Sheikholeslami, M., Ashorynejad, H.R., Ganji, D.D.

and Rashidi, M.M. \Heat and mass transfer of a micropolar

uid in a porous channel", Communications

in Numerical Analysis, pp. 1-20 (2014).

30. Cao, L., Si, X. and Zheng, L. \The

ow of a micropolar

uid through a porous expanding channel: A Lie

group analysis", Applied Mathematics and Computation,

270, pp. 242-250 (2015).

31. Das, S.K., Choi, S.U.S., Yu, W. and Predeep, T.,

Nano

uids Science and Technology, John Wiley &

Sons (2008).

32. Nimmagadda, R. and Venkatasubbaiah, K. \Conjugate

heat transfer analysis of micro-channel using novel

hybrid nano

uids", European Journal of Mechanics-

B/Fluids, 52, pp. 19-27 (2015).

33. Xuan, Y. and Roetzel, W. \Conceptions for heat

transfer correlations of nano

uids", Int. J Heat. Mass.

Tran., 43, pp. 3701-3707 (2000).

34. Aghaei, A., Khorasanizadeh, H., Sheikhzadeh, G. and

Abbaszadeh, M. \Numerical study of magnetic eld on

mixed convection and entropy generation of nano

uid

in a trapezoidal enclosure", J. Magn. Magn. Mater.,

403, pp. 133-145 (2016).

35. 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).

36. Zhang, C., Zheng, L., Zhang, X. and Chen, G. \MHD

ow and radiation heat transfer of nano

uids in porous

media with variable surface heat

ux and chemical

reaction", Applied Mathematical Modeling, 39(1), pp.

165-181 (2015).

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

\Micropolar

uid

ow and heat transfer in a permeable

channel using analytical method", J. Mol. Liq., 194,

pp. 30-36 (2014).

38. Majdalani, J., Zhou, Zamm. C. and Angew, Z., Math.

Mech., 83, pp. 181-196 (2003).

39. Aziz, A., Heat Conduction with Maple, Philadelphia

(PA): RT Edwards (2006).

40. Maxwell, J.C., A Treatise on Electricity and Magnetism

(1881).

41. Brinkman, H.C. \The viscosity of concentrated suspensions

and solutions", The Journal of Chemical al

Physic, 20, p. 571 (1952).

42. Arefmanesh, A. and Mahmoodi, M. \Eects of uncertainties

of viscosity models for Al2O3-water nano

uid

on mixed convection numerical simulations", Int. J.

Therm. Sci., 50, pp. 1706-1719 (2011).

sodium alginate (SA) non-Newtonian nanofluid flow between two vertical at plates by analytical and

numerical methods", Case Studies in Thermal Engineering,

2, pp. 14-22 (2014).

4. Ghasemi, S.E., Hatami, M., Mehdizadeh Ahangar,

GH.R. and Ganji, D.D. \Electrohydrodynamic

ow

analysis in a circular cylindrical conduit using least

square method", Journal of Electrostatics, 72, pp. 47-

52 (2014).

5. Hatami, M., Sheikholeslami, M., Hosseini, M.

and Ganji, D.D. \Analytical investigation of MHD

nano

uid

ow in non-parallel walls", J. Mol. Liq., 194,

pp. 251-259 (2014).

6. Fakour, M., Ganji, D.D. and Abbasi, M. \Scrutiny of

underdeveloped nano

uid MHD

ow and heat conduction

in a channel with porous walls", Case Studies in

Thermal Engineering, 4, pp. 202-214 (2014).

7. Fakour, M., Vahabzadeh, A. and Ganji, D.D. \Study

of heat transfer and

ow of nano

uid in permeable

channel in the presence of magnetic eld", Propulsion

and Power Research, 4, pp. 50-62 (2015).

8. Darzi, M., Vatani, M., Ghasemi, S.E. and Ganji

D.D. \Eect of thermal radiation on velocity and

temperature elds of a thin liquid lm over a stretching

sheet in a porous medium", Phys. J. Plus, 130(5), pp.

89-100 (2015).

9. Abbaszadeh, M., Ababaei, A., Abbasian Arani, A.A.

and Abbasi Sharifabadi, A. \MHD forced convection

and entropy generation of CuO-water nano

uid in a

microchannel considering slip velocity and temperature

jump", J. Braz. Soc. Mech. Sci. Eng., 36(9), pp.

775-790 (2016).

10. Sheikhzadeh, G., Aghaei, A., Ehteram, H. and Abbaszadeh,

M. \Analytical study of parameters aecting

entropy generation of nano

uid turbulent

ow in

channel and micro-channel", Thermal Sci., 20(6), pp.

2037-2050 (2016).

11. Sheikhzadeh, G., Ghasemi, H. and Abbaszadeh,

M. \Investigation of natural convection boundary

layer heat and mass transfer of MHD water-AL2O3

nano

uid in a porous medium", International Journal

of Nano Studies & Technology (IJNST), 5, pp. 110-122

(2016).

12. Rahmati, A., Roknabadi, A.R. and Abbaszadeh, M.

\Numerical simulation of mixed convection heat transfer

of nano

uid in a double lid-driven cavity using

lattice Boltzmann method", Alexandria Engineering

Journal, 55(4), pp. 3101-3114 (2016).

13. Wang, X., Xu, X. and Choi, S. \Thermal conductivity

of nanoparticle-

uid mixture", J. Thermophys Heat

Transfer., 13, pp. 474-480 (1999).

14. Selvakumar, P. and Suresh, S. \Use of Al2O3-Cu/water

hybrid nano

uid in an electronic heat sink, components",

Packaging and Manufacturing Technology, 2,

pp. 1600-1607 (2012).

15. Madhesh, D., Parameshwaran, R. and Kalaiselvam, S.

\Experimental investigation on convective heat transfer

and rheological characteristics of Cu-TiO2 hybrid

nano

uids", Exp. Therm Fluid Sci., 52, pp. 104-115

(2014).

16. Esfe, M.H., Abbasian Arani, A.A., Rezaie, M., Yan,

W. and Karimipour, A. \Experimental determination

of thermal conductivity and dynamic viscosity of Ag-

MgO/water hybrid nano

uid", International Communications

in Heat and Mass Transfer, 66, pp. 189-195

(2015).

17. Ho, C.J., Huang, J.B., Tsai, P.S. and Yang, Y.M.

\Preparation and properties of hybrid water-based suspension

of Al2O3 nanoparticles and MEPCM particles

as functional forced convection

uid", International

Communications in Heat and Mass Transfer, 37, pp.

490-494 (2010).

18. Suresh, S., Venkitaraj, K.P., Selvakumar, P. and Chandrasekar,

M. \Synthesis of Al2O3-Cu/water hybrid

nano

uids using two step method and its thermo

physical properties", Colloids and Surfaces A: Physicochemical

and Engineering Aspects, 388, pp. 41-48

(2011).

19. Suresh, S., Venkitaraj, K.P., Selvakumar, P. and

Chandrasekar, M. \Eect of Al2O3-Cu/water hybrid

nano

uid in heat transfer", Exp. Therm Fluid Sci., 38,

pp. 54-60 (2012).

20. Abbasia, S.M., Rashidib, A., Nematia, A. and Arzania,

K. \The eect of functionalisation method on the

stability and the thermal conductivity of nano

uid hybrids

of carbon nanotubes/gamma alumina", Ceram.

Int., 39, pp. 3885-3891 (2013).

21. Balla, H., Abdullah, S., MohdFaizal, W., Zulki

i, R.

and Sopian, K. \Numerical study of the enhancement

of heat transfer for hybrid CuO-Cu nano

uids

owing

in a circular pipe", Journal of Oleo Science, 62, pp.

533-539 (2013).

22. Takabi, B. and Salehi, S. \Augmentation of the heat

transfer performance of a sinusoidal corrugated enclosure

by employing hybrid nano

uid", Advances in

Mechanical Engineering, 6, pp. 1459-1470 (2014).

23. Moghadassi, A., Ghomi, E. and Parvazian, F. \A

numerical study of water based Al2O3 and Al2O3-

Cu hybrid nano

uid eect on forced convective heat

transfer", Int. J. Therm. Sci., 92, pp. 50-57 (2015).

24. Mollamahdi, M., Abbaszadeh, M. and Sheikhzadeh,

G.A. \Flow eld and heat transfer in a channel with a

permeable wall lled with Al2O3-Cu/water micropolar

hybrid nano

uid, eects of chemical reaction and

magnetic eld", Journal of Heat and Mass Transfer

Research, 3(2), pp. 101-114 (2016).

220 M. Mollamahdi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 208{220

25. Eringen, A.C., Journal of Mathematical Analysis and

Applications, 16, pp. 1-18 (1966).

26. Nadeem, S., Rehman, A., Vajravelu, K., Lee, J. and

Lee, C. \Axisymmetric stagnation

ow of a micropolar

nano

uid in a moving cylinder", Hindawi Publishing

Corporation, Mathematical Problems in Engineering

(2012).

27. Si, X., Zheng, L., Lin, P., Zhang, X. and Zhang, Y.

\Flow and heat transfer of a micropolar

uid in a

porous channel with expanding or contracting walls",

Int. J. Heat. Mass. Tran., 67, pp. 885-895 (2013).

28. Bourantas, G.C. and Loukopoulos, V.C. \Modeling the

natural convective

ow of micropolar nano

uids", Int.

J. Heat. Mass. Tran., 68, pp. 35-41(2014).

29. Sheikholeslami, M., Ashorynejad, H.R., Ganji, D.D.

and Rashidi, M.M. \Heat and mass transfer of a micropolar

uid in a porous channel", Communications

in Numerical Analysis, pp. 1-20 (2014).

30. Cao, L., Si, X. and Zheng, L. \The

ow of a micropolar

uid through a porous expanding channel: A Lie

group analysis", Applied Mathematics and Computation,

270, pp. 242-250 (2015).

31. Das, S.K., Choi, S.U.S., Yu, W. and Predeep, T.,

Nano

uids Science and Technology, John Wiley &

Sons (2008).

32. Nimmagadda, R. and Venkatasubbaiah, K. \Conjugate

heat transfer analysis of micro-channel using novel

hybrid nano

uids", European Journal of Mechanics-

B/Fluids, 52, pp. 19-27 (2015).

33. Xuan, Y. and Roetzel, W. \Conceptions for heat

transfer correlations of nano

uids", Int. J Heat. Mass.

Tran., 43, pp. 3701-3707 (2000).

34. Aghaei, A., Khorasanizadeh, H., Sheikhzadeh, G. and

Abbaszadeh, M. \Numerical study of magnetic eld on

mixed convection and entropy generation of nano

uid

in a trapezoidal enclosure", J. Magn. Magn. Mater.,

403, pp. 133-145 (2016).

35. 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).

36. Zhang, C., Zheng, L., Zhang, X. and Chen, G. \MHD

ow and radiation heat transfer of nano

uids in porous

media with variable surface heat

ux and chemical

reaction", Applied Mathematical Modeling, 39(1), pp.

165-181 (2015).

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

\Micropolar

uid

ow and heat transfer in a permeable

channel using analytical method", J. Mol. Liq., 194,

pp. 30-36 (2014).

38. Majdalani, J., Zhou, Zamm. C. and Angew, Z., Math.

Mech., 83, pp. 181-196 (2003).

39. Aziz, A., Heat Conduction with Maple, Philadelphia

(PA): RT Edwards (2006).

40. Maxwell, J.C., A Treatise on Electricity and Magnetism

(1881).

41. Brinkman, H.C. \The viscosity of concentrated suspensions

and solutions", The Journal of Chemical al

Physic, 20, p. 571 (1952).

42. Arefmanesh, A. and Mahmoodi, M. \Eects of uncertainties

of viscosity models for Al2O3-water nano

uid

on mixed convection numerical simulations", Int. J.

Therm. Sci., 50, pp. 1706-1719 (2011).

Transactions on Mechanical Engineering (B)

January and February 2018Pages 208-220