Effect of thermal radiation on magneto-nanofluids free convective flow over an ac-celerated moving ramped temperature plate

Document Type : Article

Authors

1 Department of Mathematics, O.P. Jindal university, Raigarh (C.G.), INDIA

2 Department of Applied Mathematics, Government Engineering College, Bastar (C.G.), INDIA

3 Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, INDIA

4 Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management System, Tongji University, Shanghai-201804, CHINA

Abstract

An attempt has been made to explore the effect of thermal radiation on electrically conducting, viscous and incompressible magneto-nanofluids free convective flow in the presence of an inclined magnetic field. Fluid flow is persuaded due to an accelerated movement of an infinite vertical ramped temperature plate. The water based nanofluids with the nanoparticles of alumina (Al2O3), copper (Cu) and titanium oxide (TiO2) have been accounted. In order to model the problem mathematically, the model of nanoparticle volume fraction has been employed. The exact solution of the mathematical model in closed form has been obtained analytically by making use of Laplace transform technique. The amalgamated form expressions are obtained for nanofluid velocity, nanofluid temperature, skin friction and Nusselt number, in both ramped and isothermal conditions. The consequence of various physical parameters affecting the nanofluid velocity and nanofluid temperature have examined by means of various graphs whereas, the numerical values of skin friction and Nusselt number have been reported by different tables. The numerical results have been compared for both ramped and isothermal conditions. It has been noticed that both the nanofluid velocity and temperature are smaller in magnitude in the case of ramped temperature plate than that of isothermal plate.

Keywords

Main Subjects


References
1. Choi, S.U.S. \Enhancing thermal conductivity of
uids
with nanoparticles, developments and applications of
non-Newtonian
ows", ASME FED 231/MD, 66, pp.
99-105 (1995).
2. Wang, X-Q. and Majumdar, A.S. \A review on
nano
uids-Part I: Theoretical and numerical investigations",
Braz. J. Chem. Eng., 25(4), pp. 613-630 (2008).
3. Eastman, J.A., Choi, S.U.S., Li, S., Thompson, L.J.,
and Lee, S. \Enhanced thermal conductivity through
the development of nano
uids", In Nanophase and
Nanocomposite Materials II, Materials Research Society,
S. Komarneni, J.C. Parker, H.J. Wollenberger,
Eds., Pittsburgh (1997).
4. Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E.,
and Grulke, E.A. \Anomalously thermal conductivity
enhancement in nanotube suspensions", Appl. Phys.
Letters, 79, pp. 2252-2254 (2001).
5. Keblinski, P., Phillpot, S.R., Choi, S.U.S., and Eastman,
J.A. \Mechanism of heat
ow is suspensions of
nano-sized particles (nano
uids)", Int. J. Heat Mass
Transf., 42, pp. 855-863 (2002).
6. Buongiorno, J. \Convective transport in nano
uids",
J. Heat Transf., 128, pp. 240-250 (2006).
7. Jang, S.P. and Choi, S.U.S. \E ects of various parameters
on nano
uid thermal conductivity", J. Heat
Transf., 129, pp. 617-623 (2007).
8. Daungthongsuk, W. and Wongwises, S. \A critical
review of convective heat transfer nano
uids", Renew.
Sustain. Energy Reviews, 11, pp. 797-817 (2007).
9. Seyyedi, S.M., Bararnia, H., Ganji, D.D., GorjiBandpy,
M., and Soleimani, S. \Numerical investigation
of the e ect of a splitter plate on forced convection
in a two dimensional channel with an inclined square
cylinder", Int. J. Thermal Sci., 61(0), pp. 1-14 (2012).
10. Sheikholeslami, M., GorjiBandpy, M., and Ganji, D.D.
\Natural convection in a nano
uid lled concentric
annulus between an outer square cylinder and an inner
elliptic cylinder", Scientia Iranica B, 20(4), pp. 1241-
1253 (2013).
11. Rashidi, M.M., Momoniat, E., Ferdows, M., and
Basiriparsa, A. \Lie group solution for free convective

ow of a nano
uid past a chemically reacting horizontal
plate in a porous media", Mathematical Prob. Eng.
(2014). (Article ID 239082)
12. Garoosi, F., Bagheri, G., and Rashidi, M.M. \Two
phase simulation of natural convection and mixed
convection of the nano
uid in a square cavity", Powder
Tech., 275, pp. 239-256 (2015).
13. Garoosi, F., Rohani, B., and Rashidi, M.M. \Two
phase mixture modeling of mixed convection of
nano
uids in a square cavity with internal and external
heating", Powder Tech., 275, pp. 304-321 (2015).
14. Rahman, S.U., Ellahi, R., Nadeem, S., and Zaigham
Zia, Q.M. \Simultaneous e ects of nano-particles and
slip on Je rey
uid through tapered artery with mild
stenosis", J. Molecular Liquids, 218, pp. 484-493
(2016).
15. Ellahi, R., Hassan, M., and Zeeshan, A. \Aggregation
e ects on water base nano
uid over permeable wedge
in mixed convection", Asia-Paci c J. Chem. Eng.,
11(2), pp. 179-186 (2016).
16. Ellahi, R., Zeeshan, A., and Hassan, M. \Particle
shape e ects on marangoni convection boundary layer

ow of a nano
uid", Int. J. Num. Methods Heat Fluid
Flow, 26(7), pp. 2160-2174 (2016).
17. Hamad, M.A.A. and Pop, I. \Unsteady MHD free
convection
ow past a vertical permeable
at plate in
a rotating frame of reference with constant heat source
in a nano
uid", Heat Mass Transf., 47, pp. 1517-1524
(2011).
18. Chamkha, A.J. and Aly, A.M. \MHD free convection

ow of a nano
uid past a vertical plate in the presence
of heat generation or absorption e ects", Chem. Eng.
Comm., 198, pp. 425-441 (2011).
19. Sheikholeslami, M., Hatami, M., and Ganji, D.D.
\Analytical investigation of MHD nano
uid
ow in a
semiporous channel", Powder Tech., 246, pp. 327-336
(2013).
20. Das, K. \Flow and heat transfer characteristics of
nano
uids in a rotating frame", Alexandria Eng. J.,
53, pp. 757-766 (2014).
21. Sheikholeslami, M., Gorji Bandpy, M., Ellahi, R., and
Zeeshan, A. \Simulation of MHD CuO-water nano
uid

ow and convective heat transfer considering Lorentz
forces", J. Magnetism Magnetic Materials, 369, pp.
69-80 (2014).
22. Sheikholeslami, M., Gorji Bandpy, M., and Ganji,
D.D. \MHD free convection in an eccentric semiannulus
lled with nano
uid", J. Taiwan Inst. Chem.
Engineers, 45, pp. 1204-1216 (2014).
S.M. Hussain et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 1243{1257 1255
23. Sheikholeslami, M. and Ganji, D.D. \Magnetohydrodynamic

ow in a permeable channel lled with
nano
uid", Scientia Iranica B, 21(1), pp. 203-212
(2014).
24. Nandkeolyar, R., Kameswaran, P.K., Shaw, S., and
Sibanda, P. \Heat transfer on nano
uid
ow with
homogeneous-heterogeneous reactions and internal
heat generation", J. Heat Transf., 136, pp. 122001-1
(2014).
25. Reddy, P.S. and Chamkha, A.J. \In
uence of size,
shape, type of nanoparticles, type and temperature of
the base
uid on natural convection MHD of nano
uids",
Alexandria Eng. J., 55, pp. 331-341 (2016).
26. Mahmoudi, A., Mejri, I., Abbassi, 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 uni-form heat generation/
absorption", Powder Tech., 269, pp. 275-289
(2015).
27. Ellahi, R. \The e ects of MHD and temperature
dependent viscosity on the
ow of non-Newtonian
nano
uid in a pipe: Analytical solutions", Appl. Math.
Modelling, 37(3), pp. 1451-1457 (2013).
28. Hayat, T., Muhammad, T., Qayyum, A., Alsaedi, A.,
and Mustafa, M. \On squeezing
ow of nano
uid in
the presence of magnetic eld e ects", J. Molecular
Liquids, 213, pp. 179-185 (2016).
29. Dhanai, R., Rana, P., and Kumar, L. \MHD mixed
convection nano
uid
ow and heat transfer over an
inclined cylinder due to velocity and thermal slip
e ects: Buongiorno's model", Powder Tech., 288, pp.
140-150 (2016).
30. Turkyilmazoglu, M. and Pop, I. \Heat and mass
transfer of unsteady natural convection
ow of some
nano
uids past a vertical in nite
at plate with radiation
e ect", Int. J. Heat Mass Transf., 59, pp. 167-171
(2013).
31. Rashidi, M.M., Ganesh, N.V., Abdul Hakeem, A.K.,
and Ganga, B. \Buoyancy e ect on MHD
ow of
nano
uid over a stretching sheet in the presence of
thermal radiation", J. Molecular Liquids, 198, pp. 234-
238 (2014).
32. Haq, R.U., Nadeem, S., Khan, Z.H., and Akbar,
N.S. \Thermal radiation and slip e ects on MHD
stagnation point
ow of nano
uid over a stretching
sheet", Physica E, 65, pp. 17-23 (2015).
33. Das, S. and Jana, R.N. \Natural convective magnetonano

uid
ow and radiative heat transfer past a
moving vertical plate", Alexandria Eng. J., 54, pp.
55-64 (2015).
34. Das, S., Jana, R.N., and Chamkha, A.J. \Magnetohydrodynamic
free convective boundary layer
ow of
nano
uids past a porous plate in a rotating frame", J.
Nano
uids, 4, pp. 176-186 (2015).
35. Sheikholeslami, M., Ganji, D.D., Javed, M.Y., and
Ellahi, R. \E ect of thermal radiation on magnetohydrodynamics
nano
uid
ow and heat transfer by
means of two phase model", J. Magnetism Magnetic
Materials, 374, pp. 36-43 (2015).
36. Sheikholeslami, M., Ganji, D.D., and Rashidi, M.M.
\Ferro
uid
ow and heat transfer in a semi annulus enclosure
in the presence of magnetic source considering
thermal radiation", J. Taiwan Inst. Chem. Engineers,
47, pp. 6-17 (2015).
37. Ellahi, R., Hassan, M., and Zeeshan, A. \Shape e ects
of nanosize particles in Cu-H2O nano
uid on entropy
generation", Int. J. Heat Mass Transf., 81, pp. 449-456
(2015).
38. Zeeshan, A., Majeed, A., and Ellahi, R. \E ect of
magnetic dipole on viscous ferro
uid past a stretching
surface with thermal radiation", J. Molecular Liquids,
215, pp. 549-554 (2016).
39. Das, S., Jana, R.N., and Makinde, O.D. \Transient
natural convection in a vertical channel lled with
nano
uids in the presence of thermal radiation",
Alexandria Eng. J., 55, pp. 253-262 (2016).
40. Das, S., Jana, R.N., and Makinde, O.D. \Magnetohydrodynamic
free convective
ow of nano
uids past an
oscillating porous
at plate in a rotating system with
thermal radiation and hall e ects", J. Mech., 32(02),
pp. 197-210 (2016).
41. Chandran, P., Sacheeti, N.C., and Singh, A.K. \Natural
convection near a vertical plate with ramped wall
temperature", Heat Mass Transf., 41, pp. 459-464
(2005).
42. Seth, G.S., Ansari, M.S. and Nandkeolyar, R. \MHD
natural convection
ow with radiative heat transfer
past an impulsively moving plate with ramped wall
temperature", Heat Mass Transf., 47, pp. 551-561
(2011).
43. Seth, G.S., Hussain, S.M., and Sarkar, S. \Hydromagnetic
natural convection
ow with radiative heat
transfer past an accelerated moving vertical plate with
ramped temperature through a porous medium", J.
Porous Media, 17(1), pp. 67-79 (2014).
44. Seth, G.S., Sarkar, S., Hussain, S.M., and Mahato,
G.K. \E ects of hall current and rotation on hydromagnetic
natural convection
ow with heat and mass
transfer of a heat absorbing
uid past an impulsively
moving vertical plate with ramped temperature", J.
Appl. Fluid Mech., 8(1), pp. 159-171 (2015).
45. Nandkeolyar, R., Seth, G.S., Makinde, O.D., Sibanda,
P., and Ansari, M.S. \Unsteady hydromagnetic natural
convection
ow of a dusty
uid past an impulsively
moving vertical plate with ramped temperature in the
presence of thermal radiation", ASME J. Appl. Mech.,
80, pp. 061003-(1-9) (2013).
46. Hussain, S.M., Jain, J., and Seth, G.S. \Hall e ects
on MHD natural convection
ow with heat and mass
transfer of heat absorbing and chemically reacting
uid
1256 S.M. Hussain et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 1243{1257
past a vertical plate with ramped temperature and
ramped surface concentration", Bul. Chem. Comm.,
48(4), pp. 659-670 (2016).
47. Hussain, S.M., Jain, J., Seth, G.S., and Rashidi, M.M.
\Free convective heat transfer with hall e ects, heat
absorption and chemical reaction over an accelerated
moving plate in a rotating system", J. Magnetism
Magnetic Materials, 422, pp. 112-123 (2017).
48. Nandkeolyar, R., Das, M., and Pattnayak, H. \Unsteady
hydromagnetic radiative
ow of a nano
uid
past a
at plate with ramped temperature", J. Orissa
Mathematical Soc., 32, pp. 15-30 (2013).
49. Khalid, A., Khan, I., and Sha e, S. \Exact solutions
for free convection
ow of nano
uids with ramped wall
temperature", The Europ. Physical J.-Plus, 130, p. 57
(2015).
50. Ghosh, S.K. and Bhattacharjee, P.K. \Hall e ects on
steady hydromagnetic
ow in a rotating channel in
the presence of an inclined magnetic eld", Czech. J.
Phys., 50(6), pp. 759-767 (2000).
51. Ghosh, S.K., Beg, O.A., and Narahari, M. \A study
of unsteady rotating hydromagnetic free and forced
convection in a channel subject to forced oscillation
under an oblique magnetic eld", J. Appl. Fluid Mech.,
6(2), pp. 213-227 (2013).
52. Nandkeolyar, R. and Das, M. \MHD free convective
radiative
ow past a
at plate with ramped temperature
in the presence of inclined magnetic eld", Comp.
Appl. Math., 34, pp. 109-123 (2015).
53. Oztop, H.F. and Abu-Nada, E. \Numerical study
of natural convection in partially heated rectangular
enclosures lled with nano
uids", Int. J. Heat Fluid
Flow, 29(5), pp. 1326-1336 (2008).
54. Turkyilmazoglu, M. \Unsteady convection
ow of some
nano
uids past a moving vertical
at plate with heat
transfer", J. Heat Transf., 136, pp. 031704-031704-7
(2013).
55. Kakac, S. and Pramuanjaroenkij, A. \Review of convective
heat transfer enhancement with nano
uids",
Int. J. Heat Mass Transf., 52, pp. 3187-3196 (2009).
56. Rosseland, S. Astrophysik und Atom-Theoretische
Grundlagen, Springer-Verlag, Berlin (1931).