Abstract
This article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.
- Nomenclature
- a
Half width of the channel
- b
The amplitude
- c̅
The wave velocity
- DB
Brownian diffusion coefficient
- DT
Thermophoretic diffusion coefficient
- Ec
Eckert number
- f
The nanoparticle phenomena
- f0
Nanoparticles at y=0
- f1
Nanoparticles at y=h
- g
The gravitational acceleration
- kR
The mean absorption coefficient
- k
Thermal conductivity
- L
Dimensional slip parameter
- n
The power-law exponent
- Nb
Brownian motion parameter
- Nt
The thermophoresis parameter
- P
The fluid pressure
- Pr
Prandtl number
- q
The radiative heat flux
- Q0
The volumetric rate of heat generation
- R
Radiation parameter
- Re
Reynolds number
- sign
Signum function
- Sc
Schmidt number
- T
The fluid temperature
- T0
Temperature at y=0
- T1
Temperature at y=h
- u
Axial velocity
- v
Transverse velocity
- x
Axial coordinate
- y
Transverse coordinate
- Greek symbols
- α
Angle of inclination
- β
Dimensionless slip parameter
- σ*
Stefan Boltzmann constant
- φ
The amplitude ratio
- λ
The volumetric rate of heat generation
- λ̅
The wavelength
- μ
The dynamic viscosity of fluid
- ρf
The density of the fluid
- ρp
The density of the particle
- (ρc)f
Heat capacity of the fluid
- (ρc)p
Effective heat capacity of the nanoparticle material
- θ
Angle between walls of channel
- Sij
Stress tensor components in power-law model
References
[1] R. Ben Mansour, N. Galanis, and C. T. Nguyen, Appl. Therm. Eng. 27, 240 (2007).10.1016/j.applthermaleng.2006.04.011Search in Google Scholar
[2] X. Q. Wang and A. S. Mujumdar, Int. J. Therm. Sci. 46, 1 (2007).10.1016/j.ijthermalsci.2006.06.010Search in Google Scholar
[3] M. Goyal and R. Bhargava, Appl. Nanosci. 4, 761 (2014).10.1007/s13204-013-0254-5Search in Google Scholar
[4] T. Hayat, T. Muhammad, S. A. Shehzad, and A. Alsaedi, J. Mol. Liq. 221, 93 (2016).10.1016/j.molliq.2016.05.057Search in Google Scholar
[5] M. S. Kandelousi and R. Ellahi, Z. Naturforsch. A 70, 115 (2015).10.1515/zna-2014-0258Search in Google Scholar
[6] R. Ellahi, M. H. Tariq, M. Hassan, and K. Vafai, J. Mol. Liq. 229, 339 (2017).10.1016/j.molliq.2016.12.073Search in Google Scholar
[7] K. M. Shirvan, M. Mamourian, S. Mirzakhanlari, and R. Ellahi, Powder Technol. 313, 99 (2017).10.1016/j.powtec.2017.02.065Search in Google Scholar
[8] K. M. Shirvan, R. Ellahi, M. Mamourian, and M. Moghiman, Int. J. Heat Mass Transf. 106, 1110 (2017).10.1016/j.ijheatmasstransfer.2016.11.022Search in Google Scholar
[9] M. Sajid, I. Pop, and T. Hayat, Comput. Math. Appl. 59, 493 (2010).10.1016/j.camwa.2009.06.017Search in Google Scholar
[10] M. Sheikholeslami and S. A. Shehzad, Int. J. Heat Mass Transf. 106, 1261 (2017).10.1016/j.ijheatmasstransfer.2016.10.107Search in Google Scholar
[11] F. M. Abbasi, S. A. Shehzad, T. Hayat, and B. Ahmad, J. Magnet. Magnetic Mater. 404, 159 (2016).10.1016/j.jmmm.2015.11.090Search in Google Scholar
[12] S. A. Shehzad, F. M. Abbasi, T. Hayat, and F. Alsaadi, J. Mol. Liq. 209, 723 (2015).10.1016/j.molliq.2015.05.058Search in Google Scholar
[13] T. Hayat, Y. Humaira, and A. Alsaedi, J. Braz. Soc. Mech. Sci. Eng. 37, 463 (2015).10.1007/s40430-014-0177-4Search in Google Scholar
[14] K. Vafai A. A. Khan, S. Sajjad, and R. Ellahi, Z. Naturforsch. A 70, 281 (2015).10.1515/zna-2014-0330Search in Google Scholar
[15] S. Noreen, S. Nadeem, L. Changhoon, H. K. Zafar, and U. H. Rizwan, Results Phys. 3, 161 (2013).10.1016/j.rinp.2013.08.005Search in Google Scholar
[16] M. Y. Abou-zeid, Thermal Sci. DOI 10. 2298/TSCI150215079A.10.2298/TSCI150215079ASearch in Google Scholar
[17] M. Y. Abou-zeid, Results Phys. 6, 481 (2016).10.1016/j.rinp.2016.08.006Search in Google Scholar
[18] S. Nadeem, R. U. Haq, and Z. H. Khan, Appl. Nanosci. 4, 625 (2014).10.1007/s13204-013-0235-8Search in Google Scholar
[19] M. M. Bhattia, A. Zeeshanb, and R. Ellahi, Microvasc. Res. 110, 32 (2017).10.1016/j.mvr.2016.11.007Search in Google Scholar PubMed
[20] T. Hayata, R. Sajjad, T. Muhammad, A. Alsaedi, and R. Ellahi, Results Phys. 7, 535 (2017).10.1016/j.rinp.2016.12.039Search in Google Scholar
[21] Y. Wang, T. Hayat, and M. A. Siddiqui, Math. Method. Appl. Sci. 28, 329 (2005).10.1002/mma.571Search in Google Scholar
[22] K. Vajravelu, K. V. Prasad, P. S. Datti, and B. T. Raju, Ain Shams Eng. J. 5, 157 (2014).10.1016/j.asej.2013.07.009Search in Google Scholar
[23] T. Hayat, E. Momoniat, and F. M. Mahomed, Probl. Eng. 2006, Article ID 84276 (2006).10.1155/MPE/2006/84276Search in Google Scholar
[24] J. C. Misra and S. K. Pandey, Int. J. Eng. Sci. 39, 387 (2001).10.1016/S0020-7225(00)00038-0Search in Google Scholar
[25] M. K. Chaube, D. Tripathi, O. Anwar, S. Sharma, and V. S. Pandey, Appl. Bionics Biomech. 2015, Article ID 152802 (2015).10.1155/2015/152802Search in Google Scholar PubMed PubMed Central
[26] W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho, Handbook of Heat Transfer, McGraw-Hill, New York 1998.Search in Google Scholar
[27] J. H. He, Chaos Soliton. Fract. 26, 695 (2005).10.1016/j.chaos.2005.03.006Search in Google Scholar
[28] B. Gebhart, Similarity Solutions for Laminar External Boundary Region Flows, Natural Convection, Fundamentals and Applications, Hemisphere Publishing Corporation, Washington 1985.Search in Google Scholar
[29] A. Pantokratoras, Appl. Math. Model. 29, 553 (2005).10.1016/j.apm.2004.10.007Search in Google Scholar
[30] S. E. Charmand and G. S. Kurland, Blood Flow and Microcirculation, John Wiley & Sons, New York, NY, USA 1974.Search in Google Scholar
©2017 Walter de Gruyter GmbH, Berlin/Boston
