Abstract.
This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.
Similar content being viewed by others
References
M.J. Stefan, Akad. Wissensch. Wien Math. Naturwiss. 69, 713 (1874)
R.L. Verma, Wear 72, 89 (1981)
P. Singh, V. Radhakrishnan, K.A. Nayran, Ing. Arch. 60, 274 (1990)
E.A. Hamza, J. Phys. D Appl. Phys. 32, 656 (1999)
R.A. Rajagopal, A.S. Gupta, Int. J. Eng. Sci. 19, 1009 (1981)
H.M. Duwairi, B. Tashtoush, R.A. Damseh, Heat Mass Transf. 41, 112 (2004)
M. Mustafa, T. Hayat, S. Obaidat, Meccanica 47, 1581 (2012)
M.M. Rashidi, H. Shahmohamadi, S. Dinarvand, Math. Prob. Eng. 2008, 935095 (2008)
S. Choi, ASME 66, 99 (1995)
U. Khan, N. Ahmed, S.T. Mohy-ud-Din, Neural Comput. Appl. (2016) DOI:10.1007/s00521-016-2596-x
S. Kack, A. Pramuanjaronkij, Int. J. Heat Mass Transfer 52, 3187 (2009)
K.V. Wong, O.D. Leon, Adv. Mech. Eng. 2, 519659 (2010)
R. Saidur, K.Y. Leong, H.A. Mohammad, Renew. Sustain. Energy Rev. 15, 1646 (2011)
D. Wen, G. Lin, S. Vafaei, K. Zhang, Particuology 7, 141 (2011)
I. Buongiorno, J. Heat Transf. Trans. ASME 128, 240 (2006)
Sheikholeslami, H.R. Ashorynejad, D.D. Gangi, A. Kolahdooz, Math. Probl. Eng. 2011, 258734 (2011)
Sheikholeslami, H.R. Ashorynejad, G. Domairry, I. Hashim, J. Appl. Math. 2012, 421320 (2012)
B.K. Dutta, P. Roy, A.S. Gupta, Int. Commun. Heat Mass Transf. 12, 89 (1985)
H.I. Andersson, J.B. Aarseth, N. Braud, B.S. Dandapat, J. Non-Newtonian Fluid Mech. 62, 1 (1996)
Sheikholeslami, D.D. Ganji, M.Y. Javed, R. Ellahi, J. Magn. & Magn. Mater. 374, 36 (2015)
S. Aman, I. Khan, Z. Ismail, M.Z. Salleh, Neural Comput. Appl. (2016) DOI:10.1007/s00521-016-2688-7
N. Athira, M. Zin, I. Khan, S. Shafie, J. Mol. Liq. 222, 138 (2016)
A. Khalid, I. Khan, S. Shafie, J. Mol. Liq. 221, 1175 (2016)
F. Ali, M. Gohar, I. Khan, J. Mol. Liq. 223, 412 (2016)
I. Ullah, S. Shafie, I. Khan, J. King Saud Univ. (2016) DOI:10.1016/j.jksus.2016.05.003
I. Ullah, I. Khan, S. Shafie, Nanoscale Res. Lett. 11, 527 (2016)
I. Ullah, K. Bhattaacharyya, S. Shafie, I. Khan, PLoS One 11, e0165348 (2016)
T.J. Pedley, N.A. Hill, J.O. Kessler, J. Fluid Mech. 195, 223 (1988)
A.V. Kuznetsov, D.A. Nield, Int. J. Heat Mass Transf. 65, 682 (2013)
P. Geng, A.V. Kuznetasov, Int. J. Transp. Phenom. 7, 321 (2005)
A.V. Kuznetsov, Int. Commun. Heat Mass Transf. 32, 574 (2005)
H. Xu, I. Pop, Eur. J. Mech. B Fluids 46, 37 (2014)
U. Khan, N. Ahmed, S.T. Mohy-ud-Din, J. Biol. Syst. 24, 409 (2016)
A. Raees, H. XU, S.-J. Liao, Int. J. Heat Mass Transfer 86, 174 (2015)
S.T. Mohy-ud-Din, U. Khan, N. Ahmed, S.M. Hassan, Appl. Sci. 5, 1639 (2015)
Adnan, M. Asadullah, U. Khan, N. Ahmed, S.T. Mohyud-Din, J. Mol. Liq. 224, 768 (2016)
Adnan, U. Khan, N. Ahmed, S.T. Mohyud-Din, J. Mol. Liq. 224, 1074 (2016)
S.T. Mohyud-Din, U. Khan, N. Ahmed, S.M. Hassan, Appl. Sci. 5, 1639 (2015)
Sheikholeslami, M. Azimi, D.D. Ganji, Int. J. Comput. Eng. Sci. Mech. 3, 1 (2015)
L.J. Crane, Z. Angew. Math. Phys. 21, 645 (1970)
U. Khan, N. Ahmed, S.T. Mohy-ud-Din, Appl. Therm. Eng. 113, 1107 (2017)
P.S. Gupta, A.S. Gupta, Can. J. Chem. Eng. 55, 744 (1977)
A. Ishak, R. Nazar, I. Pop, Meccanica 44, 369 (2009)
A.K. Borkakoti, A. Bharali, Quart. Appl. Math. 40, 461 (1982)
K. Vjravelu, B.V. Kumar, Int. J. Non-Linear Mech. 39, 13 (2004)
P. Vadasz (Editor), Emerging Topics in Heat and Mass Transfer in Porous Media (Springer, New York, NY, 2008)
K. Vafai (Editor), Handbook of Porous Media, 2nd edition (Taylor and Francis, New York, NY, 2005)
Sheikholeslami, D.D. Gangi, H.R. Ashorynejad, Powder Technol. 239, 259 (2013)
Sheikholeslami, T. Hayat, A. A, Int. J. Heat Mass Transfer 96, 513 (2016)
Sheikholeslami, R. MM, J. Braz. Soc. Mech. 38, 1171 (2016)
R.U. Haq, N.F.M. Noor, Z.H. Khan, Adv. Powder Technol. 27, 1568 (2016)
A.V. Kuznetsov, D.A. Nield, Int. J. Heat Mass Transfer 65, 682 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bin-Mohsin, B., Ahmed, N., Adnan et al. A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms. Eur. Phys. J. Plus 132, 187 (2017). https://doi.org/10.1140/epjp/i2017-11454-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11454-4