The bioconvection in an unsteady flow of an incompressible couple-stress fluid consists of microorganisms between two parallel plates is considered. A model containing coupled non-linear system of partial differential equations for the mass, momentum, energy, mass diffusion, and microorganisms is reduced to a set of non-linear ordinary differential equations with the help of suitable transformations. The resulting non-linear ordinary differential equations are linearized using successive linearization method and then Chebyshev collocation method is used to solve resulting system of linearized ordinary differential equations. The comprehensive investigation demonstrating the impacts of various fluid flow governing physical parameters such as the couple-stress parameter, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number and bioconvection Peclet number on the distributions of dimensionless velocity, temperature, concentration and motile microorganism is graphically presented.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Stefan, M.J.: Versuche, uber die scheinbare adh¨asion, Akadenie deer Wissenschaften in Wien, Math.-Naturw 69, 713–721 (1874)
Rashidi, M.M., Shahmohamadi, H., Dinarvand, S.: Analytic approximate solutions for unsteady two dimensional and axisymmetric squeezing flows between parallel plates. Math. Probl. Eng. ID 935095 (2008)
Mustafa, M., Hayat, T., Obaidat, S.: On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica 47(7), 1581–1589 (2012)
Petrov, A.G., Kharlamova, I.S.: The solutions of Navier–Stokes equations in squeezing flow between parallel plates. Eur. J. Mech. B. Fluids 48, 40–48 (2014)
Qayyum, M., Khan, H., Rahim, M.T., Ullah, I.: Modeling and analysis of unsteady axisymmetric squeezing fluid flow through porous medium channel with slip boundary. PLoS ONE 10(3), e0117368 (2015)
Ullah, I., Rahim, M.T., Khan, H., Qayyum, M.: Analytical analysis of squeezing flow in porous medium with MHD effect, U.P.B. Sci. Bull., Ser. A, 78(2):281–292 (2016)
Khan, H., Qayyum, M., Khan, O., Ali, M.: Unsteady squeezing flow of casson fluid with magnetohydrodynamic effect and passing through porous medium. Math. Probl. Eng. ID 4293721 (2016)
Acharya, N., Das, K., Kundu, P.: The squeezing flow of Cu-water and Cu-kerosene nanofluid between two parallel plates. Alex. Eng. J. 55, 1177–1186 (2016)
Sobamowo, M.G., Akinshilo, A.T.: On the analysis of squeezing flow of nanofluid between two parallel plates under the influence of magnetic field. Alex. Eng. J. 57, 1413–1423 (2017)
Adesanya, S.O., Ogunseye, H.A., Srinivas, J.: Unsteady squeezing flow of a radiative Eyring–Powell fluid channel flow with chemical reactions. Int. J. Therm. Sci. 125, 440–447 (2018)
Stokes, V.K.: Couple stresses in fluid. Phys. Fluids 9, 1709–1715 (1966)
Srinivasacharya, D., Srinivasacharyulu, N., Odelu, O.: Flow and heat transfer of couple stress fluid in a porous channel with expanding and contracting walls. Int. Commun. Heat Mass Transf. 36, 180–185 (2009)
Srinivasacharya, D., Kaladhar, K.: Analytical solution for Hall and ion-slip effects on couple stress fluid between the parallel disks. Math. Comput. Model. 57, 2494–2509 (2013)
Nayak, A., Dash, G.C.: Magnetohydrodynamic couple stress fluid flow through a porous medium in a rotating channel. J. Eng. Thermophys. 24, 283–295 (2015)
Khan, N.A., Khan, H., Ali, S.A.: Exact solutions for MHD flow of couple stress fluid with heat transfer. J. Egypt. Math. Soc. 24, 125–129 (2016)
Saad, H.S., Ashmawy, E.A.: Unsteady plane coquette flow of an incompressible couple stress fluid with slip boundary conditions. Int J Med Health Sci Res. 3(7), 85–92 (2016)
Hayat, T., Sajjad, R., Alsaedi, A., Muhammad, T., Ellahi, R.: On squeezed flow of couple stress nanofluid between two parallel plates. Results Phys. 7, 553–561 (2017)
Ilani, S.S., Ashmawy, E.A.: A time dependent slip flow of a couple stress fluid between two parallel plates through state space. J. Taibah Univ. Sci. 12(5), 592–599 (2018)
Madalli, V.S., Patil, S., Hiremath, A., Ramesh, K.: Analysis of the viscosity dependent parameters of couple stress fluid in porous parallel plates. Ind. Lubr. Tribol. 70(6), 1086–1093 (2018)
Platt, J.R.: Bioconvection Patterns in cultures of free-swimming organisms. Science 133, 1766–1767 (1961)
Kessler, J.O.: Hydrodynamic focusing of motile algal cells. Nature 313, 218–220 (1985)
Kuznetsov, A.V.: The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms. Eur. J. Mech. B/Fluids 25, 223–233 (2006)
Childress, S., Levandowsky, M., Spiegel, E.A.: Pattern formation in a suspension of swimming microorganisms: equations and stability theory. J. Fluid Mech. 63, 591–613 (1975)
Pedley, T.J., Hill, N.A., Kessler, J.O.: The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J. Fluid Mech. 195, 223–237 (1988)
Ghorai, S., Hill, N.A.: Development and stability of gyrotactic plumes in bioconvection. J. Fluid Mech. 400, 1–31 (1999)
Ghorai, S., Hill, N.A.: Periodic arrays of gyrotactic plumes in bioconvection. Phys. Fluids 12, 5–22 (2000)
Zhao, Q., Xu, H., Tao, L.: Unsteady bioconvection squeezing flow in a horizontal channel with chemical reaction and magnetic field effects. Math. Probl. Eng. ID 62858 (2017)
Bin-Mohsin, B., Ahmed, N.A., Khan, U., Mohyud-Din, S.T.: 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)
Motsa, S.S., Shateyi, S.: Successive linearisation solution of free convection non-Darcy flow with heat and mass transfer. Adv. Top. Mass Transf. 19, 425–438 (2006)
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, ThA: Spectral Methods—Fundamentals in Single Domains. Berlin Heidelberg, Springer-Veralg (2006)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Srinivasacharya, D., Sreenath, I. Unsteady Bioconvection in a Squeezing Flow of a Couple-Stress Fluid Through Horizontal Channel. Int. J. Appl. Comput. Math 6, 30 (2020). https://doi.org/10.1007/s40819-020-0779-8
- Couplestress fluid
- Squeezing flow
- Density of the motile microorganisms