Magneto-bio-thermal Convection in Rotating Nanoliquid ‎containing Gyrotactic Microorganism

Document Type : Research Paper


1 Department of Mathematics, The NorthCap University, Sector 23A, Gurugram, Haryana 122017, India

2 School of Mathematical Sciences, College of Science and Technology, Wenzhou Kean University, Wenzhou 325060, China

3 Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector 62, Noida 201309, India‎


The magneto-convection influenced by a gyrotactic behavior of algal suspensions along with rotation in the nanoliquid layer is investigated. Linear theory based on normal mode analysis is used to find out the inquisitive results of the problem for rigid-free and rigid-rigid boundaries. Both Galerkin-method (Number of terms (N) > 6) and shooting method (by taking forcing condition) are utilized to find the critical value of the Rayleigh number (both thermal and bio) in case of non-oscillatory stability. Both thermal and bio Rayleigh numbers are dependent on each other, thus advance or delay the convection. Rotation and magnetic field slow down the convective motion of microorganisms across the layer and destabilizes the system.


Main Subjects

[1] Sokolov, A., Goldstein, R.E., Feldchtein, F.I., Aranson, I.S., Enhanced mixing and spatial instability in concentrated bacterial suspensions, Physical Review E, 80(3), 2009, 031903.
[2] Murshed, S.M.S., Castro,, Heat Transfer of Nanofluids in Microsystems, The 26th International Symposium on Transport Phenomena (ISTP-26), Leoben, Austria, 2015.
[3] Ebrahimi, S., Sabbaghzadeh, J., Maryamalsadat, L.,Iraj, H., Cooling performance of a microchannel heat sink with nanofluids containing cylindrical nanoparticles (carbon nanotubes), Heat and Mass Transfer, 46, 2010, 549-553.
[4] Sedarous S.S., Attlesey, C.D., Nanofluids for use in electronics, Patent Application Publication, US 2012/0186789A1.
[5] Fan, X., Chen, H., Ding, Y., Plucinski, P.K., Lapkin, A.A., Potential of ‘nanofluids’ to further intensify micro reactors, Green Chemistry, 10, 2008, 670-677.
[6] Do, K.H., Jang, S.P., Effect of nanofluids on the thermal performance of a flat micro heat pipe with a rectangular grooved wick, Journal of Heat and Mass Transfer, 53(9), 2010, 2183-2192.
[7] Wong, K.V., Leon, O.De., Applications of Nanofluids: Current and Future, Advances in Mechanical Engineering, 2, 2010, 519659.
[8] Li, H., Liu, S., Dai, Z., Bao, J., Yang, X., Applications of Nanofluids in Electrochemical Enzyme Biosensors, Sensors (Besel), 9, 2009, 8547-8561.
[9] Plesset, M.S., Winet, H., Bioconvection patterns in swimming microorganism cultures as an example of Rayleigh-Taylor instability, Nature, 248, 1974, 441-443.
[10] Childress, S., Levandowsky, M., Spiegel, E.A., Pattern formation in a suspension of swimming microorganisms: equations and stability theory, Journal of Fluid Mechanics, 69(3), 1975, 591-613.
[11] Pedley, T.J., Hill, N.A., Kessler, J.O., The growth of bioconvection patterns in a uniform suspensions of gyrotactic micro-organisms, Journal of Fluid Mechanics, 195, 1988, 223-237.
[12] Pedley, T.J., Kessler, J.O., James, L.M., The orientation of spheroidal microorganisms swimming in a flow field, Proceedings of the Royal Society of London. Series B. Biological Sciences, 231, 1987, 47–70.
[13] Hill, N.A., Pedley, T.J., Kessler, J.O., Growth of bioconvection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth, Journal of Fluid Mechanics, 208, 1989, 509-543.
[14] Nield, N.A., Kuznetsov, A.V., The onset of bio-thermal convection in a suspension of gyrotactic microorganisms in a fluid layer: Oscillatory convection, International Journal of Thermal Sciences, 45(10), 2006, 990-997.
[15] Zhao, M., Xiao, Y., Wang, S., Linear stability of thermal bioconvection in a suspension of gyrotactic micro-organisms, International Journal of Heat and Mass Transfer, 126(Part A), 2018, 95-102.
[16] Amirsom, N.A., Uddin, M.J., Basir, M.F.M, Kadir, A., Beg, O.A., Ismail, A.I.M., Computation of Melting Dissipative Magnetohydrodynamic Nanofluid Bioconvection with Second order Slip and Variable Thermophysical Properties, Applied Sciences, 9(12), 2019, 1-19.
[17] Basir, M.F.M., Hafidzuddin, M.E.H., Naganthran, K., Hashim, Kasihmuddin, M.S.M., Stability analysis of unsteady stagnation-point gyrotactic bioconvection flow and heat transfer towards the moving sheet in a nanofluid, Chinese Journal of Physics, 65, 2020, 538-553.
[18] Bala, C.S., Alluguvelli, R., Naikoiti, K., Makinde, O.D., Effect of Chemical Reaction on Bioconvective Flow in Oxytactic Microorganisms Suspended Porous Cavity, Journal of Applied and Computational Mechanics, 6(3), 2020, 653-664.
[19] Kuznetsov, A.V., Avramenko, A., Effect of small particles on the stability of bioconvection in a suspension of gyrotactic microorganisms in a layer of finite depth, International Communications in Heat and Mass Transfer, 31(1), 2004, 1-10.
[20] Kuznetsov, A.V., Geng, P., The interaction of bioconvection caused by gyrotactic micro-organisms and settling of solid particles, International Journal of Numerical Methods for Heat & Fluid Flow, 15(4), 2005, 328-347.
[21] Geng, P., Kuznetsov, A.V., Effect of small solid particles on the development of bioconvection plumes, International Communications in Heat and Mass Transfer, 31(5), 2004, 629-638.
[22] Kuznetsov, A.V., Avramenko, Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium, Transport in Porous Media, 53, 2003, 95-104.
[23] Kuznetsov, A.V., The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms, International Communications in Heat and Mass Transfer, 37(10), 2010, 1421-1425.
[24] Kuznetsov, A.V., Non-oscillatory and oscillatory nanofluid bio-thermal convection in a horizontal layer of finite depth, European Journal of Mechanics B/Fluids, 30(2), 2011, 156-165.
[25] Xiong, X., Lidstrom, M.E., Parviz, B.A., Microorganisms for MEMS, Journal of Microelectromechanical Systems, 16(2), 2007, 429-444.
[26] Sonetha, V., Agarwal, P., Doshi, S., Kumar, R., Mehta, B., Microelectromechanical Systems in Medicine, Journal of Medical and Biological Engineering, 37, 2017, 580-601.
[27] Asif, A., Khawaldeh, S., Khan, M.S., Tekin, A., Design and Simulation of microfluidics device for metabolicscreening and quantitative monitoring of drug uptake in cancer cells, Journal of Electrical Bioimpedance, 9(1), 2018, 10-16.
[28] Ray, A.K.,B.V., Anwar Beg, O., Gorla, R.S.R., Murthy, P.V.S.N., Magneto-bioconvection flow of a casson thin filmwith nanoparticles over an unsteady stretching sheet: HAM and GDQ computation, International Journal of Numerical Methods for Heat & Fluid Flow, 29(11), 2019, 4277-4309.
[29] Khan, N.S., Kumam, P., Thounthong, P., Second law analysis with effects of Arrhenius activation energy and binary chemical reaction on nanofluid flow, Scientific Reports, 10, 2020, 1226.
[30] Khan, N.S., Shah, Z., Shutaywi, M., Kumam, P., Thounthong, P., A comprehensive study to the assessment of Arrhenius activation energy and binary chemical reaction in swirling flow, Scientific Reports, 10, 2020, 7868.
[31] Atif, S.M., Hussain, S., Sagheer, M., Magnetohydrodynamic stratified bioconvective flow of micropolar nanofluid due to gyrotactic microorganisms, AIP Advances, 9(2), 2019, 025208-1-16.
[32] Khan, N.S., Shah, Q., Bhaumik, A., Kimam, P., Thounthong, P., Amiri, I., Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks, Scientific Reports, 10, 2020, 1-26.
[33] Saleen, S., Rafiq, H., Qahatani, A.A., Aziz, M.A.E., Malik, M.Y., Animasaun, I.L., Magneto Jeffrey Nanofluid Bioconvection over a Rotating Vertical Cone due to Gyrotactic Microorganism, Mathematical Problems in Engineering, 2019, 2019, 3478037.
[34] Raju, C.S.K., Sandeep, N., Heat and mass transfer in MHD non-Newtonian bioconvection flow over a rotating cone/plate with cross diffusion, Journal of Molecular Liquids, 215, 2015, 115-126.
[35] Tarakaramu, N., Narayana, P.V.S., Chemical Reaction Effects on Bio-convection Nanofluid flow between two parallel plates in Rotating System with Variable Viscosity: A Numerical Study, Journal of Applied and Computational Mechanics, 5(4), 2019, 791-803.
[36] Siddheshwar, P.G., Kanchana, C., Unicellular unsteady Rayleigh-Benard convection in Newtonian liquids and Newtonian nanoliquids occupying enclosures: new findings, International Journal of Mechanical Sciences, 131-132, 2017, 1061-1072.
[37] Wakif, A., Boulahia, Z., Amine, A., Animasaun, I.L., Afridi, M.I., Qasimd, M., Sehaqui, R., Magneto-convection of alumina water nanofluid within thin horizontal layers using the revised generalised buongiorno’s model, Frontier in Heat and Mass Transfer, 12(3), 2019, 1-15.
[38] Buongiorno, J., Convective Transport in Nanofluids, Journal of Heat Transfer, 128(3), 2006, 240-250.
[39] Nield, N.A., Kuznetsov, A.V., The onset of convection in a horizontal nanofluid layer of finite depth, European Journal of Mechanics-B/Fluids, 29(3), 2010, 217-223.
[40] Borujerdi, A.N., Noghrehabadi, A.R., Rees, D.A.S., Influence of Darcy number on the onset of convection in a porous layer with a uniform heat source, International Journal of Thermal Sciences, 47(8), 2008, 1020-1025.
[41] Nield, N.A., Kuznetsov, A.V., The Effect of Local Thermal Nonequilibrium on the Onset of Convection in a Nanofluid, Journal of Heat Transfer, 132(5), 2010, 052405-7.
[42] Yadav, D., Agarwal, G.S., Bhargava, R., Effect of Internal Heat Source on the Onset of Convection in a Nanofluid Layer, Applied Mechanics and Materials, 110-116, 2011, 1827-1832.
[43] Yadav, D., Bhargava, R., Magneto-convection in a rotating layer of nanofluid, Asia-Pacific Journal of Chemical Engineering, 9(5), 2014, 663-677.
[44] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961.