Gravity-modulated Weakly Nonlinear Oscillatory Bioconvection in a Densely Packed Porous Medium
DOI:
https://doi.org/10.5890/JAND.2027.03.009Abstract
In this paper, we investigate the effect of gravity modulation on Darcy–Brinkman bioconvection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. A weakly nonlinear stability analysis is performed to examine the oscillatory mode of convection under low-amplitude modulation. Heat transport is quantified using the mean Nusselt number, evaluated through a complex Ginzburg–Landau equation (CGLE). The CGLE is derived from a solvability condition at the lowest order of the perturbation parameter. The results are presented graphically to illustrate the impact of system parameters on bioconvection. Both the Vadasz number and the modulation amplitude are found to have a significant influence on heat transfer. Conversely, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. It is also found that the convective transport process is more strongly influenced by the irregular shapes of microorganisms than by spherical-shaped ones. Gravity modulation is found to be effective in controlling heat transfer, highlighting the role of external modulation in regulating transport processes within the system.References
[1] Childress, S., Levandowsky, M., and Spiegel, E.A. (1975), Pattern formation in a suspension of swimming microorganisms: equations and stability theory, Journal of Fluid Mechanics, 69, 591-613.
[2] Chandrasekhar, S. (1982), Hydrodynamic and hydromagnetic stability, Dover, ISBN 0-486-64071-X.
[3] Drazin, P.G. and Reid, W.H. (2004), Hydrodynamic stability, second edition, Cambridge University Press.
[4] Vafai, K. (2005), Handbook of porous media, 2nd edn, CRC Press, Boca Raton.
[5] Hill, N.A., Pedley, T.J., and Kessler, J.O. (1989), Growth of bioconvection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth, Journal of Fluid Mechanics, 208, 509-543.
[6] Pedley, T.J. and Kessler, J.O. (1992), Hydrodynamic phenomena in suspensions of swimming microorganisms, Annual Review of Fluid Mechanics, 24, 313-358.
[7] Kuznetsov, A.V. and Avramenko, A.A. (2003), Stability analysis of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium, Transport in Porous Media, 53, 95-104.
[8] Nield, D.A., Kuznetsov, A.V., and Avramenko, A.A. (2004), The onset of bioconvection in a horizontal porous-medium layer, Transport in Porous Media, 54, 335-344.
[9] Kuznetsov, A.V. (2010), The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms, International Communications in Heat and Mass Transfer, 37, 1421-1425.
[10] Sharma, Y.D. and Kumar, V. (2012), The effect of high-frequency vertical vibration in a suspension of gyrotactic micro-organisms, Mechanics Research Communications, 44, 40-46.
[11] Dmitrenko, N.P. (2017), Main aspects of the process of bioconvection in nanofluids and porous media, Industrial Heat Engineering, 39(5), 19-25.
[12] Zhao, M., Wang, S., Wang, H., and Mahabaleshwar, U.S. (2019), Darcy-Brinkman bio-thermal convection in a suspension of gyrotactic microorganisms in a porous medium, Neural Computing and Applications, 31, 1061-1067.
[13] Garg, A., Sharma, Y.D., and Jain, S.K. (2023), Stability analysis of thermo-bioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium, Forces in Mechanics, 10, 100152.
[14] Belabid, J. and Allali, K. (2019), Thermo-bioconvection in horizontal porous annulus with the presence of phototactic microorganisms, International Journal of Engineering Science, 140, 17-25.
[15] Khan, S.U., Al-Khaled, K., Aldabesh, A., Awais, M., and Tlili, I. (2021), Bioconvection flow in accelerated couple stress nanoparticles with activation energy: bio-fuel applications, Scientific Reports, 11, 3331.
[16] Aziz, S., Kolsi, L., Ahmad, I., Al-F. Turjman, Omri, M., and Khan, S.U. (2021), Thermal stability and bioconvection investigation for couple stress nanofluid due to a three-dimensional accelerated frame, Waves in Random and Complex Media, 174, 4653-4674.
[17] Kopp, M.I., Yanovsky, V.V., and Mahabaleshwar, U.S.A. (2022), Bio-thermal convection in a porous medium saturated by nanofluid containing gyrotactic microorganisms under an external magnetic field, East European Journal of Physics, 4, 23-47.
[18] Azam, M. (2022), Bioconvection and nonlinear thermal extrusion in development of chemically reactive Sutterby nano-material due to gyrotactic microorganisms, International Communications in Heat and Mass Transfer, 130, 105820.
[19] Mil-Martínez, R., Vargas, R.O., Escandón, J.P., Pérez-Reyes, I., Turcio, M., Gómez-López, A., and López-Serrano, F. (2022), Thermal effect on the bioconvection dynamics of gravitactic microorganisms in a rectangular cavity, Fluids, 7(3), 113.
[20] Venezian, G. (1969), Effect of modulation on the onset of thermal convection, Journal of Fluid Mechanics, 35, 243-254.
[21] Gresho, P.M. and Sani, R.L. (1970), The effects of gravity modulation on the stability of a heated fluid layer, Journal of Fluid Mechanics, 40(4), 783-806.
[22] Malashetty, M.S. and Basavaraj, D. (2005), Effect of thermal/gravity modulation on the onset of convection of Rayleigh-Benard convection in a couple stress fluid, International Journal of Transport Phenomena, 7, 31-44.
[23] Shu, Y., Li, B.Q., and Ramaprian, B.R. (2005), Convection in modulated thermal gradients and gravity: experimental measurements and numerical simulations, International Journal of Heat and Mass Transfer, 48, 145-160.
[24] Rogers, J.L., Pesch, W., Brausch, O., and Schatz, M.F. (2005), Complex ordered patterns in shaken convection, Physical Review E, 71, 066214.
[25] Boulal, T., Aniss, S., and Belhaq, M. (2007), Effect quasiperiodic gravitational modulation on the stability of a heated fluid layer, Physical Review E, 76, 056320.
[26] Umavathi, J.C. (2013), Effect of thermal modulation on the onset of convection in a porous medium layer saturated by a nanofluid, Transport in Porous Media, 98, 59-79.
[27] Kiran, P. and Manjula, S.H. (2023), Nanofluid gravity driven oscillatory mode of convection in a porous medium, Journal of Applied Mechanics and Technical Physics, 64, 635-646.
[28] Manjula, S.H., Kiran, P., and Narayanamoorthy, S. (2020), The effect of gravity driven thermal instability in the presence of applied magnetic field and internal heating, AIP Conference Proceedings, 2261, 030042.
[29] Manjula, S.H., Kiran, P., Raj Reddy, P., and Bhadauria, B.S. (2022), The complex Ginzburg Landau model for an oscillatory convection in a rotating fluid layer, International Journal of Applied Mechanics and Engineering, 25, 75-91.
[30] Kiran, P. and Manjula, S.H. (2024), Weakly nonlinear bio-convection in a porous media under temperature modulation and internal heating, Multiscale and Multidisciplinary Modeling, Experiments and Design, 7, 1-15.
[31] Kuznetsov, A.V. (2005), Investigation of the onset of thermo-bioconvection in a suspension of oxytactic microorganisms in a shallow fluid layer heated from below, Theoretical and Computational Fluid Dynamics, 19, 287-299.
[32] Kuznetsov, A.V. (2006), Thermo-bio-convection in porous media, Journal of Porous Media, 9, 581-589.
[33] Saini, S. and Sharma, Y. (2019), Double-diffusive bioconvection in a suspension of gyrotactic microorganisms saturated by nanofluid, Journal of Applied Mechanics and Fluid Mechanics, 12(1), 271-280.
[34] Arpan, G., Sharma, Y.D., and Jain, S.K. (2023), Stability analysis of thermo-bioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium, Forces in Mechanics, 10, 100152.
[35] Akhila, P.A., Mallikarjun, B.P., and Kiran, P. (2024), Analysis of weakly nonlinear Darcy–Brinkman bio-thermal convection in a porous medium under gravity modulation and internal heating effect, International Journal of Non-Linear Mechanics, 159, 104615.
[36] Akhila, P.A., Mallikarjun, B.P., Kiran, P., and Chamkha, A.J. (2024), Study of double-diffusive gravity modulated biothermal convection in porous media under internal heating effect, The European Physical Journal Plus, 139(7), 1-19.
[37] Akhila, P.A., Mallikarjun, B.P., and Kiran, P. (2024), Weakly nonlinear analysis of Darcy–Brinkman gravity modulated biothermal convection in rotating porous media, Heat Transfer, 1-26.
[38] Akhila, P.A., Mallikarjun, B.P., Kiran, P., and Chamkha, A.J. (2025), Darcy–Brinkman gravity modulated biothermal double diffusive convection in rotating porous media, ZAMM - Journal of Applied Mathematics and Mechanics, 105. https://doi.org/10.1002/zamm.70278
[39] Kiran, P. (2015), Throughflow and g-jitter effects on binary fluid saturated porous medium, Applied Mathematics and Mechanics, 36, 1285-1304.
[40] Kiran, P. (2016), Nonlinear thermal convection in a viscoelactic nanofluid saturated porous medium under gravity modulation, Ain Shams Engineering Journal, 7(2), 639-651.
[41] Bhadauria, B.S. and Kiran, P. (2013), Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under temperature modulation, Transport in Porous Media, 100, 279-295.
[42] Srivastava, A., Bhadauria, B.S., Siddheshwar, P.G., and Hashim, I. (2013), Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under g-jitter and internal heating effects, Transport in Porous Media, 99, 359-376.
[43] Bhadauria, B.S. and Kiran, P. (2014), Weak nonlinear oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation, Transport in Porous Media, 104(3), 451-467.
[44] Kiran, P. and Bhadauria, B.S. (2015), Chaotic convection in a porous medium under temperature modulation, Transport in Porous Media, 107(3), 745-763.
[45] Kiran, P., Bhadauria, B.S., and Narasimhulu, Y. (2017), Weakly nonlinear and nonlinear magneto-convection under thermal modulation, Journal of Applied Nonlinear Dynamics, 6(4), 487-508.
[46] Bhadauria, B.S. and Kiran, P. (2014), Weak nonlinear double diffusive magnetoconvection in a Newtonian liquid under temperature modulation, International Journal of Engineering Mathematics, 2014, 1-14.
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