Study of thermally developed flow of viscous fluid over a porous stretching surface contacting gyrotatic microorganisms using buongiorno model

Document Type : Article

Authors

1 - Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan. - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60000, Pakistan.

2 Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60000, Pakistan

10.24200/sci.2021.55209.4178

Abstract

Recent trend in advanced nanotechnology has developed the thermal consequences of nanoparticles due to increasing significance in various engineering and thermal extrusion systems. In this continuation, two-dimensional flow of viscous nanoliquid in the presence of gyrotactic micro-organisms encountered by a porous stretched surface is addressed numerically. The novel aspects of Brownian diffusion and thermophoresis are studied by using Buongiorno model. The thermal radiation impact is imposed in the energy equation. A set of pertinent transformations has been suggested to transform the governing non-linear partial differential equations into system of non-linear ordinary differential equations. A famous numerical method, finite difference technique, is engaged to acquire the numerical solution of modeled dimensionless equations. The flow analysis for effects of numerous prominent parameters on velocity, temperature, concentration and motile micro-organisms profiles is presented graphically. In the presence of thermal radiation, velocity profiles detract with augment of bioconvection Rayleigh number and buoyancy ratio parameter, while opposite trend is observed for boosting the Grashoff number. The porous medium as well as the radiation enhance the fluid temperature.

Keywords


References:
 
[1]    Choi, S. U. S. “Enhancing thermal conductivity of fluids with nanoparticles”, ASME Pub. Fed., 231, pp. 99-106 (1995).
[2]    Buongiorno, J., “Convective transport in nanofluids”, J. Heat Transfer, 128, pp. 240-250 (2006).
[3]    Khan, M., Irfan, M. and Khan, W. A., “Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition”, Results Phys., 9, pp. 851-857 (2018).
[4]    Mohebbi, R., Izadi, M. and Chamkha, A. J., “Heat source location and natural convection in a C-shaped enclosure saturated by a nanofluid”, Phys. Fluids, 29(12), DOI:10.1063/1.4993866 (2017).
[5]    Mashaei, P. R., Hosseinalipour, S. M. and Bahiraei, M., “Numerical investigation of nanofluid forced convection in channels with discrete heat sources”, J. Appl. Math, 2012, DOI:10.1155/2012/259284 (2012).
[6]    Kumam P., Shah, Z., Dawar, A., et al. “Entropy generation in MHD radiative flow of CNTs Casson nanofluid in rotating channels with heat source/sink”, Math Probl. Eng., 2019, DOI:10.1155/2019/9158093 (2019).
[7]    Hassan, M., Marin, M., Alsharif, A., et al. “Convective heat transfer flow of nanofluid in a porous medium over wavy surface”, Phys. Lett. A, 382(38), pp. 2749-2753 (2018).
[8]    Guha, A. and Nayek, S., “Thermo-fluid-dynamics of natural convection around a heated vertical plate with a critical assessment of the standard similarity theory”, Phys. Fluids, 29(10), DOI:10.1063/1.4990279 (2017).
[9]    Sheikholeslami, M., Jafaryar, M., Said, Z., et al. “Modification for helical turbulator to augment heat transfer behavior of nanomaterial via numerical approach”, Appl. Therm. Eng., 182, DOI:10.1016/j.applthermaleng.2020.115935 (2020).
[10]    Sheikholeslami, M., Farshad, S. A., Shafee, A., et al. “Performance of solar collector with turbulator involving nanomaterial turbulent regime”, Renew. Energy, 163, pp. 1222-1237 (2020).
[11]    Hakeem, A. K. A., Indumathi, N., Ganga, B., et al. “Comparison of disparate solid volume fraction ratio of hybrid nanofluids flow over a permeable flat surface with aligned magnetic field and Marangoni convection”, Sci. Iran., DOI:10.24200/SCI.2020.51681.2312 (2020).
[12]    Turkyilmazoglu, M., “Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis”, Comput. Meth. Prog. Bio., 187, DOI:10.1016/j.cmpb.2019.105171 (2020).
[13]    Sadeghi, V., Baheri, S. and Arsalani, N., “An experimental investigation of the effect of using non-Newtonian nanofluid- graphene oxide /aqueous solution of sodium carboxymethyl cellulose- on the performance of direct absorption solar collector”, Sci. Iran., DOI:10.24200/SCI.2020.54994.4024 (2020).
[14]    Sheikholeslami, M., Rizwan-ul Haq, Ahmad, S., et al. “Heat transfer simulation of heat storage unit with nanoparticles and fins through a heat exchanger”, Int. J. Heat Mass Transf., 135, pp. 470-478 (2019).
[15]    Sheikholeslami, M., Behnoush, R., Milad, D., et al. “Application of nano-refrigerant for boiling heat transfer enhancement employing an experimental study”, Int. J. Heat Mass Transf., 141, pp. 974-980 (2019).
[16]    Ahmad, S., Ashraf, M. and Ali, K., “Nanofluid flow comprising gyrotactic microorganisms through a porous media”, JAFM, 13(5), pp. 1539-1549 (2020).
[17]    Khan, S. A. and Siddiqui, M. A., “Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus”, Heat Transfer, 49(3), pp. 1458-1490 (2020).
[18]    Irfan, M., Farooq, M. A. and Iqra, T., “A new computational technique design for EMHD nanofluid flow over a variable thickness surface with variable liquid characteristics”, Front. Phys., DOI:10.3389/fphy.2020.00066 (2020).
[19]    Turkyilmazoglu, M., “Multiple analytic solutions of heat and mass transfer of magnetohydrodynamic slip flow for two types of viscoelastic fluids over a stretching surface”, J. Heat Transfer, 134(7), DOI:10.1115/1.4006165 (2012).
[20]    Khan, Y., “Magnetohydrodynamic flow of linear visco-elastic fluid model above a shrinking/stretching sheet: A series solution”, Sci. Iran., 24(5), pp. 2466-2472 (2017).
[21]    Kumar, R., Sood, S., Sheikholeslami, M., et al. “Nonlinear thermal radiation and cubic autocatalysis chemical reaction effects on the flow of stretched nanofluid under rotational oscillations”, J. Colloid Interface Sci., 505, pp. 253-265 (2017).
[22]    Irfan, M., Farooq, M. A. and Iqra, T., “Magnetohydrodynamic free stream and heat transfer of nanofluid flow over an exponentially radiating stretching sheet with variable fluid properties”, Front. Phys., DOI:10.3389/fphy.2019.00186 (2019).
[23]    Akhter, S., Ashraf, M. and Ali, K., “MHD flow and heat transfer analysis of micropolar fluid through a porous medium between two stretchable disks using Quasi-linearization method”, Iran. J. Chem. Chem. Eng., 36(4), pp. 155-169 (2017).
[24]    Akhter, S. and Ashraf, M., “Numerical study of flow and heat transfer in a porous medium between two stretchable disks using Quasi-linearization method”, Therm. Sci., DOI:10.2298/TSCI180801163A (2019).
[25]    Turkyilmazoglu, M., “Stretching/shrinking longitudinal fins of rectangular profile and heat transfer”, Energy Convers. Manag., 91, pp. 199-203 (2015).
[26]    Turkyilmazoglu, M., “Latitudinally deforming rotating sphere”, Appl. Math.Model., 71, pp. 1-11 (2019).
[27]    Farooq, M., Salahuddin, A., Razzaq, M., et al. “Computational analysis for unsteady and steady magnetohydrodynamic radiating nano fluid flow past a slippery stretching sheet immersed in a permeable medium”, Sci. Iran., DOI:10.24200/SCI.2020.53055.3039 (2020).
[28]    Kuznetsov, A. V., “The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms”, Int. Commun. Heat Mass Transf., 37(10), pp. 1421-1425 (2010).
[29]    Kuznetsov, A. V., “Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganism: Oscillatory instability”, Nanoscale Res. Lett., 6, DOI:10.1186/1556-276X-6-100 (2011).
[30]    Khan, W. A., Rashad, A. M., Abdou, M. M. M., et al. “Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone”, European J. Mech. - B/Fluids, 75, pp. 133-142 (2019).
[31]    Hayat, T., Waqas, M., Shehzad, S. A., et al. “Mixed convection flow of viscoelastic nanofluid by a cylinder with variable thermal conductivity and heat source/sink”, Int. J. Numer. Method H., 26(1), pp. 214-234 (2016).
[32]    Mehryan, S. A. M., Kashkooli, F. M., Soltani, M., et al. “Fluid flow and heat transfer analysis of a nanofluid containing motile gyrotactic micro-organisms passing a nonlinear stretching vertical sheet in the presence of a non-uniform, magnetic field numerical approach”, PLOS, DOI:10.1371/journal.pone.0157598 (2016).
[33]    Akbar, N. S., “Bioconvection peristaltic flow in an asymmetric channel filled by nanofluid containing gyrotactic microorganism”, Int. J. Numer. Method H., pp.0961-5539 (2015).
[34]    Atif, S. M., Hussain, S. and Sagheer, M., “Magnetohydrodynamic stratified bioconvective flow of micropolar nano fluid due to gyrotactic microorganisms”, AIP Adv., 9(2), DOI:10.1063/1.5085742 (2019).
[35]    Zuhra, S., Khan, N. S., Shah, S., et al. “Simulation of bioconvection in the suspension of second grade nanofluid containing nanoparticles and gyrotactic microorganisms”, AIP Adv., 10(8), DOI:10.1063/1.5054679 (2018).
[36]    Atif, S., Hussain, S. and Sagheer, M., “Effect of thermal radiation on MHD micropolar Carreau nanofluid with viscous dissipation, Joule heating, and internal heating”, Sci. Iran., 26(6), pp. 3875-3888 (2019).
[37]    Nawaz, M., “Numerical study of hydrothermal characteristics in nano fluid using KKL model with Brownian motion”, Sci. Iran., 26(3), pp. 1931-1943 (2019).
[38]    Ferdows, M., Zaimi, K., Rashad, A. M., et al. “MHD bioconvection flow and heat transfer of nanofluid through an exponentially stretchable sheet”, Symmetry, 12(5), DOI:10.3390/sym12050692 (2020).
[39]    Shakiba, A. and Rahimi, A. B., “Role of movement of the walls with time-dependent velocity on flow and mixed convection in vertical cylindrical annulus with suction / injection”, Sci. Iran., DOI:10.24200/SCI.2020.54784.3917 (2020).
[40]    Ahmed, A., Khan, M., Ahmed, J., et al. “Mixed convection in unsteady stagnation point flow of Maxwell fluid subject to modified Fourier’s law, Arab. J. Sci. Eng., 45, pp. 9439-9447 (2020).
[41]    Aman, F., Hafizah, W. N., Khazim, W. M., et al. “Mixed convection flow of a nanofluid containing gyrotactic microorganisms over a stretching/shrinking sheet in the presence of magnetic field”, IOP Conf. Series: Journal of Physics: Conf. Series, 890, DOI:10.1088/1742-6596/890/1/012027 (2017).
[42]    Ahmad, S., Ashraf, M. and Ali, K., “Heat and mass transfer flow of gyrotactic microorganisms and nanoparticles through a porous medium”, Int. J. Heat and Technol., 32(2), pp. 395-402 (2020).
[43]    Sheikholeslami, M. and Rokni, H. B., “Effect of melting heat transfer on nanofluid flow in the presence of a magnetic field using the Buongiorno Model”, Chin. J. Phys., 55(4), pp. 1115-1126 (2017).
[44]    Wahid, N. S., Hafidzuddin, M. E. H., Arifin, N. M., et al. “Magnetohydrodynamic (MHD) slip Darcy flow of viscoelastic fluid over a stretching sheet and heat transfer with thermal radiation and viscous dissipation”, CFD Lett., 12(1), pp. 1-12 (2020).
[45]    Wahid, N. S., Hafidzuddin, M. E. H., Arifin, N. M., et al. “Exact analytical solution for MHD flow and heat transfer of Jeffrey fluid over a stretching sheet with viscous dissipation”, JMEST, 6(12), (2019).
[46]    Wahid, N. S., Arifin, N. M., Turkyilmazoglu, M., et al. “MHD Hybrid Cu-Al2O3/ Water nanofluid flow with thermal radiation and partial slip past a permeable stretching surface: analytical solution”, J. Nano R., 64, pp. 75-91 (2020).
[47]    Turkyilmazoglu, M., “The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface”, Int. J. Mech. Sci., 77, pp. 263-268 (2013).
[48]    Khan, S. U., Shehzad, S. A., Rauf, A., et al. “Mixed convection flow of couple stress nanofluid over oscillatory stretching sheet with heat absorption/generation effects”, Results Phys., 8, pp. 1223-1231 (2018).
[49]    Lund, L. A., Omar, Z., Khan, I., et al. “Convective effect on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid overa vertical exponentially stretching/shrinking surface: triple solutions”, Symmetry, 12, DOI:10.3390/sym12081238 (2020).
[50]    Mustafa, I., Abbas, Z., Arif, A., et al. “Stability analysis for multiple solutions of boundary layer flow towards a shrinking sheet: analytical solution by using least square method”, Phys. A Stat. Mech. Its Appl., 540, DOI:10.1016/j.physa.2019.123028 (2020).