Chemical Reaction Effects on Bio-Convection Nanofluid flow between two Parallel Plates in Rotating System with Variable Viscosity: A Numerical Study

Document Type : Research Paper


Department of Mathematics, SAS, VIT, Vellore-632014, T.N, India


In the present work, a mathematical model is developed and analyzed to study the influence of nanoparticle concentration through Brownian motion and thermophoresis diffusion. The governing system of PDEs is transformed into a coupled non-linear ODEs by using suitable variables. The converted equations are then solved by using robust shooting method with the help of MATLAB (bvp4c). The impacts of dynamic parameters on the flow, energy and concentration are discussed graphically. It is noticed that the mass transfer rate in case of regular fluid is lower than that of nanofluid and the axial velocity converges to the boundary very fast in case of temperature dependent viscosity case than the regular viscous case.


Main Subjects

[1] Choi, S.U.S., Eastman, J. A., Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of Non-Newtonian Flows, ASME MD 231, 1995, 99-105.
[2] Das, K., Duari, P.R., Kundu, P.K., Nanofluid bioconvection in presence of gyrotactic microorganisms and chemical reaction in a porous medium, J. Mech. Sci. Tech., 29(11), 2015, 4841-4849.
[3] Khan, U., Ahmed, N., Din, S.T.M., Influence of viscous dissipation and joule heating on MHD bio-convection flow over a porous wedge in the presence of nanoparticles and gyrotactic microorganisms. Springer plus, 5, 2016, 1-18.
[4] Childress, S., Levandowsky, M., Spiegel, E.A., Pattern formation in a suspension of swimming micro-organisms: equations and stability theory. J. Fluid Mech. 69, 1975, 591-613.
[5] Hill, N.A., Pedley, T.J., Kessler, J.O., Growth of bio convection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth, J. Fluid Mech. 208, 1989, 509-543.
[6] Kuznetsov, A.V., Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability, Nanoscale Res. Lett., 6(100), 2011, 1-13.
[7] Xinyu, W., Huiying, W., Cheng, P., Pressure drop and heat transfer of al2o3-h2o nanofluids through silicon Microchannels, J. Micro. Mech. Micro. Eng., 19, 2009, 105020(11).
[8] Xu, H., Pop, I., Fully developed mixed convection flow in a horizontal channel filled by a nanofluid containing both nanoparticles and gyrotactic microorganisms, European J. Mech. B/Fluids, 46, 2014, 37-45.
[9] Uddin, M.J., Alginahi, Y., Bég, O.A., Kabir, M.N., Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects, Comp. Math. Appl., 72, 2016, 2562-2581.
[10] Siddiqa, S., Hina, G.E., Begum, N., Saleem, S., Hossain, M.A., Rama Subba Reddy, G., Numerical solutions of nanofluid bioconvection due to gyrotactic microorganisms along a vertical wavy cone, Int. J. Heat Mass Transfer, 101, 2016, 608-613.
[11] Mohsin, B.B., Ahmed, N., Adnan, Khan, U., Din, S.T.M., 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, 1-12.
[12] Iqbal, Z., Mehmood, Z., Azhar, E., Maraj, E.N., Numerical investigation of Nanofluidic transport of gyrotactic microorganisms submerged in water towards Riga plate, J. Mole. Liq., 234, 2017, 296-308.
[13] Ojjela, O., Ramesh, K., Das, S.K., Second Law Analysis of MHD Squeezing Flow of Casson Fluid between Two Parallel Disks, Int. J. Chemical. Reactor Eng., 6(16), 2018,
[14] Li, Z., Sheikholeslami, M., Chamkha, A.J.,  Raizah, Z.A., Saleem, S., Control volume finite element method for nanofluid MHD natural convective flow inside a sinusoidal annulus under the impact of thermal radiation,Comp. Methods Appl. Mech. Eng.,338(15), 2018, 618-633.
[15] Mahian, O., Kolsi, L., Amani, M., Estelle, P., Ahmadi, G., Kleinstreuer, C., Marshall, J.S., Taylor, R.A., Nada, E.A., Rashidi, S., Niazmand, H., Wongwises, S., Hayat, T., Kasaeian, A., Pop, I., Recent advances in modeling and simulation of nanofluid flows-part II: Applications Physics Reports, 791, 2019, 1-59.
[16] Li, Z., Shehzad, S.A., Sheikholeslami, M., An application of CVFEM for nanofluid heat transfer intensification in a porous sinusoidal cavity considering thermal non-equilibrium model, Comp. Meth. Appl. Mech. Eng., 339(1), 2018, 663-680.
[17] Mahian, O., Kolsi, L., Amani, M., Estelle, P., Ahmadi, G., Kleinstreuer, C., Marshall, J.S., Siavashi, M., Taylor, R.A., Niazmand, H., Wongwises, S., Hayat, T., Kolanjiyil, A., Kasaeian, A., Pop, I., Recent advances in modeling and simulation of nanofluid flows-Part I: Fundamental and theory, Physics Reports, 790, 2019, 1-48.
[18] Mahian, O., Kianifar, A., Kalogirou, S.A., Pop, I., Wongwises, S., A review of the applications of nanofluids in solar energy, Int. J. Heat Mass Transfer 57, 2013, 582-594.
[19] Mahian, O., Pop, I., Sahin, A.Z., Oztop, H.F., Wongwises, S., Irreversibility analysis of a vertical annulus using TiO2/water nanofluid with MHD flow effects, Int. J. Heat Mass Transfer 64, 2013, 671-679.
[20] Mahian, O., Kleinstreuer, C., Nimr, M.A.A., Pop, I., Wongwises, S., A review of entropy generation in nanofluid flow, Int. J. Heat Mass Transfer 65, 2013, 514-532.
[21] Naseem, F., Shafiq, A., Zhao, L., Naseem, A., MHD bio convective flow of Powell eyring nanofluid over stretched surface, AIP Advances, 7, 2017, 1-21.
[22] Chakraborty, T., Das, K., Kundu, P.K., Framing the impact of external magnetic field on bioconvection of a nanofluid flow containing gyrotactic microorganisms with convective boundary conditions, Alexandria Eng. J., 2016, 1-11.
[23] Alsaedi, A. Khan, M.I., Farooq, M., Gull, N., Hayat, T., Magnetohydrodynamic stratified bio convective flow of nanofluid due to gyrotactic microorganisms, Advanced Powder Tech. 28, 2017, 288-298.
[24] Acharya, N., Das, K., Kundu, P.K., Framing the effects of solar radiation on magneto-hydrodynamics bioconvection nanofluid flow in presence of gyrotactic microorganisms, J. Mole. Liq., 222, 2016, 28-37.
[25] Sheikholeslami, M., Ganji, D.D., Javed, M.Y., Ellahi, R., Effect of Thermal Radiation on Magnetohydrodynamics Nanofluid flow and Heat Transfer by Means of two Phase Model, J. Magne. Magn. Mater, 374, 2017, 36-43. 
[26] Hsiao, K.L., Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature, Int. J. Heat Mass Transfer, 112, 2017, 983-990.
[27] Tamoor, M., Waqas, M., Khan, M.I., Alsaedi, A., Hayat, T., Magnetohydrodynamic flow of casson fluid over a stretching cylinder, Results Phys, 3,2017, 1-5.
[28] Ramzan, M., Bilal, M., Chung, J.D., Mann, A.B., On MHD radiative Jeffery nanofluid flow with convective heat and mass boundary conditions, Neural Comp. Appl., 9, 2017, 2739-2748.
[29] Tekade, S.P., Shende, D.Z., Wasewar, K.L., Hydrogen Generation in an Annular Micro-Reactor: An Experimental Investigation and Reaction Modelling by Shrinking Core Model (SCM), Int. J. Chemical Reactor Eng., 7(16), 2018. DOI:
[30] Siddiqa, S., Faryad, A., Begum, A., Hossain, M.A., Rama Subba Reddy, G., Periodic magnetohydrodynamic natural convection flow of a micropolar fluid with radiation, Int. J. Thermal Sci., 111, 2017, 215-222.
[31] Khan, M., Malik, M.Y., Salahuddin, T., Rehman, K.U., Naseer, M., Khan, I., MHD flow of Williamson nanofluid over a cone and plate with chemically reactive species, J. Mole. Liq., 231, 2017, 580-588.
[32] Devika, B., Satya Narayana, P.V., Venkataramana, S., MHD oscillatory flow of a viscoelastic fluid in a porous channel with chemical reaction, Int. J. Eng. Science Invention,2(2), 2013, 26-35.
[33] Jena, S., Mishra, S.R., Dash, G.C., Chemical reaction effect on MHD Jeffery fluid flow over a stretching sheet through porous media with heat generation/absorption, Int. J. Appl. Comp. Math., 2, 2016, 1225-1238.
[34] Javaid, S., Aziz, A., Influence of variable thermal conductivity and thermal radiation on slip flow and heat transfer of MHD power-law fluid over a porous sheet, Thermal Sci. 2016, 65-65.
[35] Satya Narayana, P.V., Venkateswarlu, B., Devika, B., Chemical reaction and heat source effects on MHD oscillatory flow in an irregular channel, Ain Shams Eng. J. 2016, 1079-1088.
[36] Hayat, T., Rashid, M., Imtiaz, M., Alsaedi, A., MHD convective flow due to a curved surface with thermal radiation and chemical reaction, J. Mole. Liq., 225, 2017, 482-489.
[37] Xun, S., Zhao, J., Zheng, L., Zhang, X., Bioconvection in rotating system immersed in nanofluid with temperature dependent viscosity and thermal conductivity, Int. J. Heat Mass Transfer, 111, 2017, 1001-1006.
[38] Sheikholeslami, M., Ganji, D.D., Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet, J. Mole. Liq., 194, 2014, 13-19.
[39] Sheikholeslami, M., Ganji, D.D., Three dimensional heat and mass transfer in a rotating system using nanofluid, Powder Tech., 253, 2014, 789-796.
[40] Mustafa, M., Khan, J.A., Numerical study of partial slip effects on MHD flow of nanofluids near a convectively heated stretchable rotating disk, J. Mole. Liq., 234, 2017, 287-295.
[41] Makinde, O.D., Mabood, F., Khan, W.A., Tshehla, M.S., MHD flow of a variable viscosity nanofluid over a radially stretching convective surface with radiative heat, J. Mole. Liq., 219, 2016, 624-630.
[42] Sheikholeslami, M., Ganji, D.D., Impact of electric field on nanofluid forced convection heat transfer with considering variable properties, J. Mole. Liq., 229, 2017, 566-573.
[43] Chen., X, Hu., Z, Lei Zhang., L, Zhen Yao., Z, Chen., X, Zheng., Y, Liu., Y, Wang., Q, Yang Liu., Y, Cui., X, Song., H., Numerical and Experimental Study on a Microfluidic Concentration Gradient Generator for Arbitrary Approximate Linear and Quadratic Concentration Curve Output, Int. J. Chemical. Reactor Eng., 1(16), 2018. doi: 10.1515/ijcre-2016-0204.
[44] Sheikholeslami, M., Ganji, D.D., Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet, J. Mole. Liq., 194, 2014, 13-19.
[45] Kumar, R., Sood, S., Shehzad, S.A., Sheikholeslami, M., Radiative heat transfer study for flow of non-Newtonian nanofluid past a Riga plate with variable thickness, J. Mole. Liq., 248, 2017, 43-152.
[46] Nield, D.A., Kuznetsov, A.V., Thermal instability in a porous medium layer saturated by a nanofluid, Int. J. Heat Mass Transfer, 52, 2009, 5796-5801.
[47] Kuznetsov, A.V., Non-oscillatory and oscillatory nanofluid bio-thermal convection in a horizontal layer of finite depth, European J. Mech. B/Fluids, 30, 2017, 156-165.
[48] Sheikholeslami, M., Ganji, D.D. Javed, M.Y. Ellahi, R., Effect of thermal radiation on Magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model, J. Magn. Magnet. Mater. 374, 2017, 36-43.
[49] Attia, H.A., Kotb, N.A., MHD flow between two parallel plates with heat transfer, Acta Mech., 117, 1996, 1257-1266.
[50] Attia, H.A., Transient MHD flow and heat transfer between two parallel plates with temperature dependence viscosity, Mech. Res. Comm., 26, 1999, 115-121.
[41] Attia, H.A., Cairo, Egypt, Influence of temperature dependence viscosity on the MHD-channel flow of dusty fluid with heat transfer, Act Mach., 151, 2001, 89-101.
[52] Attia, H.A., MHD couette flow with temperature dependent viscosity and the ion slip, Tamkang J. Sci. Eng., 8(1), 2005, 11-16.
[53] Lai, F., Kulacki, F., The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat Mass Transfer, 33(5), 1990, 1028–31.
[54] Devi, S.P.A., Prakash, M., Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet, J. Nigerian Math. Society, 34, 2015, 318-330.
[55] Brewster, M.Q., Thermal Radiative Transfer Properties, Wiley, New York, 1992.
[56] Din, S.T.M., Zaidi, Z.A., Khan, U., Ahmed, N., On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates, Aerospace Sci. Tech., 46, 2015, 514-522.