Importance of activation energy and heat source on nanoliquid flow with gyrotactic microorganisms

Document Type : Article

Authors

1 - Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan - Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

3 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80203, Jeddah 21589, Saudi Arabia

4 Department of Mathematics, CUT, Chak Shahzad, Park Road, Islamabad, Pakistan

Abstract

This article addresses salient features of gyrotactic microorganism and activation energy in flow of nanofluid by rotating disk. An exponential space dependent heat source (ESHS) process is implemented to examine the thermal transport characteristics. Additionally nanoparticles mass flux condition is considered. The solutions are numerically computed. Impacts of various physical variables appearing in the solutions of non-linear systems are carefully analyzed. The current work identifies that temperature distribution of nanoliquid enhances for higher values of thermophoresis and Brownian motion variables. Moreover activation energy and temperature difference parameters diminish the nanoparticles concentration. Comparative study is provided in order to validate our outcomes.

Keywords


References:
 
[1].    Choi, S.U.S. and Eastman, J. A. "Enhancing thermal conductivity of fluids with nanoparticles", The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD, 66, pp. 99-105 (1995).
[2].    Buongiorno, J. "Convective transport in nanofluids", J. heat transfer, 128(3), pp. 240-250 (2006).
[3].    Sheikholeslami, M., T. Hayat, and A. Alsaedi. "Numerical simulation of nanofluid forced convection heat transfer improvement in existence of magnetic field using lattice Boltzmann method", Int. J. Heat Mass Transfer, 108, pp. 1870-1883 (2017).
[4].    Tiwari, R. K. and Manab K. D. "Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids", Int. J. Heat Mass Transfer, 50(9-10), pp. 2002-2018 (2007).
[5].    Shehzad, S.A., Hayat, T., Alsaedi, A. et al. "A useful model for solar radiation", Ener. Eco. and Environ., 1(1), pp. 30-38 (2016).
[6].    Sheikholeslami, M., Hayat, T. and Alsaedi, A. "On simulation of nanofluid radiation and natural convection in an enclosure with elliptical cylinders", Int. J. Heat Mass Transfer, 115 pp. 981-991 (2017).
[7].    Alsaedi, A., Awais, M. and Hayat, T. "Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions", Commun Nonlinear Sci. and Numer. Simul., 17(11), pp. 4210-4223 (2012).
[8].    Hayat, T., Ullah, I., Muhammad, T., et al. "Magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid by a convectively heated exponentially stretching surface", J. Mol. Liq., 220, pp.1004-1012 (2016).
[9].    Hayat, T., Ullah, I., Waqas, M., et al. "Flow of chemically reactive magneto Cross nanoliquid with temperature-dependent conductivity", Applied Nanoscience, 8(6), pp. 1453-1460 (2018).
[10].    Hsiao, K.L. "Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet." Appl. Therm. Eng., 98, pp. 850-861 (2016).
[11].    Lin, Y., Zheng, L., Zhang, X., et al. "MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation", Int. J. Heat Mass Transfer, 84, pp.903-911 (2015).
[12].    Mustafa, M., Hayat, T., Pop, I., et al. "Stagnation-point flow of a nanofluid towards a stretching sheet" Int. J. Heat Mass Transfer, 54(25-26), pp.5588-5594 (2011).
[13].    Sheikholeslami, M., Hayat, T. and Alsaedi, A., "On simulation of nanofluid radiation and natural convection in an enclosure with elliptical cylinders", Int. J. Heat Mass Transfer, 115, pp.981-991 (2017).
[14].    Hayat, T., Ullah, I., Alsaedi, A., et al. "Three-dimensional mixed convection flow of Sisko nanoliquid" Int. J. Mech.l Sci., 133, pp.273-282 (2017).
[15].    Hussain, Z., Hayat, T., Alsaedi, A., et al. "Three-dimensional convective flow of CNTs nanofluids with heat generation/absorption effect: A numerical study", Comp. Methods Appl. Mech. Eng., 329, pp.40-54 (2018).
[16].    Hayat, T., Ullah, I., Alsaedi, A., et al. "MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness", Results Phys., 7, pp.189-196 (2017).
[17].    Ellahi, R., Zeeshan, A., Shehzad, N., et al. "Structural impact of Kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: application of cooling process", J. Mol. Liq., 264, pp. 607-615 (2018).
[18].    Hassan, M., Marin, M., Ellahi, R., et al. "Exploration of convective heat transfer and flow characteristics synthesis by Cu-Ag/water hybrid-nanofluids", Heat Trans. Res., 49(18), (2018).
[19].    Rashidi, S., Akar, S., Bovand, M., et al. "Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still", Renew. Energy, 115, pp. 400-410 (2018).
[20].    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).
[21].    Akbarzadeh, M., Rashidi, S., Karimi, N., et al. "Convection of heat and thermodynamic irreversibilities in two-phase, turbulent nanofluid flows in solar heaters by corrugated absorber plates", Adv. Powder Technol., 29(9), pp. 2243-2254 (2018).
[22].    Alamri, S.Z., Ellahi, R., Shehzad, N., et al."Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: an application of Stefan blowing", J. Mol. Liq., 273, pp. 292-304 (2019).
[23].    Shehzad, N., Zeeshan, A., Ellahi, R., et al. "Modelling study on internal energy loss due to entropy generation for non-darcy poiseuille flow of silver-water nanofluid: an application of purification", Entropy, 20(11), pp. 851 (2018).
[24].    Ellahi, R., Zeeshan, A., Hussain, F., et al. "Peristaltic blood flow of couple stress fluid suspended with nanoparticles under the influence of chemical reaction and activation energy", Symmetry, 11(2), pp. 276 (2019).
[25].    Ashlin, T. S., and B. Mahanthesh. "Exact solution of non-coaxial rotating and non-linear convective flow of Cu-Al2O3-H2O hybrid nanofluids over an infinite vertical plate subjected to heat source and radiative heat", J. Nanofluids, 8(4), pp. 781-794 (2019).
[26].    Shruthy, M., and B. Mahanthesh. "Rayleigh-Bénard convection in Casson and Hybrid Nanofluids: An Analytical Investigation", J. Nanofluids, 8(1), pp. 222-229 (2019).
[27].    Amala, S., and B. Mahanthesh. "Hybrid Nanofluid Flow Over a Vertical Rotating Plate in the Presence of Hall Current, Nonlinear Convection and Heat Absorption", J. Nanofluids, 7(6), pp. 1138-1148 (2018).
[28].    Animasaun, I.L., Koriko, O.K., Adegbie, K.S., et al. "Comparative analysis between 36 nm and 47 nm alumina--water nanofluid flows in the presence of Hall effect", J. Therm. Anal. Calorim., 135(2), pp. 873-886 (2019).
[29].    Golshokooh, S., Ramazani, S.A. and Hekmatzadeh, M."Investigating the effect of hybrid silica nanoparticles-copolymer on increasing oil recovery in a three dimensional porous media, Sci. Iran., 24(6), pp.3466-3475 (2017).
[30].    AfzaliTabar, M., Alaeib, M., Khojasteh, R.R., et al. "Preference of nanoporous graphene to Single-Walled Carbon Nanotube (SWCNT) for preparing silica nanohybrid Pickering emulsion for potential Chemical Enhanced Oil Recovery (C-EOR)", Sci. Iran., 24, pp.3491-9 (2017).
[31].    Karbasi, S., Zarei, M. and Foroughi, M.R. "Effects of Multi-Wall carbon Nano-Tubes (MWNTs) on structural and mechanical properties of electrospun poly (3-hydroxybutyrate) scaffold for tissue engineering applications", Sci. Iran., 23(6), p.3145 (2016).
[32].    Hakeem, A.A., Ganesh, N.V. and Ganga, B. "Heat transfer of non-Darcy MHD flow of nanofluid over a stretching/shrinking surface in a thermally stratified medium with second order slip model", Sci. Iran., 22(6), p.2766 (2015).
[33].    Harifi, T. and Montazer, M. "   hematite or magnetite/    nanoparticles synthesized on polyester fabric at various temperatures producing different superparamagnetic, self-cleaning and antibacterial textiles", Sci. Iran.,  21(6), p.2490 (2014).
[34].    Hayat, T., Muhammad, K., Ullah, I., et al. "Rotating squeezed flow with carbon nanotubes and melting heat", Phys. Scr., 94, pp.035702 (2019).
[35].    Alsedi, F.E., Ullah, I., Hayat, T., et al. "Entropy generation in non-linear mixed convective flow of nanofluid in porous space influenced by Arrhenius activation energy and thermal radiation", J. Therm. Anal. Calorim., (2019) https://doi.org/10.1007/s10973-019-08648-0.
[36].    Zhou, C. and Ma, H. "Ultrasonic degradation of polysaccharide from a red algae (Porphyra yezoensis)", J. Agric. Food Chem., 54(6), pp.2223-2228 (2006).
[37].    Bestman, A.R. "Natural convection boundary layer with suction and mass transfer in a porous medium", Int. J. Energ. Res., 14(4), pp.389-396 (1990).
[38].    Awad, F.G., Motsa, S. and Khumalo, M. "Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy", PloS one, 9(9), p.e107622 (2014).
[39].    Makinde, O.D., Olanrewaju, P.O. and Charles, W.M., "Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture", Afrika Mat., 22(1), pp.65-78 (2011).
[40].    Maleque, K. "Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation", J. Thermodyn. , 2013 (2013).
[41].    Mustafa, M., Khan, J.A., Hayat, T., et al. "Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy", Int. J.Heat Mass Transfer, 108, pp.1340-1346 (2017).
[42].    Abbas, Z., Sheikh, M. and Motsa, S.S. "Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation", Energy, 95, pp.12-20 (2016).
[43].    Zeeshan, A., Shehzad, N. and Ellahi, R. "Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions", Results phys., 8, pp.502-512 (2018).
[44].    Hayat, T., Ullah, I., Farooq, M., et al. "Analysis of non-linear radiative stagnation point flow of Carreau fluid with homogeneous-heterogeneous reactions", Microsyst. Technol., 25(4), pp.1243-1250 (2019).
[45].    Hayat, T., Ullah, I., Alsaedi, A., et al. "Numerical simulation for homogeneous-heterogeneous reactions in flow of Sisko fluid", J. Braz. Soc. Mech. Sci. Eng., 40(2), pp.73 (2018).
[46].    Archana, M., and B. Mahanthesh. "Exploration of activation energy and binary chemical reaction effects on nano Casson fluid flow with thermal and exponential space-based heat source", Multidiscip., 15(1), pp. 227-245 (2019).
[47].    Chen, H., Chen, J., Geng, Y., et al. "Three-dimensional boundary layer flow over a rotating disk with power-law stretching in a nanofluid containing gyrotactic microorganisms", Heat Tran. Asian Res., 47(3), pp.569-582 (2017).
[48].    Zia, Q.Z., Ullah, I., Waqas, Met al.  "Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface", Results Phys., 8, pp.1275-1282 (2018).
[49].    Hayat, T., Ullah, I., Waqas, M., et al. "Attributes of activation energy and exponential based heat source in flow of Carreau fluid with cross-diffusion effects", J. Non-Equil. Thermody., 44(2), pp.203-213 (2019).
[50].    Khan, A.A., Usman, H., Vafai, K., et al. "Study of peristaltic flow of magnetohydrodynamic Walter's B fluid with slip and heat transfer", Sci. Iran., 23(6) pp. 2650-2662 (2016).
[51].    El-Aziz, M.A. and Salem, A.M. "MHD-mixed convection and mass transfer from a vertical stretching sheet with diffusion of chemically reactive species and space-or temperature-dependent heat source" Can. J. Phys., 85(4), pp.359-373 (2007).
[52].    Animasaun, I.L. "Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction" J. Nigerian Math., 34(1), pp.11-31 (2015).