Abstract
The pioneer motivations for current flow model are to study the rheological aspects of chemical reactive Williamson nano-material with utilization of gyrotactic microorganisms. The peak theme of activation energy and variable thermal conductivity are also incorporated. Unlike typical investigations, current flow model is formulated with employment of slip consequences with higher order relations. The induced flow is caused by a porous stretched surface additionally impact by magnetic force. The flow equations are transmuted into dimensionless form first for which numerical simulations are performed using famous finite difference approximations. The results are verified for limiting cases by comparing with various investigations and found excellent accuracy. The physical insight of all flow parameters are graphically underlined with interesting physical appliances. Furthermore, the numerical calculation for heat transfer enhancement, change in mass flux and motile density simulations are also evaluated in tabular form. The stream line and contour plots are also prepared.
Similar content being viewed by others
References
Acharya N, Maity S, Kundu PK (2020) Influence of inclined magnetic field on the flow of condensed nanomaterial over a slippery surface: the hybrid visualization. Appl Nanosci 10:633–647
Ahmad J, Khan M, Ahmad L (2019) Stagnation point flow of Maxwell nanofluid over a permeable rotating disk with heat source/sink. J Mol Liq 287:110853
Ahmed B, Hayat T, Alsaedi A, Abbasi FM (2020) Entropy generation analysis for peristaltic motion of Carreau-Yasuda nanomaterial. Phys Scr 95(5):055804
Alwatban AM, Khan SU, Waqas H, Tlili I (2019) Interaction of Wu’s slip features in bioconvection of eyring powell nanoparticles with activation energy. Processes 7(11):859
Aly EH (2019) Dual exact solutions of graphene–water nanofluid flow over stretching/shrinking sheet with suction/injection and heat source/sink: critical values and regions with stability. Powder Technol 342:528–544
Aly B (2020) Controlled optoelectronic properties and abrupt change in photosensitivity by suppressing density of oxygen vacancies in SnO2 nanocrystalline thin films prepared at various spray-deposition temperatures. Phys Scr 95(6):065807
Amirsom NA, Uddin MJ, Md Ismail AI (2019) MHD boundary layer bionanoconvective non-Newtonian flow past a needle with Stefan blowing. Heat Transfer Asian Res 48(2):727–743
Bég OA, Espinoza DES, Kadir A, Shamshuddin MD, Sohail A (2018) Experimental study of improved rheology and lubricity of drilling fluids enhanced with nano-particles. Appl Nanosci 8:1069–1090
Buongiorno J (2006) Convective transport in nanofluids. J Heat Transfer 128:240–250
Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles, ASME Pub. Fed 231:99–106
Farooq S, Hayat T, Alsaedi A, Ahmad B (2017) Numerically framing the features of second order velocity slip in mixed convective flow of Sisko nanomaterial considering gyrotactic microorganisms. Int J Heat Mass Transf 112:521–532
Hamid M, Usman M, Zubair T, Haq RUL, Wang W (2018) Shape effects of MoS2 nanoparticles on rotating flow of nanofluid along a stretching surface with variable thermal conductivity: a galerkin approach. Int J Heat Mass Transf 124:706–714
Imtiaz M, Hayat T, Alsaedi A, Ahmad B (2016) Convective flow of carbon nanotubes between rotating stretchable disks with thermal radiation effects. Int J Heat Mass Transf 101:948–957
Khan SU, Shehzad SA, Rauf A, Ali N (2018a) Mixed convection flow of couple stress nanofluid over oscillatory stretching Sheet with heat absorption/generation effects. Results Phys 8:1223–1231
Khan M, Shahid A, Malik MY, Salahuddin T (2018b) Thermal and concentration diffusion in Jeffery nanofluid flow over an inclined stretching sheet: a generalized Fourier's and Fick's perspective. J Mol Liq 251:7–14
Khan SU, Shehzad SA, Ali N (2018c) Interaction of magneto-nanoparticles in Williamson fluid flow over convective oscillatory moving surface. J Braz Soc 40:195
Khan WA, Rashad AM, Abdou MMM, Tlili I (2019a) Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone. Eur J Mech 75:133–142
Khan SU, Waqas H, Shehzad SA, Imran M (2019b) Theoretical analysis for tangent hyperbolic nanoparticles with combined electrical MHD, activation energy and Wu’s slip features: a mathematical model. Phys Scr 94(12):125211
Khan NS, Shah Q, Bhaumik A, Kumam P, Thounthong P (2020a) Irajsadegh amiri, entropy generation in bioconvection nanofluid flow between two stretchable rotating disks. Sci Rep 10:4448. https://doi.org/10.1038/s41598-020-61172-2
Khan SU, Shehzad SA, Ali N (2020b) Bioconvection flow of magnetized Williamson nanoliquid with motile organisms and variable thermal conductivity. App Nanosci. https://doi.org/10.1007/s13204-020-01282-5
Kuznetsov AV (2010) The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. Int Commun Heat Mass Transf 37(10):1421–1425
Kuznetsov AV (2011) Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: Oscillatory instability. Nanoscale Res Lett 6:100
Mabood F, Das K (2016) Melting heat transfer on hydromagnetic flow of a nanofluid over a stretching sheet with radiation and second-order slip. Eur Phys J Plus 131:3
Mabood F, Khan WA, Ismail AIM (2015) MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study. J Magn Magn Mater 374:569–576
Mabood F, Ibrahim SM, Rashidi MM, Shadloo MS, Lorenzini G (2016) Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation. Int J Heat Mass Transfer 93:674–682
Mahanthesh B, Amala SB, Gireesha J, Animasaun IL (2019) Effectiveness of exponential heat source, nanoparticle shape factor and Hall current on mixed convective flow of nanoliquids subject to rotating frame. Multidiscip 15(4):758–778
Mondal SK, Pal D (2020) Computational analysis of bioconvective flow of nanofluid containing gyrotactic microorganisms over a nonlinear stretching sheet with variable viscosity using HAM. J Comput Des Eng 7(2):251–267
Nandeppanavar MM, Vajravelu K, Abel MS, Siddalingappa M (2012) Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. Int J Therm Sci 58:143–150
Nawaz S, Hayat H, Alsaedi A (2019) Analysis of entropy generation in peristalsis of Williamson fluid in curved channel under radial magnetic field. Comput Meth Prog Bio 180:105013
Qayyum S, Khan MI, Hayat T, Alsaedi A, Tamoor M (2018) Entropy generation in dissipative flow of Williamson fluid between two rotating disks. Int J Heat Mass Transf 127:933–942
Rana S, Nawaz M, Saleem S, Alharbi SO (2020) Numerical study on enhancement of heat transfer in hybrid nano-micropolar fluid. Phys Scr 95(4):045201
Rashad AM, Chamkha AJ, Mallikarjuna B, Abdou MMM (2018) Mixed bioconvection flow of a nanofluid containing gyrotactic microorganisms past a vertical slender cylinder. Front Heat Mass Transf 10:21
Sheikholeslami M, Bhatti MM (2017) Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. Int J Heat Mass Transf 111:1039–1049
Sheikholeslami M, Jafaryar M, Sheremet MA, Shafee A, Babazadeh H (2020) Nanomaterial thermal performance within a pipe in presence of turbulator. Appl Nanosci. https://doi.org/10.1007/s13204-020-01436-5
Siddiqui AA, Turkyilmazoglu M (2019) A new theoretical approach of wall transpiration in the cavity flow of the ferrofluids. Micromachines 10(6):373
Subbarayudu K, Suneetha S, Reddy PBA (2020) The assessment of time dependent flow of Williamson fluid with radiative blood flow against a wedge. J Propul Power 9(1):87–99
Tlili I, Khan WA, Ramadan K (2019) MHD flow of nanofluid flow across horizontal circular cylinder: steady forced convection. J Nanofluids 8(1):179–186
Turkyilmazoglu M (2019) Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models. Comput Meth Prog Bio 179:104997
Uddin MJ, Alginahi Y, Bég OA, Kabir MN (2016) Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects. Comput Math Appl 72(10):2562–2581
Waqas H, Khan SU, Imran M, Bhatti MM (2019a) Thermally developed Falkner-Skan bioconvection flow of a magnetized nanofluid in the presence of motile gyrotactic microorganism: Buongiorno’s nanofluid model. Phys ScR 94(11):115304
Waqas H, Khan SU, Hassan M, Bhatti MM, Imran M (2019b) Analysis for bioconvection flow of modified second grade fluid containing gyrotactic microorganisms and nanoparticles. J Mol Liq 291(1):111231
Williamson RV (1929) The flow of pseudoplastic materials. Ind Eng Chem Res 21:1108
Wu L (2008) A slip model for rarefied gas flows at arbitrary Knudsen number. Appl Phys Lett 93:253103
Xu L, Lee EWM (2013) Variational iteration method for the magnetohydrodynamic flow over a nonlinear stretching sheet. Abst Appl Anal 5:2013
Acknowledgment
This work is not supported by any financial support.
Author information
Authors and Affiliations
Contributions
All the authors contributed equally.
Corresponding author
Ethics declarations
Conflict of interest
Authors declared no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mabood, F., Khan, S.U. & Tlili, I. Numerical simulations for swimming of gyrotactic microorganisms with Williamson nanofluid featuring Wu’s slip, activation energy and variable thermal conductivity. Appl Nanosci 13, 131–144 (2023). https://doi.org/10.1007/s13204-020-01548-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13204-020-01548-y