Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects
Restricted accessResearch articleFirst published online 2020
Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects
In recent years, significant progress has been made in modern micro- and nanotechnologies for micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current work, a mathematical model is developed for steady convective von-Karman swirling flow from an impermeable radially stretched disk rotating in a Darcy porous medium saturated with nanofluid doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration are incorporated. The nano-bio transport model is formulated using nonlinear partial differential equations, which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate transformations. The transformed boundary value problem is solved by a Chebyshev spectral collocation method (CSCM). Impacts of key parameters on dimensionless velocity components, concentration, temperature and motile microorganism density distributions are investigated and graphically visualized. Validation with previous studies is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal slip, while nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism density number increases with the greater microorganism slip. Radial skin friction is boosted with positive values of the power law stretching parameter, whereas it is decreased with negative values. The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate and motile micro-organism density number gradient. Results from this study are relevant to novel bioreactors, membrane oxygenators, food processing and bio-chromatography.
MinkowyczWJSparrowEMAbrahamJP (eds). Nanoparticle heat transfer and fluid flow.
New York:
CRC Press, Taylor and Francis Group, 2013.
2.
ZarifiEJahanfarniaGVeysiF.Subchannel analysis of nanofluids application to VVER-1000 reactor. Chem Eng Res Des2013;
91: 625–632.
3.
GravelOLauzon-GauthierJDuchesneC, et al.
Inception of vortical coherent structures from spinning magnetic nanoparticles in rotating magnetic fields – new nanofluid microscale mixing tool. Chemical Engineering J2015;
260: 338–346.
4.
NieldDABejanA.Convection in porous media. 5th ed.Berlin:
Springer2017.
5.
ChoiSUS. Enhancing thermal conductivity of fluids with nanoparticles. In: The Proceedings of the 1995 ASME international mechanical engineering congress and exposition, San Francisco, USA, 12–17 November 1995. pp.99–105. New York: ASME.
6.
BuongiornoJ.Convective transport in nanofluids. ASME J Heat Transfer2006;
128: 240–250. DOI:10.1115/1.2150834.
7.
DasSKChoiSUSYuW, et al. Nanofluids: science and technology.
New York:
John Wiley,
2007.
8.
RahmanMMRoşcaAVPopI.Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno's model. Int J Heat Mass Transf2014;
77: 1133–1143.
9.
AcharyaNDasKKunduPK.Outlining the impact of second-order slip and multiple convective condition on nanofluid flow: a new statistical layout. Can J Phys2018;
96: 104–111.
10.
MahantheshBGireeshaBJSubbaR, et al.
Unsteady three-dimensional MHD flow of a nano Eyring-Powell fluid past a convectively heated stretching sheet in the presence of thermal radiation, viscous dissipation and joule heating. J Assoc Arab Univ Basic Appl Sci2017;
23: 75–84.
11.
HwangYPedleyTJ.Stability of downlowing gyrotactic microorganism suspensions in a two-dimensional vertical channel. J Fluid Mech2014;
749: 750–777.
12.
TsaiHLiouD-SKuoL-S, et al.
Rapid mixing between ferro-nanofluid and water in a semi-active Y-type micromixer. Sensors Actuators A2009;
153: 267–273.
13.
LiHLiuSDaiZ, et al.
Applications of nanomaterials in electrochemical enzyme biosensors, sensors. Sensors (Basel)2009;
9: 8547–8561.
14.
MunirAWangJZhouHS.Dynamics of capturing process of multiple magnetic nanoparticles in a flow through microfluidic bioseparation system. IET Nanobiotechnol2009;
3: 55–64.
15.
ChistiY.Biodiesel from microalgae. Biotechnol Adv2007;
25: 294–306.
16.
SatyanarayanaKGMarianoABVargasJVC.A review on microalgae, a versatile source for sustainable energy and materials. Int J Energy Res2011;
35: 291–311.
17.
AnejaMBégOAShamraS, et al.
Computation of electroconductive gyrotactic bioconvection under nonuniform magnetic field: Simulation of smart bio-nanopolymer coatings for solar energy. Int J Modern Physics B2020; DOI: 10.1142/S0217979220500289
18.
RoncalloOP.Comparison of two different vertical column photobioreactors for the cultivation of nannochloropsis sp. ASME J Energy Resour Technol2012;
135: 011201-011201-7.
19.
XuH.Lie group analysis of a nanofluid bioconvection flow past a vertical flat surface with an outer power-law stream. ASME J Heat Transfer2015;
137: 041101–041101.
20.
RaeesAXuHLiaoS-J.Unsteady mixed nano-bioconvection flow in a horizontal channel with its upper plate expanding or contracting. Int J Heat Mass Transf2015;
86: 174–182.
21.
SiddiqaSHinaGEBegumN, et al.
Numerical solutions of nanofluid bioconvection due to gyrotactic microorganisms along a vertical wavy cone. Int J Heat Mass Transf2016;
101: 608–613.
22.
TaskinMEFraserKHZhangT, et al.
Micro-scale modeling of flow and oxygen transfer in hollow fiber membrane bundle. J Memb Sci2010;
362: 172–183.
23.
GerbodeFOsbornJJJohnstonJB.Experience with perfusion hypothermia using an improved rotating disc oxygenator. Thorax1960;
15: 185–192.
24.
Mohamed MAA, Hassan MA and Elgazery NS.
The effects of radiation and hall current on the unsteady MHD laminar convective fluid flow through porous medium due to a porous rotating disk. Int J Theor Appl Mech2009;
4: 27–38.
25.
KármánTV.Uber laminare und turbulent Reibung (on laminar and turbulent flow). Z Angew Math Mech1921;
1: 233–252.
26.
ShevchukV.Convective heat and mass transfer in rotating disk systems.
New York:
Springer,
2009.
27.
MishraSRShamshuddinMBégOA, et al.
Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model. Heat Transfer – Asian Res2019;
48: 435–459.
28.
OA, BégWSJouri TasveerA, Béget al. Computation of asymmetric micropolar flow in a bionic prosthetic dual disk system with blowing (injection) and Reynolds number effects. In: International Conference on advances in mathematics, physics & applied science (ICAMPA), New Delhi, India, 1 March 2020.
29.
YinCZhengLZhangC, et al.
Flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate in the radial direction. Propuls Power Res2017;
6: 25–30.
30.
BégOAMaboodFNazrul IslamM.Homotopy simulation of nonlinear unsteady rotating nanofluid flow from a spinning body. Int J Eng Math2015;
2015: 1–15.
31.
KadirAMishraSRShamshuddinM, et al. Numerical simulation of Von Karman swirling bioconvection nanofluid flow from a deformable rotating disk, ICHTFM.2018. In: 20th International conference on heat transfer and fluid mechanics, WASET, Istanbul, Turkey, 16–17 August 2018.
32.
VafaiK.Porous media: applications in biological systems and biotechnology.
Florida:
CRC Press, 2010.
33.
KhaledARAVafaiK.The role of porous media in modeling flow and heat transfer in biological tissues. Int J Heat Mass Transfer2003;
46: 4989–5003.
34.
PodolaBLiTMelkonianM.Porous substrate bioreactors: a paradigm shift in microalgal biotechnology?Trends Biotechnol2017;
35: 121–132.
35.
YücelA.Heat and mass transfer about vertical surfaces in saturated porous media. AIChE Symp Ser1989;
269: 344.
36.
LaiFCKulackiFA.Coupled heat and mass transfer by natural convection from vertical surfaces in porous media. Int J Heat Mass Transf1991;
34: 1189–1194.
37.
BégOAMotsaSSKadirA, et al.
Spectral quasilinear numerical simulation of micropolar convective wall plumes in high permeability porous media. J Eng Thermophysics2016;
25: 1–24.
38.
UmavathiJCBégOA.Numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-Darcy porous medium with robin boundary conditions. J Eng Math2019; 119: 135–147.
39.
BégOABégTABhargavaR, et al.
Finite element study of pulsatile magneto-hemodynamic non-Newtonian flow and drug diffusion in a porous medium channel. J Mech Med Biol2012;
12: 1250081–1250026.
40.
AttiaHA.Steady flow over a rotating disk in porous medium with heat transfer. NAMC2009;
14: 21–26.
41.
BégOAAbdel MallequeKIslamMN.Modelling of Ostwald-dewaele non-Newtonian flow over a rotating disk in a non-Darcian porous medium. Int J Appl Math Mech2012;
8: 46–67.
42.
HayatTHaiderFMuhammadT, et al.
On Darcy-Forchheimer flow of carbon nanotubes due to a rotating disk. Int J Heat Mass Transfer2017;
112: 248–254.
43.
PorterBZauelRStockmanH, et al.
3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. J Biomech2005;
38: 543–549.
44.
SinghHAngESLimTT, et al.
Flow modelling in a novel non-perfusion conical bioreactor. Biotechnol Bioeng2007;
97: 1291–1299.
45.
TripathiDBégOACuriel-SosaJ.Homotopy semi-numerical simulation of peristaltic flow of generalized Oldroyd-B fluids with slip effects. Comput Methods Biomech Biomed Engin2014;
17: 433–442.
46.
AvramenkoAADmitrenkoNPShevchukIV, et al.
Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order. Int J Numer Meth Heat Fluid Flow2019;
29: 1786–1814.
47.
LienhardJH IV and and LienhardJHV.A heat transfer textbook. 3rd ed.
Cambridge, MA:
Phlogiston Press, 2005, pp.662–663.
48.
Schwartz K, Stephenson R, Hernandez M, et al.
The use of drip flow and rotating disk reactors for staphylococcus aureus biofilm analysis. J Vis Exp2010; 46: e2470.
49.
HajmohammadiMRMalekiHLorenziniG, et al.
Effects of Cu and Ag nano-particles on flow and heat transfer from permeable surfaces. Adv Powder Technol2015;
26: 193–199.
50.
LatiffNAUddinMJIsmailAIM.Stefan blowing effect on bioconvective flow of nanofluid over a solid rotating stretchable disk. Propuls Power Res2016;
5: 267–278.
51.
UddinMJKabirMNBégOA.Computational investigation of Stefan blowing and multiple-slip effects on buoyancy-driven bioconvection nanofluid flow with microorganisms. Int J Heat Mass Transfer2016;
95: 116–130.
52.
ZohraFTUddinMJIsmailAIM, et al.
Anisotropic slip magneto-bioconvection flow from a rotating cone to a nanofluid with Stefan blowing effects. Chin J Phys2018;
56: 432–448. DOI:10.1016/j.cjph.2017.08.031.
53.
RaguiKBoutraABennacerR, et al.
Correlating heat and mass transfer coefficients for thermosolutal convection within a porous annulus of a circular shape: case of internal pollutants spreading. Heat Mass Transfer2018;
54: 2061–2078.
54.
BégOA.Numerical methods for multi-physical magnetohydrodynamics, chapter 1. In: IbragimovMJAnisimovMA (eds) New developments in hydrodynamics research.
New York:
Nova Science,
2012, pp.1–112.
55.
CanutoCHussainiMYQuarteroniA, et al. Spectral methods in fluid dynamics.
New York:
Springer-Verlag, 1988.
56.
KaladharKReddyKMSrinivasacharyaD.Inclined magnetic field, thermal radiation and hall current effects on mixed convection flow between vertical parallel plates. ASME J Heat Transfer2019;
141: 102501.
57.
BelgacemFBGrundmannM.Approximation of the wave and electromagnetic diffusion equations by spectral methods. SIAM J Sci Comput1998;
20: 13–32. DOI:10.1137/S1064827595294344.
58.
Ma'enSSButcherEA.Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method. Int J Mech Sci2012;
60: 1–11.
59.
AlyEHSayedHM.Magnetohydrodynamic and thermal radiation effects on the boundary-layer flow due to a moving extensible surface with the velocity slip model: a comparative study of four nanofluids. J Magnet Magnet Mater2017;
422: 440–451.
60.
AgarwalPEl-SayedAA.Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation. Physica A: Stat Mech Appl2018;
500: 40–49. DOI:10.1016/j.physa.2018.02.014.
61.
UddinMJKabirMNBégOA, et al.
Chebyshev collocation computation of magneto-bioconvection nanofluid flow over a wedge with multiple slips and magnetic induction. Proc IMechE, Part L: J Nanomaterials, Nanoengineering Nanosystems2018;
232: 109–122.
62.
TianXYLiBWHuZM.Convective stagnation point flow of a MHD non-Newtonian nanofluid towards a stretching plate. Int J Heat Mass Transfer2018;
127: 768–780.
VasuBRamReddyCMurthyPVSN, et al.
Entropy generation analysis in non-linear convection flow of thermally stratified fluid in saturated porous medium with convective boundary condition. ASME J Heat Transfer2017;
139: 091701.
65.
BaiZQGuYFanCM.A direct Chebyshev collocation method for the numerical solutions of three-dimensional helmholtz-type equations. Eng Anal Boundary Elem2019;
104: 26–33.
66.
BégOAHameedMBégTA.Chebyschev spectral collocation simulation of nonlinear boundary value problems in electrohydrodynamics. Int J Comput Meth Eng Sci Mech2013;
14: 104–115.
67.
ShamshuddinMDFerdowsMRezwanO, et al. Ferromagnetic and non-magnetic nanoparticles in nanofluid flow from a stretching cylinder with magnetic induction: spectral relaxation solution. In: Proceedings of the international conference on numerical heat transfer and fluid flow (NHTFF-2020),NIT Warangal, India, 17–19 January2020.
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 Transf – Asian Res 2018; 47: 569–582.
70.
FangT.Flow and mass transfer for an unsteady stagnation-point flow over a moving wall considering blowing effects. ASME J Fluids Eng2014;
136: 071103.
71.
HansenG.Similarity analysis of boundary value problems in engineering.
New Jersey:
Prentice-Hall, 1964.
72.
ChtiouiODimitrovKGancelF, et al.
Rotating discs bioreactor, a new tool for lipopeptides production. Process Biochem2012;
47: 2020–2024.
73.
MelchiorRWSuttonSWHarrisW, et al.
Evolution of membrane oxygenator technology for utilization during pediatric cardiopulmonary bypass. Pediatric Health Med Ther2016;
7: 45–56.,
74.
QiuFGuanYSuX, et al.
Evaluation of neonatal membrane oxygenators with respect to gaseous microemboli capture and transmembrane pressure gradients. Artif Organs2010;
34: 923–929.
75.
DrummondMBraileDMLima-OliveiraAM, et al.
Technological evolution of membrane oxygenators. Rev Bras Cir Cardiovasc2005;
20: 432–437.
