Advertisement

Flow of nanofluid with Cattaneo–Christov heat flux model

  • Jawdat AlebraheemEmail author
  • M. Ramzan
Original Article

Abstract

This study explores the heat and mass transfer of Casson nanofluid flow containing gyrotactic microorganisms past a swirling cylinder. Fluid flow is generated owing to the torsional movement of the cylinder. An analysis is performed in the presence of gyrotactic microorganisms. The effects of chemical reaction, magnetohydrodynamics, heat generation/absorption, and zero mass flux condition are also considered. The Cattaneo–Christov heat flux model is initiated instead of conventional Fourier heat flux. Apposite transformations are betrothed to attain the coupled system of equations. The numerical solution is developed from the novel mathematical model via bvp4c function utilizing MATLAB software. Numerous graphs and tables are established to portray the inspiration of embroiled parameters on the flow distributions. To corroborate the presented results; a comparison to an already done published paper is also made. An excellent synchronization between the two results is obtained thus endorsing the presented model. Also, form the graphical structures and numerically erected tables, it is professed that concentration of the fluid is lessened owing to an upsurge in values of Reynolds number and Brownian motion parameter. Furthermore, diminishing density of microorganism is perceived for mounting estimates of bioconvection Péclet number.

Keywords

Gyrotactic microorganisms Swirling cylinder Cattaneo–Christov heat flux Casson nanofluid Zero mass flux condition Chemical reaction 

Lis of symbols

u, v, w

Velocity component

R

Radius of cylinder

\(\beta\)

Casson parameter

G

Constant rotating speed of cylinder

\(\lambda_{2}\)

Thermal relaxation time

\({\text{Nn}}_{x}\)

Local density number of the motile microorganisms

\(\theta\)

Dimensionless fluid temperature

\(f(\eta )\)

Dimensionless stream function

H

Strain rate at the surface of cylinder

\(M\)

Magnetic parameter

\(\Delta T\)

Characteristic temperature

\(\phi\)

Nanoparticle volume friction

\(P_{\text{e}}\)

Bioconvection Péclet number

\(\eta\)

A scaled boundary-layer coordinate

\(k_{\text{r}}\)

Rate of chemical reaction

\(N_{\text{b}}\)

Brownian motion parameter

\(D_{\text{B}}\)

Brownian diffusion coefficient

\({\text{Wc}}\)

Maximum cell swimming speed

\(D_{\text{m}}\)

Diffusivity of microorganisms

\(\gamma\)

Thermal relaxation parameter

\(\sigma\)

Electric conductivity of fluid

Cf

Skin friction coefficient

\(Nu_{x}\)

Nusselt number

T

Temperature

\(L_{\text{e}}\)

Lewis number

T

Ambient temperature

Pr

Prandtl number

p

Pressure

\(l\)

Characteristic length

Dc

Coefficient of heat generation/absorption

\(\rho\)

Density of nanofluid

Re

Local Reynolds number

\(B_{0}\)

Constant magnetic flux density

B

Magnetic field strength

\(Q_{0}\)

Volumetric rate of heat source

\(\alpha\)

Thermal diffusivity

\(\mu_{\text{f}}\)

Fluid dynamic viscosity

\(N_{\text{t}}\)

Thermophoresis parameter

\(S_{\text{b}}\)

Bioconvection Lewis number

\(\delta\)

Chemical reaction parameter

Notes

Acknowledgements

This work is funded by the Basic Science Research Unit, Scientific Research Deanship at Majmaah University under the research project no. 76/38. The author is extremely grateful to Majmaah University, Deanship of Scientific Research and Basic Science Research Unit, Majmaah University.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Akbarzadeh M, Rashidi S, Karimi N, Ellahi R (2018) Convection of heat and thermodynamic irreversibilities in two-phase, turbulent nanofluid flows in solar heaters by corrugated absorber plates. Adv Powder Technol 29(9):2243–2254CrossRefGoogle Scholar
  2. Aziz A, Khan WA, Pop I (2012) Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int J Therm Sci 56:48–57CrossRefGoogle Scholar
  3. Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128(3):240–250CrossRefGoogle Scholar
  4. Cattaneo C (1948) Sulla conduzione del calore. Atti Sem Mat Fis Univ Modena 3:83–101Google Scholar
  5. Choi SUS, Estman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publications-Fed, vol 231, pp 99–106Google Scholar
  6. Das K, Duari PR, Kundu PK (2015) Nanofluid bioconvection in presence of gyrotactic microorganisms and chemical reaction in a porous medium. J Mech Sci Technol 29(11):4841–4849CrossRefGoogle Scholar
  7. Ellahi R, Hassan M, Zeeshan A, Khan AA (2016) The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl Nanosci 6(5):641–651CrossRefGoogle Scholar
  8. Ellahi R, Zeeshan A, Hussain F, Abbas T (2018) Study of shiny film coating on multi-fluid flows of a rotating disk suspended with nano-sized silver and gold particles: a comparative analysis. Coatings 8(12):422CrossRefGoogle Scholar
  9. Ellahi R, Zeeshan A, Hussain F, Asadollahi A (2019) Peristaltic blood flow of couple stress fluid suspended with nanoparticles under the influence of chemical reaction and activation energy. Symmetry 11(2):276CrossRefGoogle Scholar
  10. Ghorai S, Hill NA (2000) Wavelengths of gyrotactic plumes in bioconvection. Bull Math Biol 62(3):429–450CrossRefGoogle Scholar
  11. Gupta A, Bhattacharya S (2018) On the growth mechanism of ZnO nano structure via aqueous chemical synthesis. Appl Nanosci 8(3):499–509CrossRefGoogle Scholar
  12. Hassan M, Marin M, Alsharif A, Ellahi R (2018) Convective heat transfer flow of nanofluid in a porous medium over wavy surface. Phys Lett A 382(38):2749–2753CrossRefGoogle Scholar
  13. Jamshed W, Aziz A (2018) Cattaneo–Christov based study of TiO2–CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation. Appl Nanosci 8(4):685–698CrossRefGoogle Scholar
  14. Javed MF, Khan MI, Khan NB, Muhammad R, Rehman MU, Khan SW, Khan TA (2018) Axisymmetric flow of Casson fluid by a swirling cylinder. Results Phys 9:1250–1255CrossRefGoogle Scholar
  15. Kessler JO (1985) Hydrodynamic focusing of motile algal cells. Nature 313(5999):218CrossRefGoogle Scholar
  16. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53(11–12):2477–2483CrossRefGoogle Scholar
  17. Khan M, Irfan M, Khan WA (2017) Impact of nonlinear thermal radiation and gyrotactic microorganisms on the Magneto-Burgers nanofluid. Int J Mech Sci 130:375–382CrossRefGoogle Scholar
  18. Khan WA, Rashad AM, Abdou MMM, Tlili I (2019) Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone. Eur J Mech B Fluids 75:133–142CrossRefGoogle Scholar
  19. Kumar PS, Gireesha BJ, Mahanthesh B, Chamkha AJ (2019) Thermal analysis of nanofluid flow containing gyrotactic microorganisms in bioconvection and second-order slip with convective condition. J Therm Anal Calorim 136(5):1947–1957CrossRefGoogle Scholar
  20. Kuznetsov AV (2011) Non-oscillatory and oscillatory nanofluid bio-thermal convection in a horizontal layer of finite depth. Eur J Mech B/Fluids 30(2):156–165CrossRefGoogle Scholar
  21. Kuznetsov AV (2012) Nanofluid bioconvection in porous media: oxytactic microorganisms. J Porous Media 15(3):233–248CrossRefGoogle Scholar
  22. Lu D, Ramzan M, Ullah N, Chung JD, Farooq U (2017) A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy. Sci Rep 7(1):17008CrossRefGoogle Scholar
  23. Lu D, Ramzan M, Ahmad S, Chung JD, Farooq U (2018a) A numerical treatment of MHD radiative flow of micropolar nanofluid with homogeneous-heterogeneous reactions past a nonlinear stretched surface. Sci Rep 8(1):12431CrossRefGoogle Scholar
  24. Lu D, Ramzan M, Bilal M, Chung JD, Farooq U (2018b) Upshot of chemical species and nonlinear thermal radiation on Oldroyd-B nanofluid flow past a bi-directional stretched surface with heat generation/absorption in a porous media. Commun Theor Phys 70(1):071CrossRefGoogle Scholar
  25. Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int J Therm Sci 50(7):1326–1332CrossRefGoogle Scholar
  26. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu Rev Fluid Mech 24(1):313–358CrossRefGoogle Scholar
  27. Platt JR (1961) ”Bioconvection Patterns” in cultures of free-swimming organisms. Science 133(3466):1766–1767CrossRefGoogle Scholar
  28. Qayyum S, Imtiaz M, Alsaedi A, Hayat T (2018) Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness. Chin J Phys 56:2404–2423CrossRefGoogle Scholar
  29. Ramzan M, Gul H, Chung JD (2017a) Double stratified radiative Jeffery magneto nanofluid flow along an inclined stretched cylinder with chemical reaction and slip condition. Eur Phys J Plus 132(11):456CrossRefGoogle Scholar
  30. Ramzan M, Chung JD, Ullah N (2017b) Radiative magnetohydrodynamic nanofluid flow due to gyrotactic microorganisms with chemical reaction and non-linear thermal radiation. Int J Mech Sci 130:31–40CrossRefGoogle Scholar
  31. Rashad AM, Nabwey HA (2019) Gyrotactic mixed bioconvection flow of a nanofluid past a circular cylinder with convective boundary condition. J Taiwan Inst Chem Eng 99:9–17CrossRefGoogle Scholar
  32. Saidur R, Leong KY, Mohammad HA (2011) A review on applications and challenges of nanofluids. Renew Sustain Energy Rev 15(3):1646–1668CrossRefGoogle Scholar
  33. Saini S, Sharma YD (2018) Numerical study of nanofluid thermo-bioconvection containing gravitactic microorganisms in porous media: effect of vertical throughflow. Adv Powder Technol 29(11):2725–2732CrossRefGoogle Scholar
  34. Sheikholeslami M (2018) Numerical investigation of nanofluid free convection under the influence of electric field in a porous enclosure. J Mol Liq 249:1212–1221CrossRefGoogle Scholar
  35. Sheikholeslami M, Ganji DD (2017) Applications of nanofluid for heat transfer enhancement. William Andrew, NorwichGoogle Scholar
  36. Wager HWT (1910) The effect of gravity upon the movements and aggregation of Euglena viridis, Ehrb., and other micro-organisms. Proc R Soc Lond B 83(562):94–96CrossRefGoogle Scholar
  37. Waqas M, Hayat T, Shehzad SA, Alsaedi A (2018) Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Phys B Condens Matter 529:33–40CrossRefGoogle Scholar
  38. Waqas M, Ijaz Khan M, Hayat T, Farooq S, Alsaedi A (2019) Interaction of thermal radiation in hydromagnetic viscoelastic nanomaterial subject to gyrotactic microorganisms. Appl Nanosci.  https://doi.org/10.1007/s13204-018-00938-7 Google Scholar
  39. Wong KV, De Leon O (2010) Applications of nanofluids: current and future. Adv Mech Eng 2:519659CrossRefGoogle Scholar
  40. Xu H, Cui J (2018) Mixed convection flow in a channel with slip in a porous medium saturated with a nanofluid containing both nanoparticles and microorganisms. Int J Heat Mass Transf 125:1043–1053CrossRefGoogle Scholar

Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceMajmaah UniversityAl-ZulfiSaudi Arabia
  2. 2.Department of Computer ScienceBahria University, Islamabad CampusIslamabadPakistan
  3. 3.Department of Mechanical EngineeringSejong UniversitySeoulKorea

Personalised recommendations