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Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy

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Abstract

The main motive of this work is to study the effects of nonlinear radiation and mixed convection for the Casson nanofluid through the thin needle. Mass transfer is further characterized by activation energy. Temperature-dependent viscosity and a variable magnetic field are assumed for the current problem. The consequences of the physical framework on the velocity, temperature and species including the impact of radiative heat flux are discussed. The partial differential equations of the physical model are achieved using the concept of boundary layer approximation and are remolded into the ordinary differential mathematical statement which is coupled nonlinear, by substituting specific similarity transformations. By making the use of built-in MATLAB bvp4c function, the results are calculated and arranged in the manner of graphs and tables. The effects of different physical parameters of our interest such as the Casson fluid parameter, Brownian motion, Prandtl number, buoyancy ratio parameter, thermal radiation, thermophoresis parameter, Schmidt number and relaxation time are examined for the velocity, concentration and temperature profiles.

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Abbreviations

\(B_{o}\) :

Uniform magnetic field strength (Tesla)

\(\sigma \) :

Electric conductivity (Siemens/m)

k :

Thermal conductivity [W/(mK)]

\(k_{e}\) :

Mean adsorption coefficient

\(D_{B}\) :

Effective diffusion coefficient (m\(^{2}\)/s)

\(T_{w}\) :

Temperature of the wall (K)

\(T_{\infty }\) :

Ambient temperature (K)

C :

Concentration (mol/m\(^{3}\))

\(C_{w}\) :

Wall concentration (mol/m\(^{3}\))

\(C_{\infty }\) :

Ambient concentration (mol/m\(^{3}\))

\(\nu \) :

Dynamic viscosity (Pa.s)

P :

Pressure (Pa)

v :

Kinematic viscosity (m\(^{2}\)/s)

\(\rho \) :

Density (kg/m\(^{3}\))

T :

Temperature (K)

\(q_{r}\) :

Radiative heat flux (W/m\(^{2}\))

Nt :

Thermophoresis parameter

(u, v):

Components of the velocity (m/s)

(x, y):

Cartesian co-ordinates (m)

\(C_{f}\) :

Local skin friction

\(\mathrm{Nu}_{x}\) :

Local Nusselt number

\(\mathrm{Sh}_{x}\) :

Local Sherwood number

Pr:

Prandtl number

R :

Radiation parameter

Re:

Reynolds number

\(\alpha \) :

Thermal diffusivity (m\(^{2}\)/s)

\(\beta \) :

Casson parameter

\(\lambda \) :

Velocity ratio parameter

Nr :

Buoyancy ratio parameter

Nb :

Brownian motion parameter

\(\sigma _{s}\) :

Stefan–Boltzmann constant (W/m\(^{2}\)K\(^{4}\))

\(\xi \) :

Constant mixed convection

\(\mathrm{Gr}_{x}\) :

Local Grashof number

\(\mathrm{Re}_{x}\) :

Local Reynolds number

Sc:

Schmidt number

\(\Gamma \) :

Relaxation time

\(\delta \) :

Temperature difference ratio

E :

Activation energy

References

  1. Lawrence, L.L.: Boundary layer over a thin needle. Phys. Fluids 10, 820–822 (1967)

    Article  Google Scholar 

  2. Ahmad, S., Arifin, N.M., Nazar, R., Pop, I.: Mixed convection boundary layer flow along vertical thin needles: assisting and opposing flows. Int. Commun. Heat Mass Trans. 35(2), 157–162 (2007)

    Article  Google Scholar 

  3. Trimbitas, R., Grosan, T., Pop, I.: Mixed convection boundary layer flow along vertical thin needles in nanofluids. Int. J. Numer. Methods Heat Fluid Flow 24(3), 579–594 (2014)

    Article  MathSciNet  Google Scholar 

  4. Hayat, T., Khan, M.I., Farooq, M., Yasmeen, T., Alsaedi, A.: Water-carbon nanofluid flow with variable heat flux by a thin needle. J. Mol. Liq. 224(A), 786–791 (2016)

    Article  Google Scholar 

  5. Ahmad, R., Mustafa, M., Hina, S.: Buongiorno’s model for fluid flow around a moving thin needle in a flowing nanofluid: A numerical study. Chin. J. Phys. 55(4), 1264–1274 (2017)

    Article  Google Scholar 

  6. Salleh, S.N.A., Bachok, N., Arifin, N.M., Ali, F.M., Pop, I.: Magnetohydrodynamics flow past a moving vertical thin needle in a nanofluid with stability analysis. Energies 11(12), 1–15 (2018)

    Article  Google Scholar 

  7. Souayeh, B., Reddy, M.G., Sreenivasulu, P.: Comparative analysis on non-linear radiative heat transfer on MHD Casson nanofluid past a thin needle. J. Mol. Liq. 284, 163–174 (2019)

    Article  Google Scholar 

  8. Sulochana, C., Ashwinkumar, G.P., Sandeep, N.: Joule heating effect on a continuously moving thin needle in MHD Sakiadis flow with thermophoresis and Brownian moment. Euro. Phys. J. Plus 132, 387 (2017)

    Article  Google Scholar 

  9. Krishna, P.M., Sharma, R.P., Sandeep, N.: Boundary layer analysis of persistent moving horizontal needle in Blasius and Sakiadis magnetohydrodynamic radiative nanofluid flows. J. Mol. Liq. 49(8), 1654–1659 (2017)

    Google Scholar 

  10. Khan, I., Waqar, A., Qasim, M., Afridi, I., Alharbi, S.O.: Thermodynamic analysis of entropy generation minimization in thermally dissipating flow over a thin needle moving in a parallel free stream of two Newtonian fluids. Entropy 21(1), 74 (2019)

    Article  Google Scholar 

  11. Akram, S., Razia, A., Afzal, F.: Effects of velocity second slip model and induced magnetic field on peristaltic transport of non-Newtonian fluid in the presence of double-diffusivity convection in nanofluids. Arch. Appl. Mech. 90, 1583–1603 (2020)

    Article  Google Scholar 

  12. Haroun, M.H.: On electrohydrodynamic flow of Jeffrey fluid through a heating vibrating cylindrical tube with moving endoscope. Arch. Appl. Mech. 90, 1305–1315 (2020)

    Article  Google Scholar 

  13. Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. USA, ASME FED 231/MD 66, 99–105 (1995)

    Google Scholar 

  14. Sarkar, J., Ghosh, P., Adil, A.: A review on hybrid nanofluids. Sustain. Energy Rev. 43, 164–177 (2015)

    Article  Google Scholar 

  15. Chen, C., Chen, B., Liu, C.C.: Entropy generation in mixed convection magnetohydrodynamic nanofluid flow in vertical channel. Int. J. Heat Mass Trans. 91, 1026–1033 (2015)

    Article  Google Scholar 

  16. Dogonchi, A.S., Ganji, D.D.: Investigation of MHD nanofluid flow and heat transfer in a stretching/shrinking convergent/divergent channel considering thermal radiation. J. Mol. Liq. 220, 592–603 (2016)

    Article  Google Scholar 

  17. Khan, M., Malik, M.Y., Salahuddin, T., Rehman, K.U., Nasir, M., Khan, I.: MHD flow of Williamson nanofluid over a cone and plate with chemically reactive species. J. Mol. Liq. 231, 80–588 (2017)

    Article  Google Scholar 

  18. Hayat, T., Nadeem, S.: Heat transfer enhancement with Ag–CuO water hybrid nanofluid. Results Phys. 7, 2317–2324 (2017)

    Article  Google Scholar 

  19. Peng, Y., Alsagri, A.S., Afrandcd, M., Moradi, R.: A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation. RSC Adv. 9(39), 22185–22197 (2019)

    Article  Google Scholar 

  20. Bilal, M., Sagheer, M., Hussain, S.: Study of magnetohydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity. Alex. Eng. J. 57, 3281–3289 (2018)

    Article  Google Scholar 

  21. Iqbal, Z., Akbar, N.S., Azhar, E., Maraj, E.N.: Performance of hybrid nanofluid (Cu–CuO/water) on MHD rotating transport in oscillating vertical channel inspired by Hall current and thermal radiation. Alex. Eng. J. 57, 1943–1954 (2018)

    Article  Google Scholar 

  22. Sheikholeslami, M., Shehzad, S.A., Li, Z.: Nanofluid heat transfer intensification in a permeable channel due to magnetic field using Lattice Boltzmann method. Phys. B: Condens. Matter 542, 51–58 (2018)

    Article  Google Scholar 

  23. Bilal, M.: Micropolar flow of EMHD nanofluid with nonlinear thermal radiation and slip effects. Alex. Eng. J. 59, 965–976 (2020)

    Article  Google Scholar 

  24. Awad, F.G., Motsa, S., Khumalo, M.: Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy. PLoS One 10, 1371 (2014)

    Google Scholar 

  25. Shafique, Z., Mustafa, M., Mushtaq, A.: Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Results Phys. 6, 627–633 (2016)

    Article  Google Scholar 

  26. Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A.: Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy. Int. J. Heat Mass Trans. 108, 1340–1346 (2017)

    Article  Google Scholar 

  27. Khan, M.I., Qayyum, S., Hayat, T., Waqas, M., Khan, M.I., Alsaedi, A.: Entropy generation minimization and binary chemical reaction with Arrhenius activation energy in MHD radiative flow of nanomaterial. J. Mol. Liq. 259, 274–283 (2018)

    Article  Google Scholar 

  28. Ramesh, G.K., Shehzad, S.A., Hayat, T., Alsaedi, A.: Activation energy and chemical reaction in Maxwell magneto-nanoliquid with passive control of nanoparticle volume fraction. J. Braz. Soc. Mech. Sci. Eng. 40(9), 422 (2018)

    Article  Google Scholar 

  29. Khan, S.U., Tlili, I.: Significance of activation energy and effective Prandtl number in accelerated flow of Jeffrey nanoparticles with gyrotactic microorganisms. J. Energy Resour. Tech. 142(11), 112101 (2020)

    Article  Google Scholar 

  30. Khan, S.U., Imran, M., Tlili, I., Waqas, H.: Activation energy and thermal radiation aspects in bioconvection flow of rate-type nanoparticles configured by a stretching/shrinking disk. J. Energy Resour. Tech. 142(11), 112102 (2020)

    Article  Google Scholar 

  31. Cao, Y., Bai, Y., Du, J., Rashidi, S.: A computational fluid dynamics investigation on the effect of the angular velocities of hot and cold turbulator cylinders on the heat transfer characteristics of nanofluid flows within a porous cavity. J. Energy Resour. Tech. 142(11), 112104 (2020)

    Article  Google Scholar 

  32. Sajid, T., Sagheer, M., Hussain, S., Bilal, M.: Darcy–Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy. AIP Adv. 8, 035102 (2018)

    Article  Google Scholar 

  33. Lu, D.C., Ramzan, M., Bilal, M., Chung, J.D., Farooq, U.: A numerical investigation of 3D MHD rotating flow with binary chemical reaction, activation energy and non-Fourier heat flux. Commun. Theor. Phys. 70, 89–96 (2018)

    Article  MathSciNet  Google Scholar 

  34. Malik, M.Y., Hussain, A., Nadeem, S.: Boundary layer flow of an Eyring–Powell model fluid due to a stretching cylinder with variable viscosity. Sci Iran. B 20(2), 313–321 (2013)

    Google Scholar 

  35. Miao, L., Massoudi, M.: Heat transfer analysis and flow of a slag-type fluid: effects of variable thermal conductivity and viscosity. Int. J. NonLinear Mech. 76, 8–19 (2015)

    Article  Google Scholar 

  36. Animasaun, I.L., Sandeep, N.: Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of a paraboloid of revolution with variable thermal conductivity and viscosity. Powder Tech. 301, 858–867 (2016)

    Article  Google Scholar 

  37. Hayat, T., Khan, M.I., Farooq, M., Gull, N., Alsaedi, A.: Unsteady three-dimensional mixed convection flow with variable viscosity and thermal conductivity. J. Mol. Liq. 223, 1297–1310 (2016)

    Article  Google Scholar 

  38. Sheikholeslami, M., Rokni, H.B.: Magnetic nanofluid natural convection in the presence of thermal radiation considering variable viscosity. Euro. Phys. J. Plus 132, 238 (2017)

    Article  Google Scholar 

  39. Bilal, M., Nazeer, M.: Numerical analysis for the non-Newtonian flow over stratified stretching/shrinking inclined sheet with the aligned magnetic field and nonlinear convection. Arch. Appl. Mech. (2020). https://doi.org/10.1007/s00419-020-01798-w

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Authors and Affiliations

  1. Department of Mathematics, University of Lahore Gujrat Campus, Gujrat, Pakistan

    M. Bilal & Y. Urva

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  1. M. Bilal
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Correspondence to M. Bilal.

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The authors declare that they have no conflict of interest.

Authors’ contributions

MB proposed the problem, modeled it and finally reviewed. UY calculated the result and prepared the initial draft.

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Bilal, M., Urva, Y. Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy. Arch Appl Mech 91, 1079–1095 (2021). https://doi.org/10.1007/s00419-020-01811-2

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