Advertisement

Modeling and analysis of von Kármán swirling flow for Oldroyd-B nanofluid featuring chemical processes

  • S. Z. AbbasEmail author
  • W. A. KhanEmail author
  • H. Sun
  • M. Ali
  • M. Waqas
  • M. Irfan
  • S. Ahmad
Technical Paper
  • 34 Downloads

Abstract

In the current era of emerging technologies, the desired demand is the outstanding efficiency to be achieved by the virtue of standard design and the selection of constituents. Out of these, a key role is the transmission of heat across the systems, and the enhancement of this transmission is the fundamental requirement to be addressed. An addition of nanoparticles with the selected liquids supported the progress toward the optimum level. For the same goal, here we design and discuss a 2D model of Oldroyd-B nanoliquid regarding the rheological aspects taking the thermophoretic and Brownian moment with the consideration of MHD. In this model, various involved physical quantities remained under discussion including chemical processes, convective heat transportation mechanism and heat source–sink aspects. The mathematical differential model non-dimensionalized using the suitable transformations obeys the fundamental laws. For the purpose of solution for the raised nonlinear ordinary system, we adopted homotopy analysis method-based algorithm, which is proved to be the best available technique for analytic solution. The outcomes are displayed graphically for various dimensionless physical quantities. Our analytical analysis indicates that \(\left( {f^{\prime}\left( \eta \right),g\left( \eta \right)} \right)\) liquid velocities deteriorate via higher estimation of \(\beta_{1}\) (Deborah number), while \(h(\eta )\) intensifies Reynolds number, radiation parameter and magnetic parameter. Moreover, nanoliquid temperature rises for larger values of Brownian moment parameter.

Keywords

Nanofluid Oldroyd-B fluid von Kármán swirling flow Heat sink–source 

List of symbols

\({\mathbf{V}}\)

Velocity vector

\(\left( {r,\theta ,z} \right)\)

Polar cylindrical coordinates

\(\rho\)

Density of fluid

\(p\)

Liquid pressure

\(\mu\)

Dynamic viscosity

\(\left( {\lambda_{2} ,\lambda_{1} } \right)\)

Retardation–relaxation times

\(B_{0}\)

Magnetic field

\(J\)

Current density

\(\tau\)

Ratio of heat capacity

\(\left( {C,T} \right)\)

Concentration/temperature of liquid

\(N_{b}\)

Brownian moment

\(S\)

Extra stress tensor

\(D_{\text{T}}\)

Thermophoresis effect

\(\frac{D}{Dt}\)

Upper-convected derivative

\(A_{1}\)

First Rivlin–Ericksen tensor

\(k_{1}\)

Chemical reaction rate constant

\(\left( {h_{\psi } ,h_{f} } \right)\)

Mass heat transfer coefficients

\(\left( {C_{f} ,T_{f} } \right)\)

Concentration/temperature of heated fluid under the sheet

\(\left( {v_{r} ,v_{\theta } ,v_{z} } \right)\)

Velocity components

\(\varOmega\)

Swirl rate

\(\eta\)

Dimensionless variable

\(\left( {f,g,h} \right)\)

Dimensionless velocities

\(\Pr\)

Prandtl number

\(\left( {\beta_{1} ,\beta_{2} } \right)\)

Deborah numbers

\(M\)

Magnetic field

\(\lambda\)

Heat generation–absorption parameter

\(\left( \gamma \right)\)

Biot number

\(N_{b}\)

Brownian motion parameter

\(N_{t}\)

Thermophoresis parameter

\({\text{Le}}\)

Lewis number

Sc

Schmidt number

\({\text{Nu}}_{r}\)

Local Nusselt number

\({\text{Re}}_{r}\)

Reynolds number

\(\omega\)

Rotation strength parameter

Notes

Acknowledgements

This project was funded by the postdoctoral international exchange program for incoming postdoctoral students, at Beijing Institute of Technology, Beijing, China.

References

  1. 1.
    Khan M, Khan WA (2015) Forced convection analysis for generalized Burgers nanofluid flow over a stretching sheet. AIP Adv 5:107138.  https://doi.org/10.1063/1.4935043 CrossRefGoogle Scholar
  2. 2.
    Khan M, Khan WA (2016) MHD boundary layer flow of a power-law nanofluid with new mass flux condition. AIP Adv 6:025211.  https://doi.org/10.1063/1.4942201 CrossRefGoogle Scholar
  3. 3.
    Hayat T, Bashir G, Waqas M, Alsaedi A (2016) MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer. J Mol Liq 223:836–844CrossRefGoogle Scholar
  4. 4.
    Khan M, Khan WA, Alshomrani AS (2016) Non-linear radiative flow of three-dimensional Burgers nanofluid with new mass flux effect. Int J Heat Mass Transf 101:570–576CrossRefGoogle Scholar
  5. 5.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710CrossRefGoogle Scholar
  6. 6.
    Khan M, Khan WA (2016) Steady flow of Burgers’ nanofluid over a stretching surface with heat generation/absorption. J Braz Soc Mech Sci Eng 38(8):2359–2367CrossRefGoogle Scholar
  7. 7.
    Hayat T, Waqas M, Alsaedi A, Bashir G, Alzahrani F (2017) Magnetohydrodynamic (MHD) stretched flow of tangent hyperbolic nanoliquid with variable thickness. J Mol Liq 229:178–184CrossRefGoogle Scholar
  8. 8.
    Sheikholeslami M, Zeeshan A (2017) Analysis of flow and heat transfer in water based nanofluid due to magnetic field in a porous enclosure with constant heat flux using CVFEM. Comput Meth Appl Mech Eng 320:68–81MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sheikholeslami M, Shamlooei M (2017) Fe3O4-H2O nanofluid natural convection in presence of thermal radiation. Int J Hydrog Energy 42(9):5708–5718CrossRefGoogle Scholar
  10. 10.
    Khan WA, Irfan M, Khan M, Alshomrani AS, Alzahrani AK, Alghamdi MS (2017) Impact of chemical processes on magneto nanoparticle for the generalized Burgers fluid. J Mol Liq 234:201–208CrossRefGoogle Scholar
  11. 11.
    Sheikholeslami M, Shehzad SA (2017) Magnetohydrodynamic nanofluid convective flow in a porous enclosure by means of LBM. Int J Heat Mass Transf 113:796–805CrossRefGoogle Scholar
  12. 12.
    Khan M, Ahmad L, Khan WA (2017) Numerically framing the impact of radiation on magnetonanoparticles for 3D Sisko fluid flow. J Braz Soc Mech Sci Eng 39(11):4475–4487CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Sheikholeslami M, Shehzad SA (2018) Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model. Int J Heat Mass Transf 120:1200–1212CrossRefGoogle Scholar
  15. 15.
    Irfan M, Khan M, Khan WA, Ayaz M (2018) Modern development on the features of magnetic field and heat sink/source in Maxwell nanofluid subject to convective heat transport. Phys Lett A 382(30):1992–2002CrossRefGoogle Scholar
  16. 16.
    Sheikholeslami M, Shehzad SA (2018) Numerical analysis of Fe3O4–H2O nanofluid flow in permeable media under the effect of external magnetic source. Int J Heat Mass Transf 118:182–192CrossRefGoogle Scholar
  17. 17.
    Animasaun IL, Mahanthesh B, Jagun AO, Bankole TD, Sivaraj R, Shah NA, Saleem S (2018) Significance of Lorentz force and thermoelectric on the flow of 29 nm CuO–Water nanofluid on an upper horizontal surface of a paraboloid of revolution. J Heat Transf 141(2):022402CrossRefGoogle Scholar
  18. 18.
    Sheikholeslami M, Rokni HB (2018) Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation. Int J Heat Mass Transf 118:823–831CrossRefGoogle Scholar
  19. 19.
    Sheikholeslami M, Seyednezhad M (2018) Simulation of nanofluid flow and natural convection in a porous media under the influence of electric field using CVFEM. Int J Heat Mass Transf 120:772–781CrossRefGoogle Scholar
  20. 20.
    Waqas M, Hayat T, Alsaedi A (2018) A theoretical analysis of SWCNT–MWCNT and H2O nanofluids considering Darcy–Forchheimer relation. Appl Nanosci 9:1183–1191.  https://doi.org/10.1007/s13204-018-0833-6 CrossRefGoogle Scholar
  21. 21.
    Muhammad T, Lu D-C, Mahanthesh B, Eid MR, Ramzan M, Dar A (2018) Significance of Darcy-Forchheimer porous medium in nanofluid through carbon nanotubes. Commun Theor Phys 70(3):361MathSciNetCrossRefGoogle Scholar
  22. 22.
    Sheikholeslami M, Jafaryar M, Hedayat M, Shafee A, Li Z, Nguyen TK, Bakouri M (2019) Heat transfer and turbulent simulation of nanomaterial due to compound turbulator including irreversibility analysis. Int J Heat Mass Transf 137:1290–1300CrossRefGoogle Scholar
  23. 23.
    Waqas M, Gulzar MM, Dogonchi AS, Javed MA, Khan WA (2019) Darcy-Forchheimer stratified flow of viscoelastic nanofluid subjected to convective conditions. Appl Nanosci.  https://doi.org/10.1007/s13204-019-01144-9 CrossRefGoogle Scholar
  24. 24.
    Sheikholeslami M, Jafaryar M, Shafee A, Li Z, Haq R-U (2019) Heat transfer of nanoparticles employing innovative turbulator considering entropy generation. Int J Heat Mass Transf 136:1233–1240CrossRefGoogle Scholar
  25. 25.
    Abbas SZ, Khan WA, Sun H, Ali M, Irfan M, Shahzed M, Sultan F (2019) Mathematical modeling and analysis of Cross nanofluid flow subjected to entropy generation. Appl Nanosci.  https://doi.org/10.1007/s13204-019-01039-9 CrossRefGoogle Scholar
  26. 26.
    Kumar PBS, 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
  27. 27.
    Sheikholeslami M, Haq R-U, Shafee A, Li Z, Elaraki YG, Tlili I (2019) Heat transfer simulation of heat storage unit with nanoparticles and fins through a heat exchanger. Int J Heat Mass Transf 135:470–478CrossRefGoogle Scholar
  28. 28.
    Sultan F, Khan WA, Ali M, Shahzad M, Sun H, Irfan M (2019) Importance of entropy generation and infinite shear rate viscosity for non-Newtonian nanofluid. J. Braz. Soc. Mech. Sci. Eng. 41:439.  https://doi.org/10.1007/s40430-019-1950-1 CrossRefGoogle Scholar
  29. 29.
    Sheikholeslami M, Haq R-U, Shafee A, Li Z (2019) Heat transfer behavior of nanoparticle enhanced PCM solidification through an enclosure with V shaped fins. Int J Heat Mass Transf 130:1322–1342CrossRefGoogle Scholar
  30. 30.
    Khan WA, Ali M, Waqas M, Shahzad M, Sultan F, Irfan M (2019) Importance of convective heat transfer in flow of non-Newtonian nanofluid featuring Brownian and thermophoretic diffusions. Int J Numer Methods Heat Fluid Flow.  https://doi.org/10.1108/HFF-01-2019-0066 CrossRefGoogle Scholar
  31. 31.
    Sheikholeslami M (2019) New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Comput Methods Appl Mech Eng 344:319–333MathSciNetCrossRefGoogle Scholar
  32. 32.
    Khan WA, Ali M (2019) Recent developments in modeling and simulation of entropy generation for dissipative cross material with quartic autocatalysis. Appl Phys A 125:397.  https://doi.org/10.1007/s00339-019-2686-6 CrossRefGoogle Scholar
  33. 33.
    Sheikholeslami M (2019) Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method. Comput Methods Appl Mech Eng 344:306–318MathSciNetCrossRefGoogle Scholar
  34. 34.
    Khan WA, Waqas M, Ali M, Sultan F, Shahzad M, Irfan M (2019) Mathematical analysis of thermally radiative time-dependent Sisko nanofluid flow for curved surface. Int J Numer Methods Heat Fluid Flow 29:3498–3514CrossRefGoogle Scholar
  35. 35.
    Sheikholeslami M, Gerdroodbary MB, Moradi R, Shafee A, Li Z (2019) Application of neural network for estimation of heat transfer treatment of Al2O3-H2O nanofluid through a channel. Comput Methods Appl Mech Eng 344:1–12CrossRefGoogle Scholar
  36. 36.
    Waqas M, Gulzar MM, Khan WA, Khan MI, Khan NB (2019) Newtonian heat and mass conditions impact in thermally radiated Maxwell nanofluid Darcy-Forchheimer flow with heat generation. Int J Numer Methods Heat Fluid Flow 29:2809–2821CrossRefGoogle Scholar
  37. 37.
    Khan WA, Ali M, Irfan M, Khan M, Shahzad M, Sultan F (2019) A rheological analysis of nanofluid subjected to melting heat transport characteristics. Appl Nanosci.  https://doi.org/10.1007/s13204-019-01067-5 CrossRefGoogle Scholar
  38. 38.
    Sheikholeslami M, Mahian O (2019) Enhancement of PCM solidification using inorganic nanoparticles and an external magnetic field with application in energy storage systems. J Clean Prod 215:963–977CrossRefGoogle Scholar
  39. 39.
    Sheikholeslami M, Arabkoohsar A, Khan I, Shafee A, Li Z (2019) Impact of Lorentz forces on Fe3O4-water ferrofluid entropy and exergy treatment within a permeable semi annulus. J Clean Prod 221:885–898CrossRefGoogle Scholar
  40. 40.
    Shahzad M, Sun H, Sultan F, Khan WA, Ali M, Irfan M (2019) Transport of radiative heat transfer in dissipative Cross nanofluid flow with entropy generation and activation energy. Phys Scr 94:115224CrossRefGoogle Scholar
  41. 41.
    Nadeem S, Haq RU, Akbar NS, Lee C, Khan ZH (2013) Numerical study of boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet. PLoS ONE 8(8):e69811CrossRefGoogle Scholar
  42. 42.
    Shehzad SA, Alsaedi A, Hayat T, Alhuthali MS (2013) Three-dimensional flow of an Oldroyd-B fluid with variable thermal conductivity and heat generation/absorption. PLoS ONE 8(11):e78240CrossRefGoogle Scholar
  43. 43.
    Khan WA, Khan M, Malik R (2014) Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption. PLoS ONE 9(8):e105107CrossRefGoogle Scholar
  44. 44.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) On 2D stratified flow of an Oldroyd-B fluid with chemical reaction: an application of non-Fourier heat flux theory. J Mol Liq 223:566–571CrossRefGoogle Scholar
  45. 45.
    Waqas M, Khan MI, Hayat T, Alsaedi A (2017) Stratified flow of an Oldroyd-B nanoliquid with heat generation. Results Phys 7:2489–2496CrossRefGoogle Scholar
  46. 46.
    Mehmood R, Rana S, Nadeem S (2018) Transverse thermopherotic MHD Oldroyd-B fluid with Newtonian heating. Results Phys. 8:686–693CrossRefGoogle Scholar
  47. 47.
    Zhang Y, Yuan B, Bai Y, Cao Y, Shen Y (2018) Unsteady Cattaneo–Christov double diffusion of Oldroyd-B fluid thin film with relaxation-retardation viscous dissipation and relaxation chemical reaction. Powder Technol 338:975–982CrossRefGoogle Scholar
  48. 48.
    Irfan M, Khan M, Gulzar MM, Khan WA (2019) Chemically reactive and nonlinear radiative heat flux in mixed convection flow of Oldroyd-B nanofluid. Appl Nanosci.  https://doi.org/10.1007/s13204-019-01052-y CrossRefGoogle Scholar
  49. 49.
    Khan M, Irfan M, Khan WA, Sajid M (2019) Consequence of convective conditions for flow of Oldroyd-B nanofluid by a stretching cylinder. J Braz Soc Mech Sci Eng 41:116.  https://doi.org/10.1007/s40430-019-1604-3 CrossRefGoogle Scholar
  50. 50.
    Sun Qiulei, Wang Shaowei, Zhao Moli, Yin Chen, Zhang Qiangyong (2019) Weak nonlinear analysis of Darcy–Brinkman convection in Oldroyd-B fluid saturated porous media under temperature modulation. Int J Heat Mass Transf 138:244–256CrossRefGoogle Scholar
  51. 51.
    Irfan M, Khan M, Khan WA (2019) Impact of homogeneous–heterogeneous reactions and non-Fourier heat flux theory in Oldroyd-B fluid with variable conductivity. J Braz Soc Mech Sci Eng 41:135.  https://doi.org/10.1007/s40430-019-1619-9 CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Mathematics and StatisticsHazara UniversityMansehraPakistan
  3. 3.Department of MathematicsMohi-ud-Din Islamic UniversityNerian SharifPakistan
  4. 4.NUTECH School of Applied Sciences and HumanitiesNational University of TechnologyIslamabadPakistan
  5. 5.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  6. 6.Department of MathematicsAbbottabad, USTAbbottabadPakistan

Personalised recommendations