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Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

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Abstract

A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von Kármán similarity functions are utilized to convert the partial differential equations (PDEs) into ordinary differential equations (ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.

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References

  1. CHOI, S. and EASTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, ASME, San Francisco (1995)

    Google Scholar 

  2. BUONGIORNO, J. Convective transport in nanofluids. ASME Journal of Heat Transfer, 128, 240–250 (2006)

    Article  Google Scholar 

  3. KHAN, W. and POP, I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer, 53, 2477–2483 (2010)

    Article  Google Scholar 

  4. HASHIM, H. A., ALSHOMRANI, A. S., and KHAN, M. Multiple physical aspects during the flow and heat transfer analysis of Carreau fluid with nanoparticles. Scientific Reports, 8, 1–14 (2018)

    Article  Google Scholar 

  5. JAFARYAR, M., SHEIKHOLESLAMI, M., LI, Z., and MORADI, R. Nanofluid turbulent flow in a pipe under the effect of twisted tape with alternate axis. Journal of Thermal Analysis and Calorimetry, 135, 305–323 (2019)

    Article  Google Scholar 

  6. HAMID, A., HAFEEZ, A., KHAN, M., ALSHOMRANI, A. S., and ALGHAMDI, M. Heat transport features of magnetic water-graphene oxide nanofluid flow with thermal radiation: stability test. European Journal of Mechanics-B/Fluids, 76, 434–441 (2019)

    Article  MathSciNet  Google Scholar 

  7. HAFEEZ, A., KHAN, M., and AHMED, J. Stagnation point flow of radiative Oldroyd-B nanofluid over a rotating disk. Computer Methods and Programs in Biomedicine, 191, 105342 (2020)

    Article  Google Scholar 

  8. FOURIER, J. B. J. Theorie Analytique de la Chaleur, Didot, Paris, 499–508 (1822)

    MATH  Google Scholar 

  9. CATTANEO, C. Sulla conduzione del calore. Atti del Seminario Matematico e Fisico dell’ Uni-versita di Modena e Reggio Emilia, 3, 83–101 (1948)

    MathSciNet  MATH  Google Scholar 

  10. CHRISTOV, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite speed heat conduction. Mechanics Research Communications, 36, 481–486 (2009)

    Article  MathSciNet  Google Scholar 

  11. CIARLETTA, M. and STRAUGHAN, B. Uniqueness and structural stability for the Cattaneo-Christov equations. Mechanics Research Communications, 37, 445–447 (2010)

    Article  Google Scholar 

  12. STRAUGHAN, B. Thermal convection with the Cattaneo-Christov model. International Journal of Heat and Mass Transfer, 53, 95–98 (2010)

    Article  Google Scholar 

  13. HAN, S., ZHENG, L., LI, C., and ZHANG, X. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model. Applied Mathematics Letters, 38, 87–93 (2014)

    Article  MathSciNet  Google Scholar 

  14. RAUF, A., SHEHZAD, S. A., ABBAS, Z., and HAYAT, T. Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion. Applied Mathematics and Mechanics (English Edition), 40(10), 1471–1486 (2019) https://doi.org/10.1007/s10483-019-2530-6

    Article  MathSciNet  Google Scholar 

  15. RAUF, A., ABBAS, Z., and SHEHZAD, S. A. Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium. Applied Mathematics and Mechanics (English Edition), 40(6), 837–850 (2019) https://doi.org/10.1007/s10483-019-2488-9

    Article  MathSciNet  Google Scholar 

  16. SULTI, F. A. Impact of Cattaneo-Christov heat flux model on stagnation-point flow towards a stretching sheet with slip effects. ASME Journal of Heat Transfer, 141, 022003 (2019)

    Article  Google Scholar 

  17. HAFEEZ, A., KHAN, M., and AHMED, J. Flow of Oldroyd-B fluid over a rotating disk with Cattaneo-Christov theory for heat and mass fluxes. Computer Methods and Programs in Biomedicine, 191, 105374 (2020)

    Article  Google Scholar 

  18. KHAN, M., AHMED, A., and AHMED, J. Transient flow of magnetized Maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory. Applied Mathematics and Mechanics (English Edition), 41(4), 655–666 (2020) https://doi.org/10.1007/s10483-020-2593-9

    Article  Google Scholar 

  19. KHAN, M., AHMED, A., IRFAN, M., and AHMED, J. Analysis of Cattaneo-Christov theory for unsteady flow of Maxwell fluid over stretching cylinder. Journal of Thermal Analysis and Calorimetry (2020) https://doi.org/10.1007/s10973-020-09343-1

    Google Scholar 

  20. VON KARMAN, T. Uberlaminare und turbulente Reibung. ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 1, 233–252 (1921)

    Article  Google Scholar 

  21. GREGG, J. L. and SPARROW, E. M. Heat transfer from a rotating disk to fluids of any Prandtl number. ASME Journal of Heat Transfer, 81, 249–251 (1959)

    Article  Google Scholar 

  22. TURKYILMAZOGLU, M. Nanofluid flow and heat transfer due to a rotating disk. Computers and Fluids, 94, 139–146 (2014)

    Article  MathSciNet  Google Scholar 

  23. AHMED, J., KHAN, M., and AHMED, L. Stagnation point flow of Maxwell nanofluid over a permeable rotating disk with heat source/sink. Journal of Molecular Liquids, 287, 110853 (2019)

    Article  Google Scholar 

  24. KHAN, M., HAFEEZ, A., and AHMED, J. Impacts of non-linear radiation and activation energy on the axisymmetric rotating flow of Oldroyd-B fluid. Physica A: Statistical Mechanics and Its Applications (2020) https://doi.org/10.1016/j.physa.2019.124085

    Google Scholar 

  25. HAFEEZ, A., KHAN, M., and AHMED, J. Thermal aspects of chemically reactive Oldroyd-B fluid flow over a rotating disk with Cattaneo-Christov heat flux theory. Journal of Thermal Analysis and Calorimetry (2020) https://doi.org/10.1007/s10973-020-09421-4

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    A. Hafeez, M. Khan, A. Ahmed & J. Ahmed

  2. Department of Basic Sciences, University of Engineering and Technology, Taxila, 47050, Pakistan

    J. Ahmed

Authors
  1. A. Hafeez
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  2. M. Khan
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  3. A. Ahmed
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  4. J. Ahmed
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Correspondence to A. Hafeez.

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Hafeez, A., Khan, M., Ahmed, A. et al. Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory. Appl. Math. Mech.-Engl. Ed. 41, 1083–1094 (2020). https://doi.org/10.1007/s10483-020-2629-9

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  • DOI: https://doi.org/10.1007/s10483-020-2629-9

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