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Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux

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Abstract

The two-dimensional (2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations (PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically. The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time. Besides, the Deborah number has a reverse effect on the pressure and surface drag force.

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References

  1. CRANE, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 21, 645–647 (1970)

    Article  Google Scholar 

  2. ABBASBANDY, S., HAYAT, T., ALSAEDI, A., and RASHIDI, M. M. Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 24, 390–401 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. LIN, Y., ZHENG, L., and CHEN, G. Unsteady flow and heat transfer of pseudoplastic nanoliquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation. Powder Technology, 274, 324–332 (2015)

    Article  Google Scholar 

  4. HAYAT, T., IMTIAZ, M., and ALSAEDI, A. Partial slip effects in flow over nonlinear stretching surface. Applied Mathematics and Mechanics (English Edition), 36(11), 1513–1526 (2015) https://doi.org/10.1007/s10483-015-1999-7

    Article  MathSciNet  MATH  Google Scholar 

  5. SAJID, M., ALI, N., JAVED, J., and ABBAS, Z. Stretching a curved surface in a viscous fluid. Chinese Physics Letters, 27, 024703 (2010)

    Article  Google Scholar 

  6. NAVEED, M., ABBAS, Z., and SAJID, M. Hydromagnetic flow over an unsteady curved stretching surface. Engineering Science and Technology: an International Journal, 19, 841–845 (2016)

    Google Scholar 

  7. SAJID, M., ALI, N., ABBAS, Z., and JAVED, T. Flow of micropolar fluid over a curved stretching surface. Journal of Engineering Physics and Thermophysics, 4, 798–804 (2011)

    Google Scholar 

  8. ROSCA, N. C. and POP, I. Unsteady boundary layer flow over a permeable curved stretching/ shrinking surface. European Journal of Mechanics-B/Fluids, 51, 61–67 (2015)

    Article  MathSciNet  Google Scholar 

  9. NAVEED, M., ABBAS, Z., and SAJID, M. MHD flow of micropolar fluid due to a curved stretching sheet with thermal radiation. Journal of Applied Fluid Mechanics, 9, 131–138 (2016)

    Article  Google Scholar 

  10. ABBAS, Z., NAVEED, M., and SAJID, M. Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. Journal of Molecular Liquids, 215, 756–762 (2016)

    Article  Google Scholar 

  11. OKECHI, N. F., JALIL, M., and ASGHAR, S. Flow of viscous fluid along an exponentially stretching curved surface. Results in Physics, 7, 2851–2854 (2017)

    Article  Google Scholar 

  12. HAYAT, T., QAYYUM, S., IMTIAZ, M., and ALSAEDI, A. Double stratification in flow by curved stretching sheet with thermal radiation and Joule heating. Journal of Thermal Science and Engineering Applications, 10, 021010 (2017)

    Article  Google Scholar 

  13. OKECHI, N. F., JALIL, M., and ASGHAR, S. Flow of viscous fluid along an exponentially stretching curved surface. Results in Physics, 7, 2851–2854 (2017)

    Article  Google Scholar 

  14. SANNI, K. M., ASGHAR, S., JALIL, N., OKECHI, N. F. Flow of viscous fluid along a nonlinearly stretching curved surface. Results in Physics, 7, 1–4 (2017)

    Article  Google Scholar 

  15. GANAPATHI, M. and POLIT, O. A nonlocal higher-order model including thickness stretching effect for bending and buckling of curved nanobeams. Applied Mathematical Modelling, 57, 121–141 (2018)

    Article  MathSciNet  Google Scholar 

  16. SHAHZAD, S. A., HAYAT, T., ALSAEDI, A., and OBID, M. A. Nonlinear thermal radiation in three-dimensional flow of Jeffrey nanofluid: a model for solar energy. Applied Mathematics and Computation, 248, 273–286 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. GAO, C. and JIAN, Y. Analytical solution of magnetohydrodynamic flow of Jeffrey fluid through a circular microchannel. Journal of Molecular Liquids, 211, 803–811 (2015)

    Article  Google Scholar 

  18. REDDY, G. B., SREENADH, S., REDDY, R. H., and KAVITHA, A. Flow of a Jeffrey fluid between torsionally oscillating disks. Ain Shams Engineering Journal, 6, 355–362 (2015)

    Article  Google Scholar 

  19. TURKYILMAZOGLU, M. and POP, I. Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid. International Journal of Heat and Mass Transfer, 57, 82–88 (2013)

    Article  Google Scholar 

  20. HAYAT, T., IMTIAZ, M., and ALSAEDI, A. Magnetohydrodynamic stagnation point flow of a Jeffrey nanofluid with Newtonian heating. Journal of Aerospace Engineering, 29, 04015063 (2016)

    Article  Google Scholar 

  21. FAROOQ, M., GULL, N., ALSAEDI, A., and HAYAT, T. MHD flow of a Jeffrey fluid with Newtonian heating. Journal of Mechanics, 31, 319–329 (2015)

    Article  Google Scholar 

  22. HAYAT, T., QAYYUM, S., IMTIAZ, M., and ALSAEDI, A. Three-dimensional rotating flow of Jeffrey fluid for Cattaneo-Christov heat flux model. AIP Advances, 6, 025012 (2016)

    Article  Google Scholar 

  23. YANG, X., QI, H. T., and JIANG, X. Y. Numerical analysis for electroosmotic flow of fractional Maxwell fluids. Applied Mathematics Letters, 78, 1–8 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. KUMAR, M. S., SANDEEP, N., KUMAR, B. R., and SALEEM, S. A comparative study of chemically reacting 2D flow of Casson and Maxwell fluids. Alexandria Engineering Journal (2017) https://doi.org/10.1016/j.aej.2017.05.010

    Google Scholar 

  25. FOURIER, J. B. J. Théorie analytique de la chaleur. Journal für die Reine und Angewandte Mathematik, 7, 116–131 (1903)

    MATH  Google Scholar 

  26. CATTANEO, C. Sulla conduzione del calore. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 3, 83–101 (1948)

    MathSciNet  MATH  Google Scholar 

  27. 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  MATH  Google Scholar 

  28. TIBULLO, V. and ZAMPOLI, V. A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids. Mechanics Research Communications, 38, 77–79 (2011)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  31. MUSTAFA, M. Cattaneo-Christov heat flux model for rotating flow and heat transfer of upperconvected Maxwell fluid. AIP Advances, 5, 047109 (2015)

    Article  Google Scholar 

  32. HAYAT, T., QAYYUM, S., IMTIAZ, M., and ALSAEDI, A. Impact of Cattaneo-Christov heat flux in Jeffrey fluid flow with homogeneous-heterogeneous reactions. PLoS One, 11, e0148662 (2016)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. HAYAT, T., IMTIAZ, M., ALSAEDI, A., and ALMEZAL, S. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 104, 296–303 (2016)

    Article  Google Scholar 

  35. HAYAT, T., KHAN, M. I., WAQAS, M., and ALSAEDI, A. On Cattaneo-Christov heat flux in the flow of variable thermal conductivity Eyring-Powell fluid. Results in Physics, 7, 446–450 (2017)

    Article  Google Scholar 

  36. HAYAT, T., KHAN, M. I., FAROOQ, M., YASMEEN, T., and ALSAEDI, A. Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. Journal of Molecular Liquids, 220, 49–55 (2016)

    Article  Google Scholar 

  37. FAROOQ, U., HAYAT, T., ALSAEDI, A., and LIAO, S. J. Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces. Numerical Algorithms, 70, 43–59 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  38. SUI, J., ZHENG, L., ZHANG, X., and CHEN, G. Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. International Journal of Heat and Mass Transfer, 85, 1023–1033 (2015)

    Article  Google Scholar 

  39. HAYAT, T., IMTIAZ, M., and ALSAEDI, A. Impact of magnetohydrodynamics in bidirectional flow of nanofluid subject to second order slip velocity and homogeneous–heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 395, 294–302 (2015)

    Article  Google Scholar 

  40. SHEHZAD, S. A., HAYAT, T., ALSAEDI, A., and MERAJ, M. A. Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid. Applied Mathematics and Mechanics (English Edition), 38(10), 1347–1356 (2017) https://doi.org/10.1007/s10483-017-2250-6

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat & S. Qayyum

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

  3. Department of Mathematics, University of Wah, Wah Cantt, 47040, Pakistan

    M. Imtiaz

Authors
  1. T. Hayat
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  2. S. Qayyum
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  3. M. Imtiaz
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  4. A. Alsaedi
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Correspondence to M. Imtiaz.

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Citation: HAYAT, T., QAYYUM, S., IMTIAZ, M., and ALSAEDI, A. Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux. Applied Mathematics and Mechanics (English Edition), 39(8), 1173–1186 (2018) https://doi.org/10.1007/s10483-018-2361-6

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Hayat, T., Qayyum, S., Imtiaz, M. et al. Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux. Appl. Math. Mech.-Engl. Ed. 39, 1173–1186 (2018). https://doi.org/10.1007/s10483-018-2361-6

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  • DOI: https://doi.org/10.1007/s10483-018-2361-6

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