Velocity Slip and Thermal Jump on Maxwell Fluid with Non-Fourier Cattaneo-Christov Heat Flux Using SRM Solutions

  • Authors

    • K. Gangadhar
    • K. V. Ramana
    • B. Rushi Kumar
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.20902
  • Cattaneo-Christov heat flux model, Stretching cylinder, Temperature Jump, MHD, Velocity slip.

  • Abstract

    The influence of the heat transfer within a boundary layer flow and magneto hydro dynamic slip flow of a Maxwell fluid over a stretching cylinder is analyzed and discussed in the present article. The effects of viscous dissipation and thermal jump are assumed. The procedure of heat transfer through hypothesis of Cattaneo-Christov heat flux is considered. We converted non-linear partial differential equations for mass, momentum and energy into a system of coupled highly non linear ordinary differential equations with proper boundary conditions by the help of suitable similarity transformations. The succeeding ordinary differential equations are solved by using Spectral relaxation technique. The solution is obtained in zero curvature parameter as well as non-zero curvature parameter.  i.e. for flow above a flat plate and flow above a cylinder. The flow and heat transfer attributes are witnessed to be encouraged in an elaborate mode by Prandtl number, thermal jump parameter, thermal relaxation parameter, Deborah number, slip velocity parameter, Eckert number and the magnetic parameter. Our findings reveal that one of the possible ways to decrease the Deborah number by boosting fluid velocity. It is also perceived that in the case of flow over a stretching cylinder, the momentum boundary layer thickness and the velocity of the fluid increases. Furthermore, an increase in slip velocity factor reduces the magnitude of skin friction.

     

     

  • References

    1. [1] Dhahir, S A (1999), On non-Newtonian flow past a cylinder in a confined flow. J. Rheol. 33, 781 doi:10.1122/1.550074

      [2] Martin, M J & Boyd, I D (2006), Momentum and heat transfer in a laminar boundary layer with slip flow. J. Thermophys. Heat Transf. 20, 710–719. doi:10.2514/1.22968

      [3] Hayat, T.; Abbas, Z.; Sajid, M.: Series solution for the upperconvictedMaxwell fluid over a porous stretching plate. Phys. Lett. Sect. A Gen. At. Solid State Phys. 358, 396–403 (2006). doi:10. 1016/j.physleta.2006.04.117.

      [4] Hayat, T, Abbas, Z & Sajid, M (2009), MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface. Chaos Solitons Fractals 39, 840–848 (2009). doi:10.1016/j.chaos.2007. 01.067.

      [5] Rashidi, M M, Beg, O A, Mehr, N F, Hosseini, A & Gorla, R S R (2012), Homotopy simulation of axisymmetric laminar mixed convection nanofluid boundary layer flow. Theor. Appl. Mech. 39, 365–390.

      [6] Shateyi, S (2013), A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction. Bound. Value Probl. 196, 1–14. doi:10.1186/1687-2770-2013-196.

      [7] Sajid, M, Abbas, Z, Ali, N, Javed, T & Ahmad, I (2014), Slip flow of a Maxwell fluid past a stretching sheet. Walailak J. Sci. Technol. 11, 1093–1103.

      [8] He, X & Cai, C (2017), Near Continuum Velocity and Temperature Coupled Compressible Boundary Layer Flow over a Flat Plate, Braz J Phys 47:182–188 DOI 10.1007/s13538-017-0488-x

      [9] Xinhui SI, Haozhe LI, Yanan SHEN, Liancun ZHENG, Effects of nonlinear velocity slip and temperature jump on pseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field, Appl. Math. Mech. -Engl. Ed. DOI 10.1007/s10483-017-2178-8

      [10] Hosseini, E, Loghmani, G B, Heydari, M, & Rashidi, M M (2017), Numerical investigation of velocity slip and temperature jump effects on unsteady flow over a stretching permeable surface, Eur. Phys. J. Plus 132: 96, DOI 10.1140/epjp/i2017-11361-8.

      [11] Daniel, Y S, Aziz, Z A, Ismail, Z & Salah, F (2017): Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet, Australian Journal of Mechanical Engineering, DOI: 10.1080/14484846.2017.1358844.

      [12] Fourier, J B J (1822), Theorie analytique de la chaleur. English translation: The analytic theory of heat, Firman Didot, Paris.

      [13] Cattaneo, C (1948), Sulla conduzione del calore. Atti Semin Mat Fis della Universita` di Modena 3:3

      [14] Christov, C I (2009), On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction. Mech Res Commun 36(4), 481–486.

      [15] Ostoja-Starzewski, M (2009), A derivation of the Maxwell–Cattaneo equation from the free energy and dissipation potentials. Int J Eng Sci 47(7), 807–810.

      [16] Tibullo, V & Zampoli, V (2011), A uniqueness result for the Cattaneo– Christov heat conduction model applied to incompressible fluids, Mech Res Commun 38(1), 77–79.

      [17] Straughan, B (2010), Thermal convection with the Cattaneo– Christov model. Int J Heat Mass Transf 53(1), 95–98

      [18] Haddad, S A M (2014), Thermal instability in Brinkman porous media with Cattaneo–Christov heat flux. Int J Heat Mass Transf 68, 659–668..

      [19] Ciarletta, M & Straughan, B (2010), Uniqueness and structural stability for the Cattaneo–Christov equations. Mech Res Commun 37(5), 445–447.

      [20] Al-Qahtani, H & Yilbas, B S (2010), The closed form solutions for Cattaneo and stress equations due to step input pulse heating. Phys B 405(18), 3869–3874.

      [21] Papanicolaou, N C, Christov, C I & Jordan, P M (2011), The influence of thermal relaxation on the oscillatory properties of two-gradient convection in a vertical slot. Eur J Mech B/Fluids 30(1), 68–75.

      [22] Han, S, Zheng, L, Li, C & Zhang, X (2014), Coupled flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model. Appl Math Lett 38:87–93

      [23] Mustafa, M (2015), Cattaneo–Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. AIP Adv 5(4),047109.

      [24] Bissell, J J (2015), On oscillatory convection with the Cattaneo- Christov hyperbolic heat-flow model. Proc R Soc A 471:20140845.

      [25] Khan, M I, Waqas, M, Hayat, T, Khan, M I & Alsaedi, A Chemically reactive flow of upper-convected Maxwell fluid with Cattaneo–Christov heat flux model, J Braz. Soc. Mech. Sci. Eng. DOI 10.1007/s40430-017-0915-5.

      [26] Raju, C S K, Sanjeevi, P, Raju, M C, Ibrahim, S M, Lorenzini, G, & Lorenzini, E, The flow of magnetohydrodynamic Maxwell nanofluid over a cylinder with Cattaneo–Christov heat flux model, Continuum Mech. Thermodyn. DOI 10.1007/s00161-017-0580-z.

      [27] Shahid, A, Bhatti, M M, Anwar, Be´g, O & Kadir, A, Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model, Neural Comput & Applic, DOI 10.1007/s00521-017-2933-8.

      [28] Khana, S M, Hammad, M, Batool, S, & Kaneez, H, (2017), Investigation of MHD effects and heat transfer for the upper-convected Maxwell (UCM-M) micropolar fluid with Joule heating and thermal radiation using a hyperbolic heat flux equation, Eur. Phys. J. Plus 132: 158, DOI 10.1140/epjp/i2017-11428-6

      [29] Sheikholeslami, M & Bhatti, M M (2017), Active method for nanofluid heat transfer enhancement by means of EHD. Int J Heat Mass Transf 109, 115–122.

      [30] Ocone,, R, Astarita G (1987), Continuous and discontinuous models for transport phenomena in polymers. AIChemE J 33, 423–435

      [31] Zhe, Z & Dengying, L (2000), The research progress of the non- Fourier heat conduction. Adv Mech 30,123–141.

      [32] Huilgol, R R, (1992), A theoretical and numerical study of non- Fourier effects in viscometric and extensional flow of an incompressible simple fluid. J Non-Newtonian Fluid Mech 43,83–102.

      [33] Motsa, S S & Makukula, Z G (2013), On spectral relaxation method approach for steady von kárman flow of a reiner-rivlin fluid with joule heating, viscous dissipation and suction/injection. Cent. Eur. J. Phys., 11(3), 363–374.

      [34] Kameswaran, P, Sibanda, P, & Motsa, S S, (2013), A spectral relaxation method for thermal dispersion and radiation effects in a nanofluid flow. Boundary Value Problems 2013, 242.

      [35] Grubka, L J, Bobba, K M (1985), Heat transfer characteristics of a continuous, stretching surface with variable temperature. ASME J Heat Transf 107, 248–25.

      [36] Ali, M E, (1994), Heat transfer characteristics of a continuous stretching surface. Heat Mass Transfer 29, 227–234.

      [37] Chen, C H (1998), Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transfer, 33,471–476.

      [38] Anuar Ishak (2010), Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect, Meccanica 45, 367–373, DOI 10.1007/s11012-009-9257-4.

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  • How to Cite

    Gangadhar, K., V. Ramana, K., & Rushi Kumar, B. (2018). Velocity Slip and Thermal Jump on Maxwell Fluid with Non-Fourier Cattaneo-Christov Heat Flux Using SRM Solutions. International Journal of Engineering & Technology, 7(4.10), 233-239. https://doi.org/10.14419/ijet.v7i4.10.20902

    Received date: 2018-10-04

    Accepted date: 2018-10-04

    Published date: 2018-10-02