Slip Velocity and Temperature Jump on Dissipative CASSON Fluid with CATTANEO-CHRISTOV Heat Flux Model: Spectral Relaxation Method

  • Abstract
  • Keywords
  • References
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  • Abstract

    A numerical analysis is performed for investigating the slip flow of a viscous dissipative Casson fluid towards a stretching sheet with Cattaneo-Christov heat flux and variable viscosity. The nonlinear partial differential equations are transformed with appropriate similarity variables into a system of nonlinear ordinary differential equations. Numerical solutions are carried out by using efficient Spectral relaxation method. Notable accuracy of the present results has been obtained with previous results in a limiting sense from the literature. It is found that thermal relaxation time has an inverse relationship with the fluid temperature. Interestingly, the fluid velocity is gradually decreasing with higher values of slip factor.




  • Keywords

    Cattaneo-Christov heat flux model, Stretching sheet, Temperature Jump, MHD, Slip velocity.

  • References

      [1] Crane, L J (1970), Flow past a Stretching Plate, Zeit. Ang.Mat. Phys. 21(4), 645–647.

      [2] Pavlov, K B (1974), Magnetohydrodynamic Flow of an In compressible Viscous Fluid Caused by the Deformation of a Plane Surface, Magnetohydr. 10, 146–148.

      [3] Gupta, P S & Gupta, A S (1977), Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing, Canadian J. Chem. Eng., 55( 6), 744–746.

      [4] Fourier, J B J (1822), Théorie Analytique De La Chaleur, Paris.

      [5] Cao, B Y, Guo, Z Y (2007), Equation of motion of a phonon gas and non-Fourier heat conduction. Journal of Applied Physics 102, 053503.

      [6] Dong, Y, Cao, B Y & Guo, Z Y (2011), Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics. Journal of Applied Physics 110, 063504.

      [7] Zhang, M K, Cao, B Y & Guo, Y C (2013), Numerical studies on dispersion of thermal waves, International Journal of Heat and Mass Transfer 67, 1072–1082.

      [8] Cattaneo, C (1948), Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 3, 83–101.

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

      [10] Straughan, B (2010) Thermal convection with the Cattaneo—Christov model, International Journal of Heat and Mass Transfer 53, 95–98.

      [11] Ciarletta, M & Straughan, B (2010), Uniqueness and structural stability for the Cattaneo—Christov equations, Mechanics Research Communications 37, 445–447.

      [12] Han, S, Zheng, L, Li, C & Zhang, X (2014), Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model, Applied Mathematics Letters 38, 87–93

      [13] Khan, A J, Mustafa, M, Hayat, T & Alsaedi, A (2015), Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface.PLoS ONE, 10(9), e0137363. doi:10.1371/journal.pone.0137363

      [14] Malik, M Y, Mair Khan, Salahuddin, T & Imad Khan, (2016), Variable viscosity and MHD flow in Casson fluid with Cattaneo–Christov heat flux model: Using Keller box method, Engineering Science and Technology, an International Journal 19, 1985–1992

      [15] Hayat, T, Qayyum, S, Imtiaz, M & Alsaedi A (2017), Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model, Results in Physics 7, 126–133

      [16] Hayat, T, Khan, M I, Farooq, M & Alsaedi A (2017), Thermally stratified stretching flow with Cattaneo–Christov heat flux, International Journal of Heat and Mass Transfer 106, 289–294.

      [17] Casson, N., Rheology of Disperse Systems, in Flow Equation

      [18] for Pigment Oil Suspensions of the Printing Ink Type. Rheo gy of Disperse Systems, Mill, C.C., Ed., London: Pergamon, 1959, 84–102.

      [19] S. Nadeem, R U Haq, C. Lee C (2012), MHD flow of a Casson fluid over an exponentially shrinking sheet, Sci. Iran. 19, 1550–1553.

      [20] Mukhopadhyay, S, De, P R, Bhattacharyya, K & Layek, G C (2013), Casson fluid flow over an unsteady stretching surface, Ain Shams Eng. J. 4, 933–938.

      [21] Mukopadhyay, S (2013), Casson fluid flow and heat transfer over a nonlinearly stretching surface, Chin. Phys. 22, 074701.

      [22] Nadeem, S, Haq, R U, Akbar, N S, Khan, Z H (2013), MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alexandria Eng. J. 52, 577–582.

      [23] Mukhopadhyaya, S, Moindala, I C & Hayat, T (2014), MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation, Chin. Phys. 23, 104701.

      [24] Mahanta, G & Shaw, S (2014), 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition, AlexandriaEng.J., http//

      [25] Mustafa, M & Khan, J A (2015), Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects, AIP Adv. 5, 077148.

      [26] Animasaun, I L, Adebile, E A & Fagbade, A I (2015), Casson fluid flow with variable thermo- physical property along Exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopic analysis Method, J. Niger. Math Soc., 2015.02.001.

      [27] Das, M, Mahato, R & Nandkeolyar, R (2015), Newtonian heating effect on unsteady hydro- magnetic Casson fluid flow past a flat plate with heat and mass transfer, Alexandria Eng. J., http://dx.doi/10.1016/j.aej.2015.07.007.

      [28] Raju, C S K, Sandeep, N, Sugunamma, V, Babu, M J & Reddy, J V R (2016), Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface, Eng. Sci. Technol. Int. J. 19 (1), 45–52.

      [29] Ramesh, K & Devakar, M (2015), Some analytical solutions for flows of Casson fluid with slip boundary conditions, Ain Shams Eng. J. 6, 967–975.

      [30] Khalid, A, Khan, I, Khan, A & Shafie, S (2015), Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium, Eng. Sci.Technol. Int. J. 18 (3),309–317.

      [31] Ibrahim S M, Kumar P V, Lorenzini G, Lorenzini E, & Mabood, F (2017), Numerical Study of the Onset of Chemical Reaction and Heat Source on Dissipative MHD Stagnation Point flow of Casson Nanofluid over a Nonlinear Stretching Sheet with Velocity Slip and convective Boundary Conditions, Journal of Engineering Thermophysics 26(2), 256–271.

      [32] Seth, G S, Tripath, R & Mishra, M K (2017), Hydromagnetic thin film flow of Casson fluid in non- darcy porous medium with Joule dissipation and Navier’s partial slip, Appl. Math. Mech. -Engl. Ed. DOI 10.1007/s10483-017-2272-7

      [33] Shateyi, S, Mabood, F & Lorenzini, G (2017), Casson Fluid Flow: Free Convective Heat and Mass Transfer over an Unsteady Permeable Stretching Surface Considering Viscous Dissipation, Journal of Engineering Thermophysics 26(1), 39–52.

      [34] B. Gebhart, (1962), Effects of viscous dissipation in natural convection, J. Fluid Mech. 14, 225–232.

      [35] Turcotte, D, Hsui, A, Torrance, K & Schubert, G (1974), Influence of viscous dissipation on B´enard convection, J. Fluid Mech. 64, 369–374.

      [36] Barletta, A, Celli, M & Rees, D (2009), The onset of convection in a porous layer induced by viscous dissipation:Alinear stability analysis, Int. J. Heat Mass Transfer 52, 337.

      [37] Barletta, A, Celli, M & Nield, D (2010),Unstably stratified Darcy flow with impressed horizontal temperature gradient, viscous dissipation and asymmetric thermal boundary conditions, Int. J. Heat Mass Transfer 53, 1621–1627.

      [38] Barletta, A & Nield, D (2010), Instability of Hadley–Prats flow with viscous heating in a horizontal porous layer, Transp. Porous Media 84, 241–256.

      [39] Barletta, A & Nield, D (2011), Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium,” Int. J. Heat Mass Transfer 54, 1641–1648.

      [40] Roy, K & Murthy, P, Soret effect on the double diffusive convection instability due to viscous dissipation in a horizontal porous channel, Int. J. Heat Mass Transfer 91, 700–715).

      [41] Khader, M M & Mziou, S (2017), Chebyshev spectral method for studying the viscoelastic slip flow due to a permeable stretching surface embedded in a porous medium with viscous Dissipation and non-uniform heat generation, Boundary Val ue Problems 2017:37, DOI 10.1186/s13661-017-0764-2

      [42] Roy, K & Murthy, PVSN (2017), Effect of viscous dissipation on the convective instability induced by inclined temperature gradients in a non-Darcy porous medium with horizontal through flow, Physics of Fluids 29, 044104; doi: 10.1063/1.4979526

      [43] Metri, P G, Guariglia, E, & Silvestrov, S (2017) Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink, AIP Conference Proceedings 1798, 020096 doi: 10.1063/1.4972688.

      [44] Palani, G, Srikanth, U, & Kim, K Y, (2017) Combined Effects of Viscous Dissipation and MHD on Free Convection Flow past a Semi-Infinite Vertical Plate with Variable Surface temperature in the Presence of Heat Source, Journal of Engineering Thermophysics, 26,113–124.

      [45] 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.

      [46] 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.

      [47] Wang, C Y (1989), Free convection on a vertical stretching surface with suction and blowing, Appl. Math. Mech. 69, 418–420.

      [48] Salahuddin, T, Malik, M Y, Hussain, A, Bilal, S & Awais, M (2016), MHD flow of Cattaneo– christov heat flux model for Williamson fluid over a stretching sheet with variable thickness: using numerical approach, J. Magn. Magn. Mater. 401, 991–997.

      [49] Malik, M Y, Khan, M, Salahuddin, T & Khan I (2016), Variable viscosity and MHD flow in casson fluid with Cattaneo–Christov heat flux model: Using Keller box method, Engineering Science and Technology, an International Journal 19, 1985–1992.




Article ID: 20905
DOI: 10.14419/ijet.v7i4.10.20905

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