International Scientific Journal

Thermal Science - Online First

online first only

Heat transfer analysis based on cattaneo-christov heat flux model and convective boundary conditions for flow over an oscillatory stretching surface

In this study, we investigate the heat transfer characteristics in unsteady boundary layer flow of Maxwell fluid by using Cattaneo-Christov heat flux model and convective boundary conditions. The flow is caused by a sheet which is stretched periodically back and forth in its own plane. The physical model that takes into account the effects of constant applied magnetic field is transformed into highly nonlinear partial differential equations under boundary layer approximations. The solution of dimensionless version of these equations is developed using homotopy analysis method. The simulations are presented in the form of temperature and velocity profiles for suitable range of physical parameters. The obtained results illustrate that an increase in Deborah number and Hartmann number suppress the velocity profiles. It is further observed that Cattaneo-Christov heat flux model predicts the suppression of thermal boundary layer thickness as compared to Fourier law.
PAPER REVISED: 2017-08-22
PAPER ACCEPTED: 2017-08-24
  1. Gupta, P. S. and Gupta, A. S., Heat and mass transfer on a stretching sheet with suction and blowing. The Canadian Journal of Chemical Engineering, 55(6), (1977), pp. 744-746.
  2. Lawrence, P. S. and Rao, B. N., Heat transfer in the flow of a viscoelastic fluid over a stretching sheet, Acta Mechanica, 93 (1992) pp. 53-61.
  3. Rollins, D. and Vajravelue, K., Heat transfer in a viscoelastic order fluid over a Continuous Stretching surface, Acta Mechanica,89 (1991) pp. 167-178.
  4. Bhattacharyya, K.,Boundary layer flow and heat transfer over an exponentially shrinking sheet. Chin.Phys.Lett.28,( 2011) 074701.
  5. Sahoo, B., Hiemenz flow and heat transfer of a third grade fluid, Communications in Nonlinear Science and Numerical Simulation, pp. 811-824.
  6. Cortell, R., Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a magnetic field, International Journal of Heat and Mass Transfer, 49 (2006) pp. 1851.
  7. Abbas, Z., Javed, T., Ali, N. and Sajid, M., Flow and Heat Transfer of Maxwell Fluid Over an Exponentially Stretching Sheet: A Non-similar Solution, Heat Transfer—Asian Research, 43 (3), 2014.
  8. Ali, N., Sajid, M., Javed, T. and Abbas, Z., Heat transfer analysis for peristaltic flow in a curved channel, International Journal of Heat and Mass Transfer, 53, (2010), pp.3319-3325.
  9. Mahantesh M., Nandeppanavar a, K. Vajravelu b, M. Subhas Abel ,Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink, Communications in Nonlinear Science and Numerical Simulation, 16 (2011) pp. 3578-3590.
  10. Osorio, A., Avila, R., and Cervantes, J., On the natural convection of water near its density inversion in an inclined square cavity, International journal of heat and mass transfer, 47 (2004), pp. 4491-4495.
  11. Karimi-Fard, M., Charrier-Mojtabi, M. C., and Vafai,K., Non-darcian effects on double-diffusive convection within a porous medium, Numerical Heat Transfer, Part A: Applications, 31,( 1997) pp. 837-852.
  12. Abo-Eldahab, E.M., El Aziz, M.A., Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream, Applied Mathematics and Computation 162 (2), (2005) pp.881-899.
  13. Mandal, I.C., Mukhopadhyay, S., Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium, Ain Shams Engineering Journal 4(1), (2013), pp. 103-110.
  14. Malik, R., Khan, M., Munir, A., Khan,W. A., Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition, PLoS ONE 9(10): e107989. doi:10. 1371/journal.pone.0107989
  15. Sharma, P.R. Ariel, P.D. and Kumar, H., Numerical solution of flow and heat transfer of a non-Newtonian fluid over a stretching sheet, Modelling, Measurement and Control B 74 (1), (2005) pp. 45-62.
  16. Khan, W.A., Culham, J. R., Yovanovich, M.M., Fluid flow around and heat transfer from an infinite circular cylinder, Journal of Heat Transfer 127 (7), (2005) pp. 785-790.
  17. Gomaa, H., Taweel, A.M. Al, Effect of oscillatory motion on heat transfer at vertical flat surfaces, International Journal of Heat and Mass Transfer, 48 (8) (2005) 1494-1504.
  18. Su, X.H., Zheng, L.C., Zhang, X.X. and Zhang, J.H., MHD mixed convective heat transfer over a permeable stretching wedge with thermal radiation and Ohmic heating, Chemical Engineering Science. 78, (2012) pp. 1-8.
  19. Roşca, A.V. and Pop, I., Flow and heat transfer over a vertical permeable stretching/ shrinking sheet with a second order slip, International Journal of Heat and Mass Transfer, 60 (2013) pp. 355-364.
  20. Zheng, L.C., Jin, X., Zhang, X. X. and Zhang, J. H., Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects, Acta Mechanica Sinica ,29(5), (2013).pp. 667-675.
  21. Ali, N., Khan,S.U. Abbas, Z., Hydromagnetic Flow and Heat Transfer of a Jeffrey Fluid over an Oscillatory Stretching Surface, Zeitschrift für Naturforschung A, 70(7)a, (2015); pp. 567-576.
  22. Fourier, J.B.J., Théorie Analytique De La Chaleur, Paris, 1822.
  23. Cattaneo, C., Sulla conduzione del calore, AttiSemin. Mat. Fis. Univ. Modena Reggio Emilia 3 (1948) pp. 83-101.
  24. Christov, C.I., On frame indifferent formulation of the Maxwell--Cattaneo model of finite-speed heat conduction, Mechanics Research Communications, 36 (2009) pp. 48-486.
  25. Oldroyd, J.G., On the formulation of rheological equations of state, Proceedings of the Royal Society A, 200 (1949) pp. 523-541.
  26. Pranesh, S. and Kiran, R., V., Study of Rayleigh-Bénard Magneto Convection in a Micropolar Fluid with Maxwell-Cattaneo Law, Applied Mathematics, (2010), 1, pp. 470-480
  27. Straughan, B., Thermal convection with the Cattaneo-Christov model, International Journal of Heat and Mass Transfer, 53 (2010) pp. 95-98.
  28. Haddad, S.A.M., Thermal instability in Brinkman porous media with Cattaneo--Christov heat flux, International Journal of Heat and Mass Transfer, 68 (2014) pp. 659-668.
  29. 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, (2014) pp. 87-93.
  30. Hayat T, Khan, 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 (2016), pp. 49-55.
  31. Khan, M. Ahmad, L. Khan, W.A. Alshomranic, A.S., Alzahranic, A.K. and Alghamdi, M.S., A 3D Sisko fluid flow with Cattaneo-Christov heat flux model and heterogeneous-homogeneous reactions: A numerical study, Journal of Molecular Liquids, 238 (2017) pp. 19-26.
  32. Li, J., Zheng, L. and Liu, L., MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects, Journal of Molecular Liquids, 221 (2016) pp. 19-25.
  33. Mustafa, M., Cattaneo-Christove heat flux model for rotating flow and heat transfer of upper convected Maxwell fluid, AIP Advances, 5 (2015), 4917306.
  34. Abbasi, F M, Mustafa, M, Shehzad, S A, Alhuthali, M S and Hayat, T., Analytical study of Cattaneo-Christov heat flux model for boundary layer flow of an Oldroyd-B fluid, Chinese Physics B, 25 (2016) 014701.
  35. Waqas, M., Hayat, T., Farooq, M., Shehzad, S.A. and Alsaedi, A., Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid, Journal of Molecular Liquids 220, pp. 642-648
  36. Shehzad, S.A., Abbasi, F.M., Hayat, T. and Ahmad, B., Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet, Applied Mathematics and Mechanics, 37 (6), pp. 761-768.
  37. Abbasi, F. M., Shehzad, S. A., Hayat, T., Alsaedi, A. and Hegazy, A., Influence of Cattaneo-Christov heat flux in flow of an Oldroyd-B fluid with variable thermal conductivity, International Journal of Numerical Methods for Heat & Fluid Flow ,pp. 2271-2282.
  38. Hayat T., Awais M., Sajid M., Mass Transfer Effects on the Unsteady Flow of UCM Fluid over a Stretching Sheet. International Journal of Modern Physics B, 25 (2011), pp. pp. 2863-78.
  39. Pahlavan, A. A., Aliakbar, V., Farahani, F. V., and Sadeghy, K. MHD flow of UCM Fluids above Stretching Sheet using Two-auxiliary-parameter Homotopy Analysis Method. Communication in Nonlinear Science and Numerical Simulation, 14 (2009), pp. pp. 473-488.
  40. Awais, M. M, Hayat, T., Alsaedi, A. and Asghar, S., Time-Dependent Three-Dimensional Boundary layer Flow of a Maxwell fluid, Computers & Fluids 91 (2014) pp. pp. 21-27.
  41. Mushtaq, A., Mustafa, M., Hayat, T. and Alsaedi, A., Effects of Thermal Radiation on the Stagnation-Point Flow of Upper-Convected Maxwell Fluid over a Stretching Sheet, Journal of Aerospace Engineering., 10.1061/(ASCE)AS.1943-5525.0000361, 04014015.
  42. Hayat, T., Shehzad, S.A., Qasim, M., Obaidat, S., Steady Flow of Maxwell Fluid with Convective Boundary Conditions, Zeitschrift für Naturforschung A,. 66a (2011) pp.417-422.
  43. Hayat, T., Iqbal , Z., Qasim, M., Obaidat S. ,Steady Flow of an Eyring Powell fluid over a moving surface with convective boundary conditions, International Journal of Heat and Mass Transfer,55 (2012) pp. 1817-1822.
  44. Hayat, T., On Mixed Convection Stagnation Point Flow of Second Grade Fluid with Convective Boundary Condition and Thermal Radiation, International Journal of Nonlinear Science and Numerical Simulation,15, (2014), pp. 27-34.
  45. Wang, C.Y., Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous, Acta Mechanica, 72 (1988) 261- 268.
  46. Liao, S.J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
  47. Abbasbandy, S., Homotopy Analysis Method for Heat Radiation Equations, International Communications in Heat and Mass Transfer, 34 (2007) pp. 380-387.
  48. Turkyilmazoglu, M., Analytic Approximate Solutions of Rotating Disk Boundary Layer Flow Subject to a Uniform Suction or Injection, International Journal of Mechanical Sciences 52( 2010), pp.1735-1744
  49. Turkyilmazoglu, M., A Note on the Homotopy Analysis Method, Applied Mathematics Letters 23 (10),( 2010) 1226-1230.
  50. Liao, S. J., Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press Beijing (2012).