THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

online first only

An iterative approach to viscoelastic boundary layer flows with heat source/sink and thermal radiation

ABSTRACT
In this study effect of radiation on the viscoelastic Walter-B fluid is investigated with heat sink/source. Sakiadis, Blasius and stagnation point flows are considered at constant surface temperature. Some suitable similarity variables have been utilized to transform governing equations into ordinary differential equations. An iterative approach based on the Legendre wavelet spectral collocation method (LWSCM) is applied for the solution of the resulting equations. The obtained results are validated by plotting the residual error curves in each case. Temperature and heat transfer rate at wall are analyzed to investigate the influence of involved parameters. It is found that the Legendre wavelet spectral collocation method (LWSCM) is very efficient and can be employed for the solutions of various non- Newtonian flow problems.
KEYWORDS
PAPER SUBMITTED: 2018-02-02
PAPER REVISED: 2018-11-27
PAPER ACCEPTED: 2018-12-09
PUBLISHED ONLINE: 2019-01-13
DOI REFERENCE: https://doi.org/10.2298/TSCI180202003I
REFERENCES
  1. H. Blasius, Grenzschichten in Flussigkeitenmitkleiner Reibung, Z. Angew Math. Phys. 56 (1908) pp.1-37
  2. B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces I: boundary layer equations for two dimensional and axisymmetric flow, AIChE J. 7 (1961) pp. 26-28
  3. B.C. Sakiadis, Boundary layer behavior on continuous solid surface II: boundary layer on a continuous flat surface, AIChE. J. 7 (1961) pp. 221-225
  4. L. J. Crane, Flow past a Stretching Plate, Z. Angew Math. Phys. 7 (1961) pp. 26-28
  5. P. S. Gupta and A. S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, J. Chem. Eng. 55 (1977) pp. 744-748
  6. J. Vleggar, Laminar boundary-layer behaviour on continuous, accelerating surfaces, Chem. Eng. Sci. 32 (1977) pp.1517-1525
  7. F. K. Tsou, E. M. Sparrow, and R. J. Goldstein, Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat Mass Transf. 10 (1967) pp. 219-235
  8. H. S. Takhar, S. Nitu and I. Pop, Boundary layer flow due to a moving plate: variable fluid properties, Acta Mech. 90 (1991) pp.37-42
  9. K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder, Dingler's Polytech. J. 326 (1911) pp.321-410
  10. R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. Lett. A 357 (2006) pp. 298-305
  11. R. Cortell, A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet, Int. J. Non-Linear Mech. 41, (2006) pp. 78-85
  12. Z. Abbas, M. Naveed, M. Naeem and Q. M. Z. Zia, Analytical investigation of Maxwell fluid flow with radiation in an axisymmetric semi-porous channel by parameterized perturbation method, J. Brazilian Soci. Mech. Sci. Engng. (2018) 40:65.
  13. Z. Abbas, M. Rafiq and M. Naveed, Analysis of Eyring Powell liquid flow in curved channel with Cattaneo-Christove heat flux model, J. Brazilian Soci. Mech. Sci. Engng. (2018) 40:390.
  14. Sheikholeslami, M. and Zeeshan A., Analysis of flow and heat transfer in water based nanofluid due to magnetic field in a porous enclosure with constant heat flux using CVFEM, imulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model, Comput. Methd. Appl. Mech. Engng. 320 (2017), pp. 68-81.
  15. K. Sadeghy, A.H. Najafi and M. Saffaripour, Sakiadis flow of an upper-convected Maxwell fluid, Int. J. Non-Linear Mech. 40 (2005) pp. 1220-1228
  16. I. C. Liu, Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field, Int. J. Non-Linear Mech. 40 (2005) pp. 465-474
  17. P.D. Ariel, T. Hayat, S. Asghar, The flow of an elastico-viscous fluid past a stretching sheet with partial slip, Acta Mech. 187 (2006) pp. 29-35
  18. S.J. Liao, A. Campo, Analytic solutions of the temperature distribution in Blasius viscous flow problems, J. Fluid Mech. 453 (2002) pp. 411-425
  19. S.J. Liao, On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluid over a stretching sheet, J. Fluid Mech. 488 (2003) pp. 189-212
  20. H. Xu, S.J. Liao, Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate, J. Non-Newton. Fluid Mech. 129 (2005) pp. 46-55
  21. T. Hayat, Z. Abbas and M. Sajid, Series solution for the upper-convected Maxwell fluid over a porous stretching plate, Phys. Lett. A 358 (2006) pp. 396-403
  22. T. Hayat and M. Sajid, Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int. J. Heat Mass Transf. 50 (2007) pp. 75-84.
  23. R. Cortell, Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys. Lett. A 372 (2008) pp. 631-636
  24. R. Cortell, Radiation effects in the Blasius flow, Appl. Math. Comp. 198 (2000) pp. 333-338
  25. R. Cortell, Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Comput. Math. Appl., 53 (2007) pp. 305-316
  26. R. Cortell, Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation, Phys. Lett. A, 372 (2008) pp. 2431-2439
  27. Sheikholeslami, M., Shehzad, S. A. Zhixiong, L. and Shafee, A., Numerical modeling for alumina nanofluid magnetohydrodynamics convective heat transfer in a permeable medium using Darcy law, Int. J. Heat Mass Transf. 127 (2018), pp. 614-622.
  28. Naveed, M., Abbas, Z. and Sajid, M., Thermophoresis and Brownian effects on the Blasius flow of a nanofluid due to a curved surface with thermal radiation, Eur. Phys. J. Plus, (2016) 131:214.
  29. M. Sajid, T. Hayat, Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet, Int. Comm. Heat Mass Transf. 35 (2008) pp. 347-356
  30. P. D. Ariel, Flow of viscoelastic fluids through a porous channel-I, Int. J. Numer. Meth. Fluids 17 (1993) pp. 605-633
  31. P. D. Ariel, A new finite-difference algorithm for computing the boundary layer flow of viscoelastic fluids in hydromagnetics, Comput. Meth. Appl. Mech. Eng. 124 (1995) pp. 1-13
  32. P. D. Ariel, On extra boundary condition in the stagnation point flow of a second grade fluid, Int. J. Eng. Sci. 40 (2002) pp.145-162
  33. K. Sadeghy and M. Sharifi, Local similarity solution for the flow of a second grade viscoelastic fluid above a moving plate, Int. J. Non-Linear Mech. 39 (2004) pp. 1265-1273
  34. M. Sajid, Z. Abbas, T. Javed and N. Ali, Boundary layer flow of an Oldroyd-B fluid in the region of stagnation point over a stretching sheet, Can. J. Phys. 88 (2010) pp. 635-640
  35. T. Hayat, M. Nawaz and M. Sajid, Effect of heat transfer on the flow of a second grade fluid in divergent/convergent channel, Int. J. Numer. Meth. Fluids 64 (2010) pp. 761-776
  36. M. Sajid, N. Ali, A. M. Siddiqui, Z. Abbas and T. Javed, Effects of permeability on swimming of a micro-organism in an Oldroyd-B fluid, J. Porous Media 17 (2014) pp. 59-66
  37. A. Raptis and C. Perdikis, Viscoelastic flow by the presence of radiation, ZAMM 78 (1998) pp. 277-279
  38. M. A. Seddeek, Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow, Int. J. Heat Mass Transf. 45 (2002) pp. 931-935
  39. A. Raptis, C. Perdikis and H.S. Takhar, Effect of thermal radiation on MHD flow, Appl. Math. Comput. 153 (2004) pp. 645-649
  40. D. W. Beard and K. Walters, Elastico-viscous boundary-layer flows. I. Two-dimensional flow near a stagnation point, Proc. Camb. Phil. Soc. 60 (1964) pp. 667-674
  41. M. Sajid. S. A. Iqbal. N. Ali and T. Hayat, A Legendre wavelet spectral collocation technique resolving anomalies associated with velocity in some boundary layer flows of Walter-B liquid, Meccanica, (2016) DOI 10.1007/s11012-016-0428-9
  42. R.C. Bataller, Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition, Appl. Math. Comp. 206 (2008) pp. 832-840.