THERMAL SCIENCE

International Scientific Journal

HEAT AND MASS TRANSFER IN 3-D MHD WILLIAMSON-CASSON FLUIDS FLOW OVER A STRETCHING SURFACE WITH NON-UNIFORM HEAT SOURCE/SINK

ABSTRACT
A mathematical model has been proposed for investigating the flow, heat, and mass transfer in Williamson and Casson fluid-flow over a stretching surface. For controlling the temperature and concentration fields we considered the space and temperature dependent heat source/sink and homogeneous-heterogeneous reactions, respectively. Numerical results are carried out for this study by using Runge-Kutta based shooting technique. The effects of governing parameters on the flow, heat and mass transfer are illustrated graphically. Also computed the skin-friction coefficients for axial and transverse directions along with the local Nusselt number. In most of the studies, homogeneous-heterogeneous profiles were reduced into a single concentration equation by assuming equal diffusion coefficients. For the physical relevance, without any assumptions we studied the individual behavior of the homogeneous-heterogeneous profiles. It is found that the rate of heat and mass transfer in Casson fluid is significantly large while equated with the heat and mass transfer rate of Williamson fluid.
KEYWORDS
PAPER SUBMITTED: 2016-04-26
PAPER REVISED: 2017-04-03
PAPER ACCEPTED: 2017-04-05
PUBLISHED ONLINE: 2017-05-06
DOI REFERENCE: https://doi.org/10.2298/TSCI160426107R
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 1, PAGES [281 - 293]
REFERENCES
  1. Sakiadis, B. C., Boundary layer behavior on continuous solid surface: Boundary layer equations for two-dimensional and axisymmetric flow, J. Amer. Inst. Chem. Eng. 7 (1961), pp. 26-28.
  2. Ali, M. E., Al-Yousef, F., Laminar mixed convection from a continuously moving vertical surface with suction or injection, Heat and Mass Transfer 33 (1998), 4, pp. 301-306, 1998.
  3. Magyari, E., Ali, M. E., Keller, B., Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities, Heat and Mass Transfer 38, (2001) ,(1-2), pp. 65-74.
  4. Chamka, A. J., MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction, Int. Comm. Heat Mass Trans. 30 (2003), pp. 413-422.
  5. Raptis, A., Perdikis, C., Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field, Int. J. Non-linear Mech. 41 (2006), pp. 527-529.
  6. P. M. Patil, P. S. Kulkarni, Effects of chemical reaction on free convective flow of a polar fluid through a porous medium in the presence of internal heat generation, Int. J. Thermal Sci. 47 (2008), pp. 1043-1054.
  7. Ali, M. E., The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface, Int. J. of Thermal Science, 45 (2006),1 pp. 60-69.
  8. Cortell, R., MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species, Chemical Engineering and Processing, 46 (2007) pp. 721-728.
  9. Raju, C. S. K., N. Sandeep, and S. Saleem. Effects of induced magnetic field and homogeneous-heterogeneous reactions on stagnation flow of a Casson fluid. Engineering Science and Technology, an International Journal 19.2 (2016) 875-887.
  10. Haq, R. U., Nadeem, S., Khan, Z. H., Okedayo, T. G., Convective heat transfer and MHD effects on casson nanofluid flow over a shrinking sheet, Cent. Eur. J. Phys. 12 (2014), pp. 862-871.
  11. A. Hussain, M. Z. Salleh, R. M. Tahar, I. Khan, Unsteady boundary layer flow and heat transfer of a casson fluid past an oscillating vertical plate with Newtonian heating, Plos One 9 (2014), pp. e108763.
  12. Raju, C. S. K., Sandeep, N., Sugunamma, V., Jayachandrababu, M., Ramanareddy, J. V., Heat and mass transfer in magneto hydrodynamic casson fluid over an exponentially permeable stretching surface, Eng. Sci. Tech., an Int. J. , (2015), dx.doi.org/10.1016/j.jestch.2015.05.010.
  13. Nadeem, S., Haq, R. U., Lee, C., MHD flow of a casson fluid over an exponentially shrinking sheet, Scientia Iranica B 19 (2012), pp. 1550-1553.
  14. Nadeem, S., Haq, R. U., Akbar, N. S., Khan, Z. H., MHD three-dimensional casson fluid flow past a porous linearly stretching sheet, Alexandria Engineering J. 52 (2013), pp. 577-582.
  15. Ramzan, M., Farooq, M., Alsaedi, A., Hayat, T., MHD three-dimensional flow of couple stress fluid with Newtonian heating, Eur. Phys. J. Plus 49 (2013), pp. 128.
  16. Hayat, T., Shehzad, S. A., Alsaedi, A., Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation, Applied Mathematics and Mech. 34 (2013), pp. 823-832.
  17. Ali, M. E., The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities, Heat and Mass Transfer 40 (2004), (3-4), pp. 285-291.
  18. Mahantha, G., Shaw, S., 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition, Alexandria Eng. J. 54 (2015), pp. 653-659.
  19. Sandeep, N., Raju, C. S. K., Sulochana, C., Sugunamma, V., Effects of aligned magnetic field and radiation on the flow of ferrofluids over a flat plate with non-uniform heat source/sink, Int. J. Sci. Eng. 8 (2015), pp. 151-158.
  20. Hayat, T., Saeed, Y., Asad, S., Alsaedi, A., Soret and dufour effects in the flow of Williamson fluid over an unsteady stretching surface with thermal radiation, Z. Naturforsch. 70 (2015), pp. 235-243.
  21. Khan, N. A., Khan, S., Riaz, F., Boundary layer flow of Williamson fluid with chemically reactive species using scaling transformation and homotopy analysis method, Math. Sci. Lett. 3 (2014), pp. 199-205.
  22. Hayat, T., Abbas, Z., Sajid, M., Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction, Physics Letters A, 372 (2008) , (14), pp. 2400-2408.
  23. Annimasun, I. L., Raju, C. S. K., Sandeep, N., Unequal diffusivities case of homogeneous-heterogeneous reactions within viscoelastic fluid flow in the presence of induced magneticfield and nonlinear thermal radiation, Alexandria Engineering journal, (2015), dx.doi.org/10.1016/j.aej.2016.01.018.
  24. Hayat, T., Tanveer, A., Yasmin, H., Alsaedi, A., Homogeneous-heterogeneous reactions in peristaltic flow with convective conditions, Plos one 9 (2014), pp. e113851.
  25. Bachok, N., Ishak, A., Pop, I., On the stagnation point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), pp. 4296-4302.
  26. Chatterjee, A., Heat transfer enhancement in laminar impinging flows with a non-Newtonian inelastic fluid, J. Non Newtonian Fluid Mech. 211 (2014), pp. 50-61.
  27. Delenda, N., Hirata, S. C., Ouarzazi, M. N., Primary and secondary instabilities of viscoelastic mixutres saturating a porous medium: Application to separation of species, J. Non Newtonian Fluid Mech. 181-182 (2012), pp. 11-21.
  28. Sandeep, N., Sulochana, C. Dual solution for unsteady mixed convection flow of MHD Micropalar fluid over a stretching/shrinking sheet with non-uniform heat source/sink, Engineering Science and Technology, an International Journal, 18(2015), pp. 1-8.
  29. Chaudhary, M. A., Merkin, J. H., A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow: I. Equal Diffusivities, Fluid Dynamics Res. 16 (1995), pp. 311-333.
  30. Ahmad, K., Nazar, R., Magnetohydrodynamic three-dimensional flow and heat transfer over a stretching surface in a viscoelastic fluid, J. Science and Technology 3 (2011), pp. 33-46.
  31. Ramesh, G. K., B. J. Gireesh, and C. S. Bagewadi. "Heat Transfer in MHD Dusty Boundary Layer flow of over an inclined stretching surface with non-uniform heat source/sink, Advances in Mathematical Physics, volume-Article ID 657805 (2012) 13.
  32. Awais, M., Saleem, S., Hayat, T., & Irum, S. (2016). Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis. Acta Astronautica, 129, 271-276.
  33. Ramesh G.K., Numerical study of the influence of heat source on stagnation point flow towards a stretching surface of a Jeffrey fluid nanoliquid, Journal of Engineering, Volume 2015, Article ID: 382061.
  34. Nadeem, S., and S. Saleem. Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles. International Journal of Heat and Mass Transfer 85 (2015) 1041-1048.
  35. Ramesh, G. K., Ali J. Chamkha, and B. J. Gireesha. MHD mixed convection flow of a viscoelastic fluid over an inclined surface with a nonuniform heat source/sink. Canadian Journal of Physics 91.12 (2013) 1074-1080.
  36. Saleem, Salman, Sohail Nadeem, and Muhammad Awais. Time-Dependent Second-Order Viscoelastic Fluid Flow on Rotating Cone with Heat Generation and Chemical Reaction. Journal of Aerospace Engineering 29.4 (2016) 04016009.
  37. Awais, M., Hayat, T., Irum, S., & Saleem, S. (2015). Dual Solutions for Nonlinear Flow Using Lie Group Analysis. PloS one, 10(11), e0142732.
  38. Nadeem, S., Z. Ahmed, and S. Saleem. The Effect of Variable Viscosities on Micro polar Flow of Two Nanofluids. Zeitschrift für Naturforschung A 71.12 (2016) 1121-1129.
  39. Raju, C. S. K., and N. Sandeep, Unsteady three-dimensional flow of Casson-Carreau fluids past a stretching surface. Alexandria Engineering Journal 55(2) (2016) 1115-1126.
  40. Nadeem, S, S. T. Hussain, C. Lee, Flow of Williamson fluid over a stretching sheet, Brazilian Journal Chemical Engineering, 30 (2013) 619-625.

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