THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Masood Khan

,

Mehwish Manzur

,

Masood ur Rahman

BOUNDARY-LAYER FLOW AND HEAT TRANSFER OF CROSS FLUID OVER A STRETCHING SHEET

ABSTRACT
The current study is a pioneering work in presenting the boundary-layer equations for the 2-D flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of PDE is turned down into highly non-linear ODE by applying suitable similarity transformations. The stretching sheet solutions are presented via. a numerical technique namely the shooting method and graphs are constructed. The impact of the emerging parameters namely the power-law index, n, the local Weissenberg number, We, and the Prandtl number on the velocity and temperature fields are investigated through graphs. The numerical values of the local skin friction coefficient and the local Nusselt number are also presented in tabular form. Additionally, the graphs are sketched for the local skin friction coefficient and the local Nusselt number. It is observed that with growing values of the local Weissenberg number the velocity profiles exhibited a decreasing trend while opposite behavior is seen for the temperature field. Further, comparisons are made with previously available literature for some limiting cases and an excellent agreement is achieved.
KEYWORDS
Cross fluid, stretching sheet, heat transfer, numerical solution
PAPER SUBMITTED: 2016-09-19
PAPER REVISED: 2017-04-22
PAPER ACCEPTED: 2017-04-28
PUBLISHED ONLINE: 2017-05-06
DOI REFERENCE: https://doi.org/10.2298/TSCI160919111K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 1, PAGES [307 - 318]
REFERENCES
  1. Bird, R.B., Curtiss, C.F., Armstrong, R.C.,Hassager, O., Dynamics of Polymeric Liquids, Wiley, New York, 1987
  2. Bird, R.B., Useful non-Newtonian models, Annual Review of Fluid Mechanics, 8 (1976), pp. 13-34
  3. Hassanien, I.A., Abdullah, A.A., Gorla, R.S.R., Flow and heat transfer in a power-law fluid over a non-isothermal stretching sheet, Mathematical and Computer Modelling, 28 (1998), pp. 105-116
  4. Matsuhisa, S., Bird, R.B., Analytical and numerical solutions for laminar flow of the non-Newtonian Ellis fluid, American Institute of Chemical Engineers Journal, 11 (1965), pp. 588-595
  5. Sisko, A.W., The flow of lubricating greases, Industrial and Engineering Chemistry, 50 (1958), pp. 1789-1792
  6. Cross, M.M., Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems, Journal of Colloid Science, 20 (1965), pp. 417-437
  7. Barnes, H.A., Hutton, J.F.,Walters, K., An Introduction to Rheology, Elsevier Science, Amsterdam, 1989
  8. Rao, M.A., Rheology of Fluid, Semisolid, and Solid Foods, Springer, New York, 2014
  9. Steffe, J.F., Rheological Methods in Food Process Engineering, Freeman, USA, 1992
  10. Gan, Y.X., Continuum Mechanics-Progress in Fundamentals and Engineering Applications, InTech, China, 2012
  11. Bingham, E.C., Fluidity and Plasticity, McGraw-Hill, New York, 1922
  12. Escudier, M.P., et al., On the reproductivity of the rheology of shear-thinning liquids, Journal of Non-Newtonian Fluid Mechanics, 97 (2001), pp. 99-124
  13. Xie, J., Jin, Y.C., Parameter determination for the Cross rheology equation and its application to modeling non-Newtonian flows using the WC-MPS method, Engineering Applications of Computational Fluid Mechanics, 10 (2015), pp. 111-129
  14. Sakiadis, B.C., Boundary layer behavior on continuous solid surfaces, American Institute of Chemical Engineers Journal, 7 (1961), pp. 26-28
  15. Crane, L.J., Flow past a stretching sheet, Zeit Angew Math. Phys., 21 (1970), pp. 645-647
  16. Andersson, H.I., Bech, K.H., Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, International Journal of Non-Linear Mechanics, 27 (1992), pp. 929-936
  17. Howell, T.G., Jeng, D.R., Witt, K.J.D., Momentum and heat transfer on a continuous moving surface in a power law fluid, Journal of Heat and Mass Transfer, 40 (1997), pp. 1853-1861
  18. Khan, M., Rahman, M., Flow and heat transfer to modified second grade fluid over a non-linear stretching sheet, AIP Advances, 5 (2015), 087157
  19. Myers, T.G., Application of non-Newtonian models to thin film flow, Physical Review, 72 (2005), 066302
  20. Mabood, F., Khan, W.A., Analytical study for unsteady nanofluid MHD flow impinging on heated stretching sheet, Journal of Molecular Liquid, 219 (2016), 216-223
  21. Mabood. F., Ibrahim. S.M., Khan. W.A., Framing the features of Brownian motion and thermophoresis on radiative nanofluid flow past a rotating stretching sheet with magnetohydrodynamics, Results in Physics, 6 (2016), 1015-1023
  22. Mabood. F., Ibrahim. S.M., Rashidi. M.M., Shadloo. M.S., Lorenzini. G., Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation, International Journal of Heat and Mass transfer, 93 (2016), 674-682
  23. Rahman. M.U., Manzur. M., Khan. M., Mixed convection heat transfer to modified second grade fluid in the presence of thermal radiation, Journal of Molecular Liquids, 223 (2016), 217-223
  24. Khan. M., Rahman. M.U., Manzur. M., Axisymmetric flow and heat transfer to modified second grade fluid over a radially stretching sheet, Results in Physics, 7 (2017), 878-889
  25. Osswald. T.A., Rudolph, N., Polymer Rheology: Fundamentals and Applications, Hanser, 2014
  26. Cortell, R., Viscous flow and heat transfer over a nonlinearly stretching sheet, Applied Mathematics and Computation, 184 (2007), pp. 864-873
  27. Cortell, R., Effects of viscous dissipation and radiation on the thermal boundary layer over a non-linearly stretching sheet, Physics Letter, A 372 (2008), pp. 631-636
  28. Hamad, M.A.A., Ferdows, M., Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet, Applied Mathematics and Mechanics English, 33 (2012), pp. 923-930
  29. Wang, C.Y., Free convection on a vertical stretching surface, Journal of Applied Mathematics and Mechanics (ZAMM), 69 (1989), pp. 418-420
  30. Gorla, R.S.R., Sidawi, I., Free convection on a vertical stretching surface with suction and blowing, Applied Science Research, 52 (1994), pp. 247-257
  31. Hamad, M.A.A., Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field, International Communications inHeat and Mass Transfer, 38 (2011), pp. 487-492
PDF VERSION [DOWNLOAD]
Boundary-layer flow and heat transfer of cross fluid over a stretching sheet

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence