## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2016-09-19

PAPER REVISED: 2017-04-22

PAPER ACCEPTED: 2017-04-28

PUBLISHED ONLINE: 2017-05-06

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 1**, PAGES [307 - 318]

- Bird, R.B., Curtiss, C.F., Armstrong, R.C.,Hassager, O., Dynamics of Polymeric Liquids, Wiley, New York, 1987
- Bird, R.B., Useful non-Newtonian models, Annual Review of Fluid Mechanics, 8 (1976), pp. 13-34
- 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
- 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
- Sisko, A.W., The flow of lubricating greases, Industrial and Engineering Chemistry, 50 (1958), pp. 1789-1792
- Cross, M.M., Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems, Journal of Colloid Science, 20 (1965), pp. 417-437
- Barnes, H.A., Hutton, J.F.,Walters, K., An Introduction to Rheology, Elsevier Science, Amsterdam, 1989
- Rao, M.A., Rheology of Fluid, Semisolid, and Solid Foods, Springer, New York, 2014
- Steffe, J.F., Rheological Methods in Food Process Engineering, Freeman, USA, 1992
- Gan, Y.X., Continuum Mechanics-Progress in Fundamentals and Engineering Applications, InTech, China, 2012
- Bingham, E.C., Fluidity and Plasticity, McGraw-Hill, New York, 1922
- 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
- 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
- Sakiadis, B.C., Boundary layer behavior on continuous solid surfaces, American Institute of Chemical Engineers Journal, 7 (1961), pp. 26-28
- Crane, L.J., Flow past a stretching sheet, Zeit Angew Math. Phys., 21 (1970), pp. 645-647
- 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
- 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
- Khan, M., Rahman, M., Flow and heat transfer to modified second grade fluid over a non-linear stretching sheet, AIP Advances, 5 (2015), 087157
- Myers, T.G., Application of non-Newtonian models to thin film flow, Physical Review, 72 (2005), 066302
- 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
- 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
- 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
- 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
- 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
- Osswald. T.A., Rudolph, N., Polymer Rheology: Fundamentals and Applications, Hanser, 2014
- Cortell, R., Viscous flow and heat transfer over a nonlinearly stretching sheet, Applied Mathematics and Computation, 184 (2007), pp. 864-873
- 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
- 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
- Wang, C.Y., Free convection on a vertical stretching surface, Journal of Applied Mathematics and Mechanics (ZAMM), 69 (1989), pp. 418-420
- 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
- 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