# OBLIQUE STAGNATION POINT FLOW OF A NON-NEWTONIAN NANOFLUID OVER STRETCHING SURFACE WITH RADIATION: A NUMERICAL STUDY

## Main Article Content

## Abstract

In this study, we discussed the enhancement of thermal conductivity of elastico-viscous fluid filled with nanoparticles, due to the implementation of radiation and convective boundary condition. The flow is considered impinging obliquely in the region of oblique stagnation point on the stretching surface. The obtained governing partial differential equations are transformed into a system of ordinary differential equations by employing a suitable similarity transformation. The solution of the resulting equations is computed numerically using Chebyshev Spectral Newton Iterative Scheme (CSNIS). An excellent agreement with the results available in literature is obtained and shown through tables. The effects of involving parameters on the fluid flow and heat transfer are observed and shown through graphs. It is importantly noted that the larger values of Biot number imply the enhancement in heat transfer, thermal boundary layer thickness and concentration boundary layer thickness.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2131>. Date accessed: 23 june 2017. doi: https://doi.org/10.2298/TSCI150411163G.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Tamada, K.J., Two-dimensional stagnation-point ﬂow impinging obliquely on an oscillating ﬂat plate, J. Physical Soc. Jpn., 47 (1979), pp. 310–311.

[3] Dorrepaal, J.M., An exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point ﬂow in two dimension, J. Fluid Mech. 163 (1986), pp. 141–147.

[4] Reza, M., Gupta, A.S., Steady two-dimensional oblique stagnation point ﬂow towards a stretching surface, Fluid Dynamic Research, 37 (2005), pp. 334–340.

[5] Chiam, T.C., Stagnation point flow towards a stretching plate, J. Phys. Soc. Jpn., 63 (1994), pp. 2443–2444.

[6] Lok, Y.Y., et al., Non-orthogonal stagnation point flow towards a stretching sheet, Int. J. Nonlin. Mech., 41 (2006), pp. 622-627.

[7] Reza, M., Gupta, A.S., Some aspects of non-orthogonal stagnation-point ﬂow towards a stretching surface, Eng. 2 (2010), pp. 705–709.

[8] Drazin, P.G., Riley, N., The Navier-Stokes equations, a classiﬁcation of flows and exact solutions, London Mathematical Society, Lecture notes series, Cambridge University Press, 2007.

[9] Tooke, R.M., Blyth, M.G., A note on oblique stagnation-point ﬂow, Phys. Fluids, 20 (2008), pp. 1–3.

[10] Weidman, P.D., Putkaradze, V., Axisymmetric stagnation ﬂow obliquely impinging on a circular cylinder, Eur. J. Mech. B. Fluids, 22 (2003), pp. 123–131.

[11] Weidman, P.D., Putkaradze, V., Erratum to “axisymmetric stagnation ﬂow obliquely impinging on a circular cylinder”, Eur. J. Mech. B, Fluids, 24 (2004), pp. 788–790.

[12] Erfani, E., et al., The Modified Differential Transform Method For Solving Off-Centered Stagnation Flow Toward A Rotating Disc, Int J Comput Methods, 7 (2010), 4, pp. 655-670.

[13] Husain, I., et al., Two-dimensional oblique stagnation point flow towards a stretching surface in a viscoelastic fluid, Central Eur. J. Phys. 9 (2011), pp. 176-182.

[14] Mahapatra, T.R., et al., Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation, Meccanica, 47 (2012), pp. 1325-1335.

[15] Lok, Y.Y., et al., Oblique stagnation slip ﬂow of a micropolar ﬂuid, Mechanica, 45 (2010), pp. 187–198.

[16] Yajun, L.V., Liancun, Z., MHD Oblique Stagnation-point Flow and Heat Transfer of a Micro polar Fluid towards to a Moving Plate with Radiation, Int. J. Eng. Sci. Innovative Tech, 2 (2013), pp. 200-209.

[17] Javed, T., et al., Numerical Study of Unsteady Oblique Stagnation Point Flow Over a Oscillating Flat Plate, Can J Phys, 10.1139/cjp-2014-0270.

[18] Buongiorno, J., Hu, L.W., Nanofluid Coolants for Advanced Nuclear Power Plants, Proceedings of ICAPP, Seoul, 2005, Paper No. 5705, pp. 15–19.

[19] Maxwell, J.C., A Treatise on Electricity and Magnetism, 2nd Edition, Oxford Univ. Press, Cambridge, 1904.

[20] Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, in: Developments and Application of Non-Newtonian Flows, ASME ,FED-Vol. 231/MD-vol. 66 (1995), pp. 99–105.

[21] Buongiorno, J., Convective transport in nanofluids, ASME J. Heat Transfer, 128 (2006), pp. 240–250.

[22] Kuznetsov, A.V., Nield, D.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int J Thermal Sci, 49 (2010), pp. 243–247.

[23] Kuznetsov, A.V., Nield, D.A., Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, Int J Thermal Sci, 50 (2011), pp. 712–717.

[24] Makinde, O. D., Aziz, A., Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int J Thermal Sci, 50 (2011), pp. 1326–1332.

[25] Hassani, M., et al., An analytical solution for boundary layer flow of a nanofluid past a stretching sheet, Int J Therm Sci, 50 (2011), pp. 2256–2263.

[26] Rana, P., Bhargava, R., Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study, Commun Nonlinear Sci Numer Simulat, 17 (2012), 1, pp. 212–226.

[27] Hamad, M.A.A., Ferdows, M., Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: a Lie group analysis, Commun Nonlinear Sci Numer Simulat, 17 (2012), 1, pp. 132–40.

[28] Sheikholeslami, M., et al., Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field, J. Taiwan Institute Chem. Eng., 46 (2015), pp. 43-50.

[29] Turkyilmazoglu, M., Nanofluid flow and heat transfer due to a rotating disk, Computer and fluids, 94 (2014), pp. 139-146.

[30] Rahman, M.M., et al., Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno’s model, Int. J. Heat Mass Transfer, 77 (2014), pp. 1133-1143.

[31] Rashidi, M.M., et al., Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation, J. Molecular Liquids, 198 (2014), pp. 234-238.

[32] Kameswaran, P.K., et al., Homogeneous–heterogeneous reactions in a nanofluid flow due to a porous stretching sheet, Int. J. Heat Mass Transfer, 57 (2013), pp. 465-472.

[33] Abbasi, F.M., et al., Peristaltic transport of magneto-nanoparticles submerged in water: Model for drug delivery system, Phasica E, 68 (2015), pp. 123-132.

[34] Bachok, N., et al., Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, Int J Thermal Sci, 49 (2010), pp. 1663–1668.

[35] Sebdani, S.M., et al., Effect of nanofluid variable properties on mixed convection in a square cavity, Int J Thermal Sci., 52 (2012), pp. 112–126.

[36] Rashidi, M.M., et al., Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media, Math Probl Eng., (2014), Article ID 239082.

[37] Abolbashari, M.H., et al., Entropy Analysis for an Unsteady MHD Flow Past a Stretching Permeable Surface in Nanofluid, Powder Technol., 267 (2014), pp. 256–267.

[38] Makinde, O.D. Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating, Appl Math Mech., (Engl Ed) 33, (2012), 12, pp. 1545–1554.

[39] Hayat, T., et al., Heat transfer analysis in the flow of Walters' B fluid with a convective boundary condition, Chin. Phys. B, 23 (2014), 084701 (8).

[40] Husain, I., et al., Two-dimensional oblique stagnation-point flow towards a stretching surface in a viscoelastic fluid, Cent. Eur. J. Phys., 9 (2011), 1, pp. 176-182.

[41] Beard, D.W., Walters, K., Elastico-viscous boundary-layer flows. I. Two-dimensional flow near a stagnation point, Proc. Cambridge Philos. Soc. 60, (1964), pp. 667–674.

[42] Trefethen, L.N., Spectral Methods in MATLAB, Society for Industrial and Applied Mathematics, SIAM, Philadelphia, Pa, USA, 2000.

[43] Motsa, S. S., et al., Spectral Relaxation Method and Spectral Quasi-linearization Method for Solving Unsteady Boundary Layer Flow Problems, Advances in Mathematical Physics, (2014), Article ID 341964.

[44] Motsa, S. S., A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems, Journal of Applied Mathematics, (2013), Article ID 423628.

[45] Garg, V.K. and Rajagopal, K.R., Flow of a non-Newtonian fluid past a wedge, Acta Mech., 88, (1991), pp. 113.

[46] Vajravelu K. and Roper T., Flow and heat transfer in a second grade fluid over a stretching sheet, Int. J. Non-linear Mech., 34, (1999), pp.1031-1036.

[47] Labropulu, F., et al., Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer, Int. J. Therm. Sci., 49 (2010), pp. 1042-1050.

[48] Weidman, P.D., et al., A.M.J., The effect of transpiration on self-similar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44 (2006), pp. 730–737.

[49] Paullet, J., Weidman, P., Analysis of stagnation point flow toward a stretching sheet, Int. J. Nonlinear Mech., 42 (2007). pp. 1084–1091.

[50] Rosca, A.V., Pop, I., Flow and heat transfer over a vertical permeable stretching/ shrinking sheet with a second order slip, Int. J. Heat Mass Transfer, 60 (2013), pp. 355–364.