# SIMILARITY METHOD FOR BOUNDARY LAYER FLOW OF A NON-NEWTONIAN VISCOUS FLUID AT A CONVECTIVELY HEATED SURFACE

## Main Article Content

## Abstract

The similarity method is presented for the determination of the velocity and the temperature distribution in the boundary layer next to a horizontal moving surface heated convectively from below. The basic partial differential equations are transformed to a system of ordinary differential equations subjected to boundary conditions.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2191>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI150722208B.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

[2] Altan, T.Oh S., Gegel, H., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, 1979

[3] Aziz, A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Comm. Nonlinear Sci. Numer. Simulat., 14 (2009), 4, pp. 1064-1068

[4] Bognár, G., Analytic solutions to the boundary layer problem over a stretching wall, Computers and Mathematics with Applications, 61 (2011), 8, pp. 2256-2261

[5] Bognár, G., On similarity solutions to boundary layer problems with upstream moving wall in non- Newtonian power-law fluids, IMA J. Applied Mathematics, 77 (2012), 4, pp. 546-562

[6] Bognár, G., Hriczó, K., Similarity Solution to a thermal boundary layer model of a non-Newtonian fluid with a convective surface boundary condition, Acta Polytechnica Hungarica, 8 (2011), 6, pp. 131-140

[7] Chen, M., Blowup criterion for viscous, compressible micropolar fluids with vacuum, Nonlinear Anal. RWA, 13 (2012), 2, pp. 850-859

[8] Erickson, L.E., et al., Heat and mass transfer on a moving continuous flat plate with suction or injection, Ind. Eng. Chem. Fundam., 5 (1966), 1, pp. 19-25

[9] Fan, J.R., et al., Similarity solution of mixed convection over a horizontal moving plate, Heat and Mass Transfer, 32 (1997), 3, pp. 199-206

[10] Gupta, P.S., Gupta, A.S., Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng., 55 (1977), 6, pp. 744-746

[11] Grubka, L.J., Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, J. Heat Transfer – Trans. ASME, 107 (1985), 1, pp. 248-250

[12] Hori, Y., Hydrodynamic Lubrication, Springer-Verlag, Tokyo, 2006

[13] Ishak, A., Similarity solution for flow and heat transfer over a permeable surface with convective boundary condition, Appl. Math. Comput., 217 (2010), 2, pp. 837-842

[14] Kolár, V., Similarity solution of axisymmetric non-Newtonian wall jets with swirl, Nonlinear Anal. RWA, 12 (2011), 6, pp. 3413–3420

[15] Magyari, E., The moving plate thermometer, Int. J. Therm. Sci., 47 (2008), 11, pp. 1436-1441

[16] Mang, T., Dresel, W., Lubricants and Lubrications, Wiley-VCH, Weinheim, 2001

[17] Qin, Y., et al., The Cauchy problem for a 1D compressible viscous micropolar fluid model: Analysis of the stabilization and the regularity, Nonlinear Anal. RWA, 13 (2012), 3, pp. 1010- 1029

[18] Sakiadis, B.C., Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow, AIChE J., 7 (1961), 1, pp. 26-28

[19] Sakiadis, B.C., Boundary-layer behavior on continuous solid surfaces. II: The boundary layer on a continuous at surface, AIChE J., 7 (1961), 2, pp. 221-225

[20] Tadmor, Z., Klein, I., Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series, Van Norstrand Reinhold, New York, 1970

[21] Tsou, F.K., et al., Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat Mass Transfer, 10 (1967), 2, pp. 219-235

[22] Uddin, M.J., et al., New similarity solution of boundary layer flow along a continuously moving convectively heated horizontal plate by deductive group method, Thermal Sciences, 2014 doi:10.2298/TSCI130115014U

[23] Vajravelu, K., Flow and heat transfer in a saturated porous medium over a stretching surface, Z. Angew. Math. Mech., 74 (1994), 12, pp. 605-614