## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Similarity method for boundary layer flow of a non-Newtonian viscous fluid at a convectively heated surface

**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.

**KEYWORDS**

PAPER SUBMITTED: 2015-07-22

PAPER REVISED: 2016-08-26

PAPER ACCEPTED: 2016-08-26

PUBLISHED ONLINE: 2016-09-05

- Ali, M.E., Heat transfer characteristics of a continuous stretching surface, Heat and Mass Transfer, 29 (1994), 4, pp. 227-234
- Altan, T.Oh S., Gegel, H., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, 1979
- 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
- Bognár, G., Analytic solutions to the boundary layer problem over a stretching wall, Computers and Mathematics with Applications, 61 (2011), 8, pp. 2256-2261
- 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
- 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
- Chen, M., Blowup criterion for viscous, compressible micropolar fluids with vacuum, Nonlinear Anal. RWA, 13 (2012), 2, pp. 850-859
- 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
- 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
- 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
- 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
- Hori, Y., Hydrodynamic Lubrication, Springer-Verlag, Tokyo, 2006
- 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
- Kolár, V., Similarity solution of axisymmetric non-Newtonian wall jets with swirl, Nonlinear Anal. RWA, 12 (2011), 6, pp. 3413-3420
- Magyari, E., The moving plate thermometer, Int. J. Therm. Sci., 47 (2008), 11, pp. 1436-1441
- Mang, T., Dresel, W., Lubricants and Lubrications, Wiley-VCH, Weinheim, 2001
- 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
- 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
- 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
- Tadmor, Z., Klein, I., Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series, Van Norstrand Reinhold, New York, 1970
- 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
- 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
- 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