Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. (English) Zbl 1153.76025
Summary: This study aims to analyze the effects of thermal radiation on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow), both under a convective surface boundary condition. The resulting similarity energy equation is solved numerically, and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number \(Pr\), radiation parameter \(N_{\text R}\) and parameter \(a\), which characterizes our convection processes, are graphed and tabulated. Quite different behaviours were encountered for a Blasius flow compared with a Sakiadis flow. A comparison with previously published results in a special case shows good agreement.
MSC:
| 76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |
| 76M55 | Dimensional analysis and similarity applied to problems in fluid mechanics |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
| [1] | Weyl, H., On the differential equations of the simplest boundary-layer problems, Ann. Math., 43, 381-407 (1942) · Zbl 0061.18002 |
| [2] | Blasius, H., Grenzschichten in Flussigkeiten mit kleiner reibung, Z. Math. Phys., 56, 1-37 (1908) · JFM 39.0803.02 |
| [3] | Sakiadis, B. C., Boundary-layer behaviour on continuous solid surfaces. Boundary-layer equations for 2-dimensional and axisymmetric flow, AIChE J., 7, 26-28 (1961) |
| [4] | Sakiadis, B. C., Boundary-layer behaviour on continuous solid surfaces. The boundary-layer on a continuous flat plate, AIChE J., 7, 221-225 (1961) |
| [5] | Magyari, E., The moving plate thermometer, Int. J. Therm. Sci., 47, 1436-1441 (2008) |
| [6] | Howarth, L., On the solution of the laminar boundary layer equations, Proc. Roy. Soc. London A, 164, 547-579 (1938) · JFM 64.1452.01 |
| [7] | Abussita, A. M.M., A note on a certain boundary-layer equation, Appl. Math. Comput., 64, 73-77 (1994) · Zbl 0811.34013 |
| [8] | Asaithambi, A., A finite-difference method for the Falkner-Skan equation, Appl. Math. Comput., 92, 135-141 (1998) · Zbl 0973.76581 |
| [9] | Wang, L., A new algorithm for solving classical Blasius equation, Appl. Math. Comput., 157, 1-9 (2004) · Zbl 1108.65085 |
| [10] | Kuo, B. L., Thermal boundary-layer problems in a semi-infinite flat plate by the differential transformation method, Appl. Math. Comput., 150, 303-320 (2004) · Zbl 1059.76061 |
| [11] | Liao, S. J., An explicit, totally analytic approximate solution for Blasius viscous flow problems, Int. J. Non-Linear Mech., 34, 759-778 (1999) · Zbl 1342.74180 |
| [12] | Cortell, R., Numerical solutions of the classical Blasius flat-plate problem, Appl. Math. Comput., 170, 706-710 (2005) · Zbl 1077.76023 |
| [13] | He, J. H., A simple perturbation approach to Blasius equation, Appl. Math. Comput., 140, 217-222 (2003) · Zbl 1028.65085 |
| [14] | Ahmad, F.; Al-Barakati, W. H., An approximate analytic solution of the Blasius problem, Comm. Nonlinear Sci. Num. Simul. (2008) |
| [15] | He, J. H., Approximate analytical solution of Blasius equation, Comm. Nonlinear Sci. Num. Simul., 3, 260-263 (1998) · Zbl 0918.34016 |
| [16] | Amir, A.-P.; Setareh, B.-B., On the analytical solution of viscous fluid flow past a flat plate, Phys. Lett. A, 372, 3678-3682 (2008) · Zbl 1220.76027 |
| [17] | Fang, T., Further study on a moving-wall boundary layer problem with mass transfer, Acta Mech., 163, 183-188 (2003) · Zbl 1064.76032 |
| [18] | Fang, T., Similarity solutions for a moving-flat plate thermal boundary layer, Acta Mech., 163, 161-172 (2003) · Zbl 1064.76031 |
| [19] | Fang, T., Influence of fluid property variation on the boundary layers of a stretching sheet, Acta Mech., 171, 105-118 (2004) · Zbl 1067.76029 |
| [20] | Fang, T., Boundary layer flow over a shrinking sheet with power-law velocity, Int. J. Heat Mass Transfer (2008) · Zbl 1157.76010 |
| [21] | Fang, T.; Liang, W.; Lee, Ch-F. F., A new solution branch for the Blasius equation: a shrinking sheet problem, Comput. Math. Appl. (2008) · Zbl 1165.76324 |
| [22] | Fang, T.; Lee, Ch.-F. F., A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate, Appl. Math. Lett., 18, 487-495 (2005) · Zbl 1074.76042 |
| [23] | Cortell, R., Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing, Fluid Dyn. Res., 37, 231-245 (2005) · Zbl 1153.76423 |
| [24] | Cortell, R., Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. Math. Comput., 184, 864-873 (2007) · Zbl 1112.76022 |
| [25] | Cortell, R., Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface, J. Mat. Process. Technol., 203, 176-183 (2008) |
| [26] | Pantokratoras, A., The Blasius and Sakiadis flow with variable fluid properties, Heat Mass Transfer, 44, 1187-1198 (2008) |
| [27] | Pantokratoras, A., Asymptotic profiles for the Blasius and Sakiadis flows in a Darcy-Brinckman isotropic porous medium either with uniform suction or with zero transverse velocity, Transp. Porous Med. (2008) |
| [28] | Hossain, M. A.; Takhar, H. S., Radiation effects on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Transfer, 31, 243-248 (1996) |
| [29] | Hossain, M. A.; Alim, M. A.; Rees, D., The effect of radiation on free convection from a porous vertical plate, Int. J. Heat Mass Transfer, 42, 181-191 (1999) · Zbl 0953.76083 |
| [30] | Hossain, M. A.; Khanafer, K.; Vafai, K., The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate, Int. J. Therm. Sci., 40, 115-124 (2001) |
| [31] | Raptis, A.; Perdikis, C.; Takhar, H. S., Effect of thermal radiation on MHD flow, Appl. Math. Comput., 153, 645-649 (2004) · Zbl 1050.76061 |
| [32] | Cortell, R., Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Phys. Lett. A, 372, 631-636 (2008) · Zbl 1217.76028 |
| [33] | Cortell, R., Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet, Comput. Math. Appl., 53, 305-316 (2007) · Zbl 1138.80003 |
| [34] | Cortell, R., Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation, Phys. Lett. A, 372, 2431-2439 (2008) · Zbl 1220.76028 |
| [35] | Cortell, R., Radiation effects in the Blasius flow, Appl. Math. Comput., 198, 333-338 (2008) · Zbl 1134.76012 |
| [36] | Cortell, R., A numerical tackling on Sakiadis flow with thermal radiation, Chin. Phys. Lett., 25, 1340-1342 (2008) |
| [37] | Aziz, A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Comm. Non-linear Sci. Num. Simul. (2008) |
| [38] | Cortell, R., Fourth order Runge-Kutta method in 1D for high gradient problems, (Topping, B. H.V., Developments in Computational Engineering Mechanics (1995), Civil-Comp. Press: Civil-Comp. Press New York), 121-124 |
| [39] | Taigbenu, A. E.; Onyejekwe, O. O., Green’s function-based integral approaches to nonlinear transient boundary value problems (II), Appl. Math. Modell., 23, 241-253 (1999) · Zbl 1006.80004 |
| [40] | Fang, T.; Guo, F.; Lee, C. F., A note on the extended Blasius equation, Appl. Math. Lett., 19, 613-617 (2006) · Zbl 1126.34301 |
| [41] | Chang, C. W., The Lie-group shooting method for boundary layer equations in fluid mechanics, J. Hydrodynam., 18, 3, 103-108 (2006) |
| [42] | White, F., Viscous Fluid Flow (2006), McGraw-Hill: McGraw-Hill New York |
| [43] | El-Mistikawy, T. M.A., Limiting behavior of micropolar flow due to a linearly stretching porous sheet, Eur. J. Mech. B/Fluids (2008) · Zbl 1156.76344 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
