## Boundary layer flow and heat transfer with variable fluid properties on a moving flat plate in a parallel free stream.(English)Zbl 1251.76033

Summary: The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite-difference scheme known as Keller-box method. Numerical results for the flow and the thermal fields for both cases are obtained for various values of the free stream parameter and the Prandtl number. It is found that dual solutions exist for both cases when the fluid and the plate move in the opposite directions. Moreover, fluid with constant properties shows drag reduction characteristics compared to fluid with variable viscosity.

### MSC:

 76M20 Finite difference methods applied to problems in fluid mechanics 76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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### References:

 [1] B. C. Sakiadis, “Boundary layer behavior on continuous solid surface: the boundary layer on a continuous flat surface,” AIChE Journal, vol. 7, pp. 221-225, 1961. [2] J. B. Klemp and A. Acrivos, “A method for integrating the boundary-layer equations through a region of reverse flow,” The Journal of Fluid Mechanics, vol. 53, pp. 177-191, 1972. · Zbl 0242.76019 [3] T. A. Abdelhafez, “Skin friction and heat transfer on a continuous flat surface moving in a parallel free stream,” International Journal of Heat and Mass Transfer, vol. 28, no. 6, pp. 1234-1237, 1985. · Zbl 0839.76088 [4] M. Y. Hussaini, W. D. Lakin, and A. Nachman, “On similarity solutions of a boundary layer problem with an upstream moving wall,” SIAM Journal on Applied Mathematics, vol. 47, no. 4, pp. 699-709, 1987. · Zbl 0634.76034 [5] N. Afzal, A. Badaruddin, and A. A. Elgarvi, “Momentum and heat transport on a continuous flat surface moving in a parallel stream,” International Journal of Heat and Mass Transfer, vol. 36, no. 13, pp. 3399-3403, 1993. · Zbl 0810.76016 [6] M. V. A. Bianchi and R. Viskanta, “Momentum and heat transfer on a continuous flat surface moving in a parallel counterflow free stream,” Wärme-Und Stoffübertragung, vol. 29, no. 2, pp. 89-94, 1993. [7] H.-T. Lin and S.-F. Huang, “Flow and heat transfer of plane surfaces moving in parallel and reversely to the free stream,” International Journal of Heat and Mass Transfer, vol. 37, no. 2, pp. 333-336, 1994. · Zbl 0803.76077 [8] C. H. Chen, “Heat transfer characteristics of a non-isothermal surface moving parallel to a free stream,” Acta Mechanica, vol. 142, no. 1, pp. 195-205, 2000. · Zbl 0970.76026 [9] E. Magyari and B. Keller, “Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls,” European Journal of Mechanics. B. Fluids, vol. 19, no. 1, pp. 109-122, 2000. · Zbl 0976.76021 [10] N. Afzal, “Momentum transfer on power law stretching plate with free stream pressure gradient,” International Journal of Engineering Science, vol. 41, no. 11, pp. 1197-1207, 2003. [11] T. Fang, “Similarity solutions for a moving-flat plate thermal boundary layer,” Acta Mechanica, vol. 163, no. 3-4, pp. 161-172, 2003. · Zbl 1064.76031 [12] T. Fang, “Further study on a moving-wall boundary-layer problem with mass transfer,” Acta Mechanica, vol. 163, no. 3-4, pp. 183-188, 2003. · Zbl 1064.76032 [13] E. M. Sparrow and J. P. Abraham, “Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid,” International Journal of Heat and Mass Transfer, vol. 48, no. 15, pp. 3047-3056, 2005. · Zbl 1189.76143 [14] P. D. Weidman, D. G. Kubitschek, and A. M. J. Davis, “The effect of transpiration on self-similar boundary layer flow over moving surfaces,” International Journal of Engineering Science, vol. 44, no. 11-12, pp. 730-737, 2006. · Zbl 1213.76064 [15] N. Riley and P. D. Weidman, “Multiple solutions of the Falkner-Skan equation for flow past a stretching boundary,” SIAM Journal on Applied Mathematics, vol. 49, no. 5, pp. 1350-1358, 1989. · Zbl 0682.76026 [16] T. Fang, W. Liang, and Chia-f.F. Lee, “A new solution branch for the Blasius equation-a shrinking sheet problem,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3088-3095, 2008. · Zbl 1165.76324 [17] A. Ishak, R. Nazar, and I. Pop, “Flow and heat transfer characteristics on a moving flat plate in a parallel stream with constant surface heat flux,” Heat and Mass Transfer/Waerme- und Stoffuebertragung, vol. 45, no. 5, pp. 563-567, 2009. [18] I. Pop, R. S. R. Gorla, and M. Rashidi, “The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate,” International Journal of Engineering Science, vol. 30, no. 1, pp. 1-6, 1992. [19] E. M. A. Elbashbeshy and M. A. A. Bazid, “The effect of temperature-dependent viscosity on heat transfer over a continuous moving surface,” Journal of Physics D, vol. 33, no. 21, pp. 2716-2721, 2000. · Zbl 0952.76550 [20] A. Pantokratoras, “Further results on the variable viscosity on flow and heat transfer to a continuous moving flat plate,” International Journal of Engineering Science, vol. 42, no. 17-18, pp. 1891-1896, 2004. · Zbl 1211.76043 [21] T. Fang, “Influences of fluid property variation on the boundary layers of a stretching surface,” Acta Mechanica, vol. 171, no. 1-2, pp. 105-118, 2004. · Zbl 1067.76029 [22] H. I. Andersson and J. B. Aarseth, “Sakiadis flow with variable fluid properties revisited,” International Journal of Engineering Science, vol. 45, no. 2-8, pp. 554-561, 2007. · Zbl 1213.76062 [23] A. Ishak, R. Nazar, N. Bachok, and I. Pop, “MHD mixed convection flow near the stagnation-point on a vertical permeable surface,” Physica A, vol. 389, no. 1, pp. 40-46, 2010. · Zbl 1197.80011 [24] N. Bachok, A. Ishak, and I. Pop, “Mixed convection boundary layer flow near the stagnation point on a vertical surface embedded in a porous medium with anisotropy effect,” Transport in Porous Media, vol. 82, no. 2, pp. 363-373, 2010. [25] N. Bachok, A. Ishak, and I. Pop, “Boundary-layer flow of nanofluids over a moving surface in a flowing fluid,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1663-1668, 2010. [26] H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Zeitschrift für Angewandte Mathematik und Physik, vol. 56, pp. 1-37, 1908. · JFM 39.0803.02 [27] T. Fang, F. Guo, and Chia-f.F. Lee, “A note on the extended Blasius equation,” Applied Mathematics Letters, vol. 19, no. 7, pp. 613-617, 2006. · Zbl 1126.34301 [28] F. C. Lai and F. A. Kulacki, “The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium,” International Journal of Heat and Mass Transfer, vol. 33, no. 5, pp. 1028-1031, 1990. [29] T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer Study Editions, Springer, New York, NY, USA, 1988. · Zbl 0702.76003 [30] J. X. Ling and A. Dybbs, “The effect of variable viscosity on forced convection over a flat plate submersed in a porous medium,” Journal of Heat Transfer, vol. 114, no. 4, pp. 1063-1065, 1992.
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