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Strouhal number effects on dynamic boundary layer evolution over a wedge surface from initial flow to steady flow: analytical approach

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present work studies the effects of the physical parameter characterizing the laminar flow regime, namely the Strouhal number, on the evolution of the unsteady dynamic boundary-layer developed along a wedge surface. Similarity method is used to transform unsteady momentum equation to dimensionless form. Using superposition method between diffusion and convective flows solutions, an ad hoc velocity profile formula is proposed. The obtained results confirm perfectly the numerical data given by Blasius, Falkner-Skan and Williams-Rhyne for all Strouhal numbers. A new accurate analytical function of the local skin friction is established for all time values and for different wedge surface directions. In order to give further clarification on the flows evolutions from diffusion flow to convective flow, in the whole space domain, new skin friction coefficient curves are plotted for all Strouhal numbers and for different wedge surface directions.
Rocznik
Strony
26--39
Opis fizyczny
Bibliogr. 21 poz., tab., wykr.
Twórcy
  • Matter Sciences Department, Faculty of Sciences -University of Amar Telidji B.P 37 G, Laghouat 03000, ALGERIA
  • Thermodynamics and Energetical Systems Laboratory, Faculty of Physics/USTHB B.P 32 El Alia, 16111 Bab Ezzouar-Algiers, ALGERIA
Bibliografia
  • [1] Stewartson K. (1951): On the impulsive motion of a flat plate in a viscous fluid (Part I).– Quart. J. Mec. App. Math., vol.4, pp.182-198. https://doi.org/10.1093/qjmam/4.2.182.
  • [2] Stewartson K. (1973): On the impulsive motion of a flat plate in a viscous fluid (Part II).– Quart. J. Mec. App. Math., vol. 22, pp.143-152, https:// doi :10.1093/QJMAM/26.2.143.
  • [3] Tokuda N. (1968): On the impulsive motion of a flat plate in a viscous fluid.– J. Fluid Mec., vol.33, pp.657-675, doi: 10.1017/S0022112068001606.
  • [4] Watkins C.B.(1975): Heat transfer in the boundary layer over an impulsively started flat plate.– ASME, J. Heat Trans., vol.97, No.3, pp.482-484, 1975ATJHT.97.482W.
  • [5] Hall M.G. (1969): The boundary layer over an impulsively started flat plate.– Proc. Royal Soc. Lon. A, vol.310, pp.401-414, https://www.jstor.org/stable/2416386.
  • [6] Dennis S.C.R. (1972): The motion of a viscous fluid past an impulsively started semi-infinite flat plate.– J. App. Math, vol.10, No.1, pp.105-107, https://doi.org/10.1093/imamat/10.1.105.
  • [7] Seshadri R., Sreeshylan N. and Nath G. (2002): Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion.– Int. J. Heat and Mass Trans., vol.45, No.6, pp.1345-1352, https://doi.org/10.1016/S0017-9310(01)00228-9.
  • [8] Williams J.C. and Rhyne T.H.(1980): Boundary layer development on a wedge impulsively set into motion.– SIAM, J. App. Math., vol.38, No.2, pp.215-124, https://doi.org/10.1137/0138019.
  • [9] Nazar N., Amin N. and Pop, I.(2004): Unsteady boundary layer flow due to stretching surface in a rotating fluid.–Mec. Res. Commu., vol.31, No.1, pp.121-128, https://doi.org/10.1016/j.mechrescom.2003.09.004.
  • [10] Sajid M., Ahmad I., Hayat T. and Ayub M. (2009): Unsteady flow and heat transfer of a second grade fluid over a stretching sheet.– Commun. Nonl. Sci. Num. Simul., vol.14, No.1, pp.96-108, https://doi.org/10.1016/j.cnsns.2007.07.014.
  • [11] Liao S.J. (2004): On the homotopy analysis method for nonlinear problems.– Appl. Math. Comput., vol.147, No.2, pp.499-513, https://doi.org/10.1016/S0096-3003(02)00790-7.
  • [12] Liao S. J. (2006): An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate.– Commun. Nonlin. Sci. Num. Simul., vol.11, No.3, pp.326-339, https://doi.org/10.1016/j.cnsns.2004.09.004.
  • [13] Hang X. Liao, S.J. and Ioan P. (2007): Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate.– Europ. J. Mec. B / Fluids, vol.26, No.1, pp.15-27. https://doi.org/10.1016/j.euromechflu.2005.12.003.
  • [14] Hang X., Liao, S. J. and Ioan P. (2008): Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body.– Int. J. Therm. Sci., vol.47, No.5, pp. 600-608, https://doi.org/10.1016/j.ijthermalsci.2007.05.001.
  • [15] Howarth L. (1938): On the solution of the laminar boundary layer equations.– Proc. Royal Soc. Lon. A, vol.164, pp.547-579, https://doi.org/10.1098/rspa.1938.0037.
  • [16] Bachiri M. and Bouabdallah A. (2011): Analytical approach of unsteady boundary-layer flow over a semi-infinite plate for all Strouhal numbers.– ASME, J. Appl. Mec., vol.78, No.2., pp.1-5, https://doi.org/10.1115/1.4002571.
  • [17] Bachiri M. and Bouabdallah A. (2012): Analytical study of the convection heat transfer from an isothermal wedge surface to fluids.– ASME, J. Heat Trans., vol.134, No.6., pp.1-5, https://doi.org/10.1115/1.4006030.
  • [18] Zheng Z.C. and Ghate A.S. (2015): A solution of two-parameter asymptotic expansions for a two-dimensional unsteady boundary layer.– Appl. Math. Comput., vol.270, No.1, pp.90-104, https://doi.org/10.1016/j.amc.2015.08.016.
  • [19] Hafidzuddin M.E.H., Roslinda N., Norihan M.A. and Ioan P. (2018): Unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.– Int. J. Num. Metho. for Heat and Fluid Flow., vol.28, No.6, pp.1457-1470, https://doi.org/10.1108/HFF-11-2016-0440.
  • [20] Nagler J. (2019): Higher order solution of Boundary layer formation as a result of impulsive start of motion.– ZAMM, J. Appl. Math. Mech., vol.99, No.3., pp.1-7, https://doi.org/10.1002/zamm.201800124.
  • [21] Bulgakov V.N., Kotenev V.P. and Ozhgibisova l. (2020): Analytical study of laminar boundary layer near blunted Bodies.– Math. Mod. Comp. Simul., vol.12, pp.60-69, https://doi.org/10.1134/S0234087919060054.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-51a0352c-90db-46e2-b32b-5757e0a44ed5
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