New similarity method analysis of the transient thermal boundary layer on a horizontal flat plate: Strouhal and Prandtl numbers effect

Yıl 2024, Cilt: 10 Sayı: 3, 737 - 745, 21.05.2024

Mohamed Bachiri Ahcene Bouabdallah Aidaoui Lakhdar Yahia Lasbet

Öz

The present project highlights the behavior of the unsteady heat transfer phenomenon developing along a horizontal surface in terms of both Strouhal and Prandtl numbers. Based on the changes that occur in the gouverning equation of the studied problem, an adequate analytical law of the velocity is proposed to solve unsteady momentum equation. This result presented a good agreement with Rayleigh’s exact solution and numerical solutions of Blasius and Williams–Rhyne for diferents values of Strouhal numbers adopted in this study. The obtained velocity expression is included in the unsteady energy equation in order to establish the temperature profile for all considered Strouhal and Prandtl numbers. Taking into account the existence of the velocity-temperature coupling in the heat boundary layer equation, the proposed formula is used to solve unsteady energy equation for all Strouhal and Prandtl numbers. As the main results, a new analytic expression of the local heat transfer coefficient for all Strouhal and Prandtl numbers is established and interesting curves are plotted to explain the heat transfer evolutions from diffusion flow to the convective flow.

Anahtar Kelimeler

Horizontal Surface, Nusselt, Similarity Solution, Strouhal Number, Unsteady Heat Transfer

Kaynakça

• [1] Stewartson K. On the impulsive motion of a flat plate in a viscous fluid, Part-I. Quart J Mech Appl Math 1951;4:182–198. [CrossRef]
• [2] Stewartson K. On the impulsive motion of a flat plate in a viscous fluid, Part-II. Quart J Mech Appl Math 1973;26:143–152. [CrossRef]
• [3] Tokuda N. On the impulsive motion of a flat plate in a viscous fluid. J Fluid Mech 1968;33:657–675. [CrossRef]
• [4] Watkins CB. Heat transfer in the boundary layer over an impulsively started flat plate. ASME J Heat Trans 1975;97:282–484. [CrossRef]
• [5] Hall MG. The boundary layer over an impulsively started flat plate. Proc Roy Soc Lond 1969;310:401–414. [CrossRef]
• [6] Dennis SC. The motion of a viscous fluid past an impulsively started semi-infinite flat plate. J Inst Math Appl 1972;10:105–117. [CrossRef]
• [7] Williams JC, Rhyne TH. Boundary layer development on a wedge impulsively set into motion. SIAM J Appl Math 1980;38:215–224. [CrossRef]
• [8] Liao SJ. An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Commun Nonlinear Sci Numer Simul 2006;11:326–339. [CrossRef]
• [9] Hang X, Liao SJ, Pop I. Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Eur J Mech B Fluids 2007;26:15–27. [CrossRef]
• [10] Simon DH, Ingham B, Pop I. Unsteady heat transfer in impulsive Falkner–Skan flows: Constant wall temperature case. Eur J Mech B Fluids 2002;21:447–468. [CrossRef]
• [11] Revnic C, Grosan T, Pop I. Unsteady boundary layer flow and heat transfer over a stretching sheet. AIP Conf Proc 2008;1046:119–125. [CrossRef]
• [12] Zheng ZC, Ghate AS. A solution of two-parameter asymptotic expansions for a two-dimensional unsteady boundary layer. Appl Math Comput 2015;270:90–104. [CrossRef]
• [13] Hafidzuddin MEH, Roslinda N, Norihan MA, Ioan P. Unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity. Int J Numer Method 2018;28:1457–1470. [CrossRef]
• [14] Nagler J. Higher order solution of Boundary layer formation as a result of impulsive start of motion. Zamm J Appl Math Mech 2019;99:e201800124. [CrossRef]
• [15] Bulgakov VN, Kotenev VP, Ozhgibisova IuS. Analytical study of laminar boundary layer near blunted bodies. Math Mod Comput Sim 2019;31:82–94.
• [16] Bachiri M, Bouabdallah A. Analytical approach of unsteady boundary-layer flows over a semi-infinite plate for all strouhal numbers. J Appl Mech 2011;78:024501. [CrossRef]