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

Abstract

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.

Keywords

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

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