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ISSN Online: 2379-1748

8th Thermal and Fluids Engineering Conference (TFEC)
March, 26-29, 2023, College Park, MD, USA

Semi-Analytical Solution for Statistical Turbulent Boundary Layer over an Isothermal Horizontal Flat Plate

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DOI: 10.1615/TFEC2023.rhe.046000


Turbulent heat transfer, involving a wide range of fluids, is commonly encountered in many practical and engineering applications. The solutions for statistical turbulent heat transfer are widely employed for the design of such thermal systems, involving wall laws for a wide range of Prandtl numbers (Pr). Some of the identified research gaps, based on the literature review, are as follows: (a) limited availability of data on thermally-hydraulically developing, turbulent, boundary layers for fluids with a wide variation in Pr, and (b) the wall laws for temperature are inadequate for statistical, turbulent, thermal boundary layers involving different fluids such as air, water, oil, etc. These fundamental, practical, and challenging aspects are addressed in this paper. A semi-analytical approach is proposed for analyzing a thermally-hydraulically developing, statistical, turbulent boundary layer, for incompressible and Newtonian fluid flow over an isothermal, horizontal, smooth, flat plate for 0.008≤ Pr ≤585.3. This extends the similarity variable-based formulation for the Reynolds-average turbulent boundary layer equation, including the equation for energy. The resulting ill-posed problem is numerically solved using the combination of the boundary layer update scheme and the Runge-Kutta method. Following are the novel outcomes: (a) the non-dimensional statistical temperature T+ scales with Pry+ inside of the thermal boundary layer, and (b) a Nusselt number correlation is deduced for liquid metals and oils with 0.008≤ Pr ≤585.3. The findings will be useful for adopting the wall laws and heat transfer analyses with liquid metals and oils.