Abstract |
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The article presents a review of universal functions widely used in different areas of boundary layer theory for many years up to the present. Universal functions considerably simplified the computation and analysis of problems due to their independence to the characteristics of specific problems. For example, some differential equations in universal variables may be calculated once for all problems, and then these tabulated data may be used to get numerical solutions of any specific problem without solving the initial differential equation. Different kinds of universal functions are considered, from simple equations of dimensionless numbers in similarity theory and Blasius-Howarth series in early works, to universal parametric boundary layer equations, Merk-Chao series and superposition series of consecutive derivatives in modern investigations. Various universal solutions adopted from almost 100 articles published since the famous Howarth study of Blasius series in 1935 show the breadth of universal approaches with application in laminar, turbulent and transition boundary layers including separation and reattachment, in solving non-isothermal and conjugate heat transfer problems as well as in planetary boundary layer problems in meteorology. |
Keywords and phrases
universal functions, analytical methods, boundary layer flows, turbulence, heat transfer, atmospheric boundary layer, applications.
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