HEAT TRANSFER AND FLUID DYNAMICS ON INCLINED SMOOTH AND ROUGH SURFACES BY THE APPLICATION OF THE SIMILARITY AND INTEGRAL METHODS

Abstract

The main objective of the analysis is to review and discuss the principles of the similarity method applied to the boundary layer on inclined surfaces, in laminar regime, and that can be extended to a turbulent regime. The emphasis applies to theoretical aspects related to the concept of similarity, but theoretical results were obtained to compare with empirical expressions and experimental results. Results are obtained for the hydrodynamic and thermal fields, such as coefficient of friction and Stanton number, as a function of the pressure gradient parameter and the Prandtl number. The fourth order Runge-Kutta method is applied, starting from the expansion in power series as the first approximation for the mathematical solution of hydrodynamic and thermal problems, in laminar regime. The Integral Method is applied to obtain an approximate solution for the flow in turbulent regime, by similarity variables method. Numerical and graphical results are presented in sufficient numbers to emphasize the consistency of the model developed in the determination of parameters related to thermal and hydrodynamic boundary layers on smooth and rough surfaces.

DOI: https://doi.org/10.56238/sevened2025.036-107