Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
THEORETICAL ANALYSIS AND DETERMINATION OF HYDRODYNAMIC AND THERMAL BOUNDARY LAYERS THROUGH OF GENERALIZED INTEGRAL TRANSFORM TECHNIQUE
Submission Author:
Marinaldo Medeiros , PB
Co-Authors:
Marinaldo Medeiros, Carlos Antonio Cabral Santos
Presenter: Marinaldo Medeiros
doi://10.26678/ABCM.COBEM2021.COB2021-1205
Abstract
The Boundary layer theory is considered to be the cornerstone of our knowledge about the fluid flow over a surface which not only some intriguing physical phenomena of fluid dynamics, but also pivotal in practical problems of engineering. The present work had as object of study, the development of the temperature and velocity profile along the flow direction and the determination of the thermal and hydrodynamic boundary layers thicknesses in the laminar flow. The hybrid analytical-numerical solution of the thermal and hydrodynamic problem on a flat plate is presented taking into account the effects of velocity, convection and heat conduction on the boundary conditions of the system of equations. The equations for the amount of movement and energy are transformed using a change of variable to determine of the hydrodynamic and thermal boundary layers thicknesses, respectively. The main objective of this article is to have a more general view of the behavior of the thermal and hydrodynamic boundary layers in a conduction-external convection conjugated problem in a steady state using a developing velocity profile. Hybrid solutions to the proposed problem are obtained by using the Generalized Integral Transform Technique (GITT) by applying filters in temperature and velocity boundary conditions to make the problem homogeneous, being solved by the NDSolve routine of the Matemathica 12.1 software. To solve the coupled problem it was necessary to use, in the hydrodynamic field, the exact analytical solution of the hydrodynamic boundary layer thickness, while in the thermal field the relation between the Prandtl number and the thermal boundary layer thickness was used. GITT was able to solve the problem of the hydrodynamic and thermal boundary layers, making it possible to determine the hydrodynamic boundary layer thickness without using the similarity method, which shows an unprecedented treatment in solving this problem. The evolution of the position of the hydrodynamic boundary layer was calculated and compared with the Blasius solution and with approximate solutions using polynomial functions, obtaining very close results with errors of the order of 1%. In the thermal field, the temperature distribution found was compared with the Blasius solution and other works published in the literature, obtaining convergence in the fourth decimal place.
Keywords
Boundary Layer Thickness, Conduction-Convection Conjugate Problem, Generalized Integral Transform Technique (GITT)
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