Numerical study of a Magnetic Fluid Boundary Layer using the Vorticity-Stream function Formulation

Arthur Campos¹; Rafael Gabler Gontijo¹; Francisco Ricardo Cunha¹

¹ UnB

doi:10.20906/CPS/COB-2015-1578

Resumo

This paper performs a numerical study of a magnetic fluid flow over a flat plate. The goal is to explore several new features of this boundary layer problem. The main difference from classical laminar boundary layers is that in the present work the flow interacts with controllable magnetic fields. This interaction opens the doors for several new possible applications, such as boundary layer control and fluid friction reduction. In order to perform this study we developed a non commerical research code based on the finite difference method using a vorticity-stream function formulation. The proposed formulation avoids the necessity of using a pressure-velocity coupling algorithm as long as we are dealing with a barotropic fluid flow. The numerical method is described in details and the results are compared with a rigorous scaling analysis performed by the authors. The code validation is done by comparing the non magnetic problem with the classical Blasius theoretical solution. The idea of this paper is to show that the interaction between the magnetic and velocity fields leads to a new and interesting flow with several possible patterns depending on the magnetic field boundary conditions. We also explore different constitutive equations for describing the magnetic stress using different generalizations of the Maxwell stress tensor. We intend through this work to study how different constitutive relations affect the main vector fields of the problem. A detailed study on the magnetization evolutive equation is also presented and discussed.

Palavras-chave: Vorticity-Stream Function; magnetic fluid; magnetization model; Maxwell's stresses; constitutive equation