A CLASS OF EXACT SOLUTION TO THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

• Main Authors: Nugroho, Gunawan, A.M.S., Ali, Abdul Karim, Z. A.
• Format: Article
• Published: 2010
• Subjects: TJ Mechanical engineering and machinery
• Online Access: http://eprints.utp.edu.my/6236/1/A_Class_of_Exact_Solution_to_the_Three-Dimensional_Incompressible_Navier-Stokes_Equations_%28080609%29.pdf; http://eprints.utp.edu.my/6236/
• Institution: Universiti Teknologi Petronas

An exact solution of the three-dimensional incompressible Navier-Stokes equations with the continuity equation is produced in this work. The solution is proposed to be in the form where is a potential function that is defined as , with the application of the transformed coordinate . The potential function is firstly substituted into the continuity equation to produce the solution for and . The resultant expression is used sequentially in the Navier-Stokes equations to reduce the problem to the class of nonlinear ordinary differential equations in terms, in which the pressure term is presented in a general functional form. General solutions are obtained based on the particular solutions of where the equation is reduced to the form of linear differential equation. A method for finding closed-form solutions for general linear differential equations is also proposed.