Homework 03 - optional-Revised.pdf - Mostafa Najafiyazdi...

This preview shows page 1 - 2 out of 2 pages.

Mostafa NajafiyazdiAdvanced Fluid Dynamics (MECH 562)Department of Mechanical EngineeringFundamentals of Fluid Mechanics (MECH 610)McGill UniversityPractice Homework #3Optional (bonus point)Deadline: Sunday April 22, 2018Can be submitted by teams of up to 2 peopleQuestion #1: Free Convection on a Vertical SurfaceConsider a fluid with farfield temperatureTtouching a hot vertical plane at temperatureTw.Thetemperature slightly affects fluid density resulting in free convection, i.e. hot fluid moves upward and coldfluid washes downward.A good approximation for Navier-Stokes equations is calledBoussinesq approximationfor buoyancydriven flows (see Fig.).In this approximation, the fluid is consideredincompressibleand the effect ofbouyancy is modeled in a gravitation based term (read here for more information).As a result, the steady state governing equations for natural convection for a 2D heated vertical plateare∂u∂x+∂v∂y= 0,(1)u∂u∂x+v∂u∂y=ν2u∂y2+(T-T)|{z}Boussinesqapproximation,(2)and

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture