1. Objective Discuss Energy and Concentration conservation equations
Provide example
Introduce Turbulence

2. From the previous classes
Momentum equation
Sum of all forces in x direction
Internal source
x direction
y direction
z direction

3. From the previous classes Newtonian fluids
Viscous stress are proportional to the rate of deformation (e)
Elongation:
Shearing deformation:
For incompressible flow
Viscous stress:
viscosity

4. Momentum equations for Newtonian fluids
After substitution:
x direction:
y direction:
z direction:

5. From the previous classes Momentum equations for Newtonian fluids
x direction:
for incompressible flow
y direction:
z direction:

6. Energy equations for Newtonian fluids
Conservation of energy for the
fluid particle:
Energy
(heat) flux
source
dissipation :

7. Conservation Equations

8. Application Example: 2D flow
gravitation
Natural convection at vertical surface - steady boundaries:
-ρg 0
Twall
Boussinesq
approximation ∞
Twall>T∞ 0 0

9. Application Example: 2D flow
Driving force for
natural convection

10. Conservation Equationsy z x

11. Concentration equation
Conservation of mass of considered gas (chemical species):
mgas=const
mgas=C∙mair= C∙ρ∙dxdydz=const
mgas,in
mgas,out dy
incompressible flow dz
C=const dx
Diffusion coefficient
C – concentration of: H2O , VOC, CO, CO2 , and other gasses
What about particles?

12. Turbulence Forced convection on flat plate

13. Turbulence

14. Size of eddies
hurricane
nozzle
2 in
Eddy ~ 1/100 in
~200 miles

15. Transition from laminar to turbulent flow

16. Turbulence in the vicinity of human body
PT-Teknik.dk

17. Example (HW1)
The figure below shows a turbulent boundary layer due to forced convection above the flat plate.
The airflow above the plate is steady-state.
Consider the points A and B above the plate and line l parallel to the plate.
Point A y
Flow direction
Point A
Point B
line l
For the given time step presented on the figure above plot the velocity
Vx and Vy along the line l.
b) Is the stress component txy lager at point A or point B? Why?
c) For point B plot the velocity Vy as function of time.