1. Compressibility and Heat Transfer Effects on Boundary Layers L. Sankar November 30, 2004

2. OVERVIEW Up to M= 1 or so, compressibility plays very little role on the boundary layer growth rate, and characteristics. Empirical corrections may be used in approaches such as Thwaites’ method and Head’s method. In this lecture, we are interested in seeing what happens at higher speeds, M=1 and above. We are also interested in convective heat transfer over flat plates, at subsonic speeds. We consider laminar flows only. See Text (Bertin and Smith, Chapter 4:8) for turbulent flows.

3. Some Background Equations Please see www.ae.gatech.edu/~lsankar/AE3021 for the derivation of thewww.ae.gatech.edu/~lsankar/AE3021 Navier-Stokes equations, and the boundary layer approximation of the equations.

4. Alternate Form of Energy Equation

5. Some Definitions

6. Laminar Compressible Viscous Flow over an Adiabatic Flat Plate In our specific situation, q = 0 for the adiabatic wall since there is No heat transfer from the fluid to the solid.

7. Solution to this Problem (Pr=1)

8. Viscous Flow Over a Flat Plate Conducting Wall held at constant T Convective Heat transfer T= T wall We again look at laminar flow, Pr=1 to get a feel for the solution. We look at low subsonic cases – representative what happens In flow over turbines, radiator fins etc.

9. Governing Equations

10. Governing Equations (Continued)

11. Examination of the Solution

13. Heat transfer Rate