1. Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: 248-370-2224Fax: 248-370-4416 Email: wang@oakland.eduwang@oakland.edu Contact Information:

2. Turbulent Boundary Layer with Heat Transfer by Dr. Xia Wang

3. Similarity Analysis Near Asymptotic Method Provide the criterion to avoid the turbulent boundary layer separation; (airfoil, turbine blade; diffuser) Surface roughness effects on the external flow; (air pollution above the urban city, suburban ) Turbulent boundary layer with forced convection heat transfer (external cooling ; airfoil) Boundary Layer Control Boundary layer modeling Turbulent Boundary Layers: Topics

4. Problems in Simulation and Measurement Both Computational tools and measurement tools cannot solve the problems in the real applications with very high Re number such as Atmosphere, flight, submarine et al.

5. Research Approaches Scales: Similarity analysis –The scales for TBL are dictated by equations and their boundary layer conditions alone. –The energy equation becomes independent of Pe in the limit as Pe->  ; thus, any solution of equations must also be independent of Pe in this limit. (Asymptotic Invariance Principle: AIP) Functions: Near-Asymptotic method enables us to find the functions describing the temperature or velocity profiles in the overlap region at the finite Pe or Re.

6. Temperature: Outer Scaling Classical Scaling New Scaling

7. Velocity Profiles Classical ScalingNew Scaling

8. Temperature: Inner Scalings Classical Scaling New Scaling

9. Composite Profiles

10. Conclusions Similarity analysis of the equations of motion is applied to investigate the momentum BL and the thermal BL: –The TBL with separation is still equilibrium flow. – A separation criterion based on the shape factor, Hsep=2.76, is proposed for the APG TBLs with the eventual separation. – Two different temperature scales are shown for both the inner and outer temperature profiles, – The temperature profiles, when normalized by new temperature scales, are independent of Pe, PG, and upstream effects, which yields the true asymptotic temperature profiles. –A composite temperature profile is found, which can be used to predict –Heat transfer law (in power law form); –Thermal displacement thickness;