Compressibility and Heat Transfer Effects on Boundary Layers

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Compressibility and Heat Transfer Effects
onBoundary Layers

• L. Sankar
• November 30, 2004

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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 Heads method.
• In this lecture, we are interested in seeing what
  happens at higher speeds, M1 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 48) for turbulent flows.

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Some Background Equations
Please see www.ae.gatech.edu/lsankar/AE3021 for
the derivation of the Navier-Stokes equations,
and the boundary layer approximation of the
equations.
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Alternate Form of Energy Equation
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Some Definitions
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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.
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Solution to this Problem (Pr1)
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Viscous Flow Over a Flat PlateConducting Wall
held at constant TConvective Heat transfer
T Twall
We again look at laminar flow, Pr1 to get a feel
for the solution. We look at low subsonic cases
representative what happens In flow over
turbines, radiator fins etc.
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Governing Equations
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Governing Equations (Continued)
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Examination of the Solution
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Examination of the Solution
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Heat transfer Rate