- Author
-
Zien, T. F.
- Title
- Approximate Calculation of Heat Transfer in Transpired Boundary Layers.
- Coporate
- Naval Ordnance Lab., White Oak, MD
- Report
-
NOLTR 73-17,
1973,
67 p.
- Keywords
-
boundary layers
|
heat transfer
|
mass transfer
|
surface heat
|
prandtl number
- Identifiers
- laminar boundary layer; integral model; nonsimilar flows
- Abstract
- An approximate method of calculating the surface heat transfer in a transpired boundary layer is presented. The method is based on a generalization of Volkov's original idea for refining the Karman-Pohlhausen momentum integral technique. A simple, yet non-trivial, configuration of a semi-infinite, isothermal flat plat with uniform surface mass flux is used to demonstrate the method. The flow is assumed to be laminar. Results are presented for both incompressible boundary layers (for two Prandtl numbers, Pr = 1 and 0.7) and compressible boundary layers (for Pr = 1). Comparisons are made with exact (numerical) solutions or other available approximate results. Extremely simple and crude profiles for velocity and temperature are used in the calculation. Very satisfactory results are obtained, requiring, at most, the numerical integration of a single first-order ordinary differential equation. The same profiles are also used in the usual Karman-Pohlhausen procedure for the purpose of establishing the relative merit of the present method on the basis of equal simplicity. It is demonstrated that the present method, being clearly superior to the usual Karman-Pohlhausen technique, combines accuracy with simplicity to an unusual degree. The insensitivity of the results to the choice of profiles is also in evidence. These results are indicative of the potential of the method for its development into an efficient tool for studying boundary-layer flows of a more complex nature.