Heat Transfer in Compressible Laminar Boundary-Layers

Author: Lal, Shankar

Year: 1955

Degree: Dissertation (Ph.D.)

Advisor: Lagerstrom, Paco A.

Committee Member: Unknown, Unknown

Option: Aeronautics; Mathematics

DOI: 10.7907/BRKX-WV81

Abstract

This report is concerned with the investigation of skin-friction and heat-transfer in the two-dimensional flow of a viscous compressible fluid.

The boundary-layer equations are first transformed by the Howarth-Stewartson transformation and then it is shown that for fluids of Prandtl Number unity, if the Chapman viscosity law be assumed to hold, then any boundary-layer problem with the free stream Mach Number different from zero can be formally reduced to a problem for which the free stream Mach Number is equal to zero.

The momentum method is then used to solve the boundary-layer equations in the Howarth-Stewartson form, for the case when the free stream Mach Number is zero. The basic equations developed are first used to solve the case of those specific pressure gradients which lead to "similarity flows". Other investigators have solved the exact equation for these flows on the differential analyser. The results obtained in this report, with the aid of very simple methods, agree to within a few percent with these more exact but laborious computations.

The use of the method for the case of arbitrary pressure gradients is then developed. Three ways of solving the resulting equations are discussed. In particular, an integral solution for the square of the momentum thickness, analogous to the one existing for incompressible fluids but with different exponents, is given. The application of the method is demonstrated by solving an illustrative example.

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