The problem of determining the hydrodynamic entrance length in a rectangular channel is solved by the method of linearizing the Navier-Stokes equation. The resulting equation is regarded as an equation to generate a mathematical expression for the axial velocity in the entire region, making smooth transition from a uniform profile to the fully developed one. From this expression, the entrance length, defined as where 99 per cent of the fully developed center-line velocity is attained, is calculated for channels of six aspect ratios. The pressure drops are also calculated and presented herein. A comparison is made with the limited amount of experimental and theoretical data.
Most composite research to date has been concerned with mechanical properties. However, with anticipated use of composite materials in high temperature aero-space structures and other applications, thermal properties have become essential design information. This paper summarizes the results of a rigorous analysis to determine the steady-state effective thermal conductivities of fiber-matrix type of composites. A principal purpose of the present work is to investigate a class of heat conduction problems for which the proximity effects of the embedded fibers are significant. The fibers are considered dispersed uniformly in a matrix of resin. The dispersion patterns or configurations considered are: (1) uni-directional fibers in a matrix, as the simplest geometry, and (2) 0/90 configuration in which uni-directional tapes are overlaid at 90 deg to each other. The method of analysis is to solve a two-region steady-state heat conduction equation analytically or numerically. The analysis assumes prior knowledge of the geometry and the thermal conductivities of the composite constituents.
A method of cooling turbine blades internally by continuous injection through an interior baffle is analyzed. The analytical model consists of a two-dimensional channel formed by a solid wall (blade surface) and a porous plate (injection source). Based on incompressible- and laminar-flow assumptions, the velocity and the temperature fields are determined. The Nusselt numbers for a power-law surface-temperature variation are obtained and expressed in terms of the Prandtl and the Reynolds numbers. A related problem of cooling the turbine disk is also solved.
Boundary layer characteristics on the pressure-side of a turbine airfoil were investigated experimentally in a three-blade cascade tunnel. The blades had a chord length of 21 in. to facilitate flow visualization and high-speed photography. The investigation revealed the existence of the Gortler’s vortices appearing in spurts in regions of severe curvature. In the trailing edge region, Karman vortices were detected and found to interact strongly with the Gortler’s vortices convected thereto.
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