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assumed assumption base pressure boundary-layer flow compressible turbulent control volume coolant flow rate coolant injection coolant mass injection coolant slot height Crocco and Lees dead-air region defined by equations denotes developed turbulent boundary displacement thickness effect of wall effectiveness of coolant effectiveness of film energy enthalpy profiles evaluation experimental external stream film cooling flat plate flow field flow Mach number flow separation fully developed turbulent Hc/Hw heat transfer Hw/Hoo incompressible indicates interaction internal dissipative flow jet mixing region laminar mass flux mean heat-transfer rate mean heating rate mixing coefficient mixing layer momentum NACA nondimensional NPr,t Npr^t obtained oncoming boundary layer oncoming boundary-layer thickness overall effectiveness parameter Prandtl-Meyer fan present approach pressure gradient rearward-facing slot rearward-facing step recompression region region increases Reynolds number scale factor separated region shearing stress shock wave shown in figure slot exit small coolant solution supersonic turbulent boundary layer upstream wall temperature