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【正文】 energy generation (q=0) Boundary approximations Boundary layer approximations ???????????????xvyvxuyuvu,???????? xTyTVelocity boundary layer Thermal boundary layer 0322 ????????? ????????? yvxuxuxx ???0322 ????????? ????????? yvxuyvyy ??????????? ??????????? ??????? yuxvyuyxxy ????Basing on foregoing simplifications and approximations Mathematical model for the convection transfer in different boundary layers Equations may be solved to determine the spatial variations of u, v, T in the different boundary layers. For inpressible, constant property flow, equations (1) and (2) are uncoupled from (4). That is, it may be solved for the velocity field. u(x, y) and v(x, y). Then the velocity gradient could be evaluated, and the wall shear stress could be obtained. Through the appearance of u and v in equation (4), the temperature is coupled to the velocity field. The convection heat coefficient may be determined. 0?????? yvxu221yuvxpyuvxuu?????????????0???yp222???????????????????yucyTyTvxTup????1??2??3??4Note: 02????????? ??yucp?In most situation viscous may be neglected relative to other terms. In fact it is only for sonic flow or the high speed motion of lubricating oils. 0???ypThe pressure does not vary in the direction normal to the surface. It in the boundary layer depends only on x and is equal to the pressure in the freestream outside the boundary layer. It be treated as known quantity. Purpose: 1. One major motivation has been to cultivate an appreciation for the different physical processes. These processes will affect wall friction, as well as energy transfer in boundary layers. 2. A second motivation arises from the fact that the equations may be used to identify key boundary layer similarity parameters, as well as important analogies between momentum and heat transfer. Boundary Layer Similarity: The Normalized Convection Transfer Equations 221yuvxpyuvxuu????????????? 22yuvyuvxuu????????222???????? ??????????? yucy TyTvxTup??22 TyTvxTu???????? ?Strong similarity Same form This equation describes lowspeed, forced convection flows, which are found in many engineering applications. 22yyvxu ????????? ????? ??? ,:e q u a t i o n uu?? ??? ,:e q u a t i o n TTAdvection terms Diffusion term Nondimensionalizing Implications of this similarity may be developed in a rational manner by first nondimensionalizing the governing equations. Boundary layer similarity parameters Independent dimensionless variables LyyLxx ?? ?? a ndCharacteristic length Dependent dimensionless variables VvvVuu ?? ?? a ndVelocity upstream of the surface ssTT TTT ?????2Vpp ???22??????????????????????yuVLvxpyuvxuu22????????????????yTVLyTvxTu ??VLReL ?????VLVLPrReL ?? ???PrSimilarity parameters Reynolds Number: ?VLReL ?Prandtl Number: ???PrDimensionless boundary layer equations: 221??????????????????????yuRexpyuvxuuL221????????????????yTPrReyTvxTuL0?????? ???? yv
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