Heat Transfer Handbook part 49. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 472 FORCED CONVECTION EXTERNAL FLOWS T Tm tT dU P v e dy q q m q t dT -pcp a h dy These can be integrated to yield u f dy T - T L Zïy Hdy 689 Algebraic Turbulence Models The simplest class of turbulence closure models is the zero-equation model or firstorder closure model. Prandtl s mixing length model is an example of this class where the eddy diffusivities e and eH are modeled in terms of the gradients of the mean flow e dU dy and eH Cf2 dU dy where is the mixing length. Here C is found from Pry c iH JL e Pry where Prr is the turbulent Prandtl number. Near-Wall Region in Turbulent Flow The mean momentum equation can be written near the wall as du du pu pv dx dy dp 0 dy dx In a region close to the wall the approximations pU 0 dx U U y and the normal velocity at the wall - V V0 HEAT TRANSFER FROM SINGLE OBJECTS IN UNIFORM FLOW 473 can be made. With these the momentum equation becomes dii d t dp P 0 dy dy dx which can be integrated using t t0 and m 0 at y 0 T 1 pvou dp y T0 T0 dx T0 Near hie wall a friction velccity v can be defined as TP f which tields 1 2 T0 V v I I P Moreover normalized variables can be defined near the wall u u U u v Cf 2 yv v V vo v 0 v fl dp dx P P 2 O 2 and substitution of eqs. into eq. yields 1 v u p y To In the absence of pressure gradient and transpiration p 0 v0 0 T du 1 or to p v e to dy In a region very close to the wall called the viscous sublayer v e and eq. can be integrated from the wall to a nearby location say 0 y 5 in the flow iu to r I du I Jo fl Jo dy or u y 474 FORCED CONVECTION EXTERNAL FLOWS In a region farther out from the wall turbulence effects become important. However the near-wall region still has effectively constant total shear stress and total heat flux T to p v p v l p v kV dy dy dy dy dy where the mixing length near the wall is taken as Ky with k being the von Karman constant. In the fully
