The Reynolds Analogy(雷诺比拟) The Reynolds Analogy(cont.) With the Stanton number新坦顿数)defined, Scr RePr hNi 尝常多离 dy Re dy With Pr1,the Reynolds analogy,which relatesm prameersofte relocity and thermul bowary layers,is 国m学 子-9 Modified Reymolds (Chilton-Colbumn)Anslogy: -An empirical result eendapplicabilry of the Reynoldsanloy .Hence,boundary the solutionsa of the same form 咖品 子-m 0.6ch<60 乱-. →ca 学- 一piicnb旅o laminar fowf中*h-食. ®上西过 工港研丸所 用上4生 Example I:Average Nu Example I:Average Nu ANALYSIS:For a peescribed goomey m-红时 1500W) 1只 Ke3-()-15m2/s/n m(VL:/v2)-1m A· Hence..u值operties(化与.人Rt=RL2Ao,A-P% nw忘，- (6t2k2-(n ASStMPTIONS:(1)Steady-stste conditions.(2) diation,(匀Blade shapesre geomri山yiiu, : The eat rae fohe e小告安 -T w明 92=2066V 霸上4生 工整梅表研完所 G粉正5K红 工童物藏祸九所 Example 2:Reynolds Analogy (ii)If the Reyuolds uumbers were not equal ()knowledge of the specifie C 厂 限0时RTIES:Preveribed.Air:￥=163：104mh.k=0022W的K.升=Q72 可二亿Rec后克 A万 ne,W油R4-V7水-100的046310mn=1.230 用上水生 周上生 工漫物研充所 44 The Reynolds Analogy (雷诺比拟） • Equivalence of dimensionless momentum and energy equations for negligible pressure gradient : Advection terms Diffusion * * 2* * *   TT T 1 * * 2* * * * * *2 1 Re uu u u v x y y       * * * 2* * * * * * *2 * * 2* * * * * *2 1 Re 1 Re Pr L L u u dp u u v x y dx y TT T u v xy y              dp*/dx*~0 Pr~1 工程热物理研究所 * * * * *2 1 Re TT T u v x y y       • Hence, for equivalent boundary conditions, the solutions are of the same form: * * * * * * * * y y 0 0 u T u T y y         L y y * * 2 * 0 2 / 2 Re s f L y u C V y          * * * * 0 ,ReL f y hL T Nu f x k y      Re 2 C Nu f  • With Pr = 1, the Reynolds analogy, which relates important parameters of the velocity and thermal boundary layers, is 2 Cf  St With the Stanton number( ) defined as, 斯坦顿数    p h Nu St Vc Re Pr difi d ld ( hil lb ) l The Reynolds Analogy (cont.) 工程热物理研究所 • Modified Reynolds (Chilton-Colburn) Analogy: – An empirical result that extends applicability of the Reynolds analogy: 2 3 Pr 0.6 Pr 60 2 f H C  St j   Colburn j factor for heat transfer – Applicable to laminar flow if dp*/dx* ~ 0. – Generally applicable to turbulent flow without restriction on dp*/dx*. Example 1: Average Nu 工程热物理研究所 Example 1: Average Nu 工程热物理研究所 工程热物理研究所 Example 2: Reynolds Analogy 工程热物理研究所