Convection correlations:laminar flow in circular tubes .2.The entry region(cont'd) for the combined entry length 0.14 ·For values of [RepPr/(L/DΨ(u/u,P4}≥2 T.=C 0.48≤Pr<16,700 0.0044<(u14,)<9.75 All fluid properties evaluated at the mean T Tm =(Tmi+Tm.o)/2 Heat Transfer #6 Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Convection correlations: laminar flow in circular tubes • 2. The entry region(cont’d) for the combined entry length • For values of 1/3 0.14 / Re Pr 1.86 s D D L D Nu Re Pr/( / ) / 2 1/3 0.14 D L D s All fluid properties evaluated at the mean T / 2 Tm Tm,i Tm,o Ts C 0.48 Pr 16,700 0.0044 / 9.75 s
Convection correlations:turbulent flow in circular tubes A lot of empirical correlations are available. For smooth tubes,the fully developed flow Heating: Nup =0.023Res Pr4 Cooling: Nup=0.023Res Pr03 For rough tubes,coefficient increases with wall roughness.For fully developed flows Nua (f/8)ReD-1000)Pr 1+12.7f18)2(Pr23-1) Consider the entry length Short tubes NuD≈Nup,fa NuD C =1+ Nup,fd (x/D)m For liquid metals,see textbook p461. Heat Transfer #7 Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Convection correlations: turbulent flow in circular tubes • A lot of empirical correlations are available. • For smooth tubes, the fully developed flow Heating: Cooling: • For rough tubes, coefficient increases with wall roughness. For fully developed flows • Consider the entry length • For liquid metals, see textbook p461. 4/5 0.4 0.023Re Pr NuD D 4/5 0.3 0.023Re Pr NuD D 1 12.7( / 8) (Pr 1) ( / 8)(Re 1000)Pr 1/ 2 2/3 f f Nu D d Nu D NuD, fd or m D fd D x D C Nu Nu ( / ) 1 , Short tubes