HEAT TRANSFER chAPTER 8 Internal flow 们au Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 8 Internal flow
Internal flow Heat Transfer Where we’ ve been. Introduction to internal flow, basic concepts energy balance Inviscid flow regio Boundary layer region (r,x) Hydrodynamic entrance region Fully developed region Where we’ re going Developing heat transfer coefficient relationships and correlations for internal flow Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Internal Flow Heat Transfer Where we’ve been …… • Introduction to internal flow, basic concepts, energy balance. Where we’re going: • Developing heat transfer coefficient relationships and correlationsfor internal flow ro
Internal flow Heat Transfer KEY POINTS THIS LECTURE Convection correlations Laminar flow Turbulent flow Other topics Non-circular flow channels Concentric tube annulus Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 3 Internal Flow Heat Transfer KEY POINTS THIS LECTURE • Convection correlations – Laminar flow – Turbulent flow • Other topics – Non-circular flow channels – Concentric tube annulus
Convection correlations: laminar flow in circular tubes 1. The fully developed region from the energy equation, we can obtain the exact solution for constant surface heat flux hD 4.36 k for constant surface temperature hD 3.66T=C k Note: the thermal conductivity k should be evaluated at T' Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 4 Convection correlations: laminar flow in circular tubes • 1. The fully developed region from the energy equation,we can obtain the exact solution. for constant surface heat flux for constant surface temperature Note: the thermal conductivity k should be evaluated at . = 4.36 k hD NuD q s = C = 3.66 k hD NuD Ts = C Tm
Convection correlations: laminar flow in circular tubes ·2. The entry region for the constant surface temperature condition D 0.0668RepP D Nun=3.66+ 2/3 1+0.04 Ren pr thermal entry length -Thermal e Combined entry lensth Constant surface Pr=0.7) heat flua Entrance terion Fuly developed region 10 4.36 Constant srface temperature 0001 0005001 0050.1 0.5 G Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Convection correlations: laminar flow in circular tubes • 2. The entry region for the constant surface temperature condition thermal entry length 2/3 Re Pr L D 1 0.04 Re Pr L D 0.0668 3.66 + = + D D NuD
Convection correlations: laminar flow in circular tubes 2. The entry region(contd) for the combined entry length ReD pr/3 0.14 Nun=1.86 LID For values of Rep pr/(L/D)](m/y≥2 T=C 0.48<Pr<16.700 00044<(c/,)<975 Allfluid propertiesevaluated at the mean T +T,)2 m, 7 1,O Heat Transfer 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 Tm = (Tm,i +Tm,o )/ 2 Ts = C 0.48 Pr 16,700 0.0044 ( / s ) 9.75
Convection correlations: turbulent flow in circular tubes A lot of empirical correlations are available For smooth tubes, the fully developed flow Nun=0.023 Re 4/5D0.4 Heating Cooling: Nup=0.023 Re 4/5D-0.3 For rough tubes, coefficient increases with wall roughness. For fully developed flows Nua-1+127/8)(P2 (f/8)ReD-1000 Consider the entry length Short tubes N uD NuD≈ND,fa or =1+ N D, fd (x/D) For liquid metals, see textbook p461 Heat Transfer 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 NuD NuD, fd or m D f d D x D C Nu Nu ( / ) 1 , = + Short tubes
Internal convection heat transfer coefficient (summary) 1. For laminar and fully developed flow(88.4.1) 1. q constant: N lD=436 Eq.8.53 ii. s constant N 3.36 Eq.8.55 2. For laminar flow in entry region(before fully developed flow,88.4.2 D i. Ts constant 0.0668二 Ren pr Ni 3.66+ 2/3 Eq.8.56 1+0.04 Ren pr Combined entry length with full tube 0.14 Re P N 186 D LID Eq.8.57 3. For turbulent and fully developed (s8.5) Heating Nu=0.023 Re 45 Pr0.4 ii. Cooling Nu=0.023 Re 4/5 Pr 3q.8.60 Allfluidproperties evaluated at the mean t +T) 2 m, 7 2,O Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Internal convection heat transfer coefficient (summary) 1. For laminar and fully developed flow (§8.4.1): i. q” constant: ii. Ts constant: 2. For laminar flow in entry region (before fully developed flow, §8.4.2: i. Ts constant : ii. Combined entry length with full tube: 3. For turbulent and fully developed (§8.5) i. Heating ii. Cooling 2/3 Re Pr L D 1 0.04 Re Pr L D 0.0668 3.66 + = + D D NuD 1/3 0.14 / Re Pr 1.86 = s D D L D Nu All fluid properties evaluated at the mean T Tm = (Tm,i +Tm,o )/ 2 Eq. 8.53 Eq. 8.55 Eq. 8.56 Eq. 8.57 Eq. 8.60 4/5 0.4 0.023Re Pr NuD = D 4/5 0.3 0.023Re Pr NuD = D NuD = 4.36 NuD = 3.36
Example: Oil at 150'C flows slowly through a long, thin walled pipe of 30-mm inner diameter. The pipe is suspended in a room for which the air temperature is 20 C and the convection coefficient at the outer tube surface is 11 W/mK Estimate the heat loss per unit length of tube KNOWN: Oil flowing slowly through a long, thin-walled pipe suspended in a room. FIND: Heat loss per unit length of the pipe, conv SCHEMATIC: oom air 11W =20eC conv conv Pipe. D:30mm-.m 150° ASSUMPTIONS: (I)Steady-state conditions, (2) Tube wall thermal resistance negligible, 3) Fully developed flow, (4) Radiation exchange between pipe and room negligible PROPERTIES: Table A-5, Unused engine oil(m150C=423 K ): k=0.133 W/m-K Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Example: Oil at 150℃flows slowly through a long, thinwalled pipe of 30-mm inner diameter. The pipe is suspended in a room for which the air temperature is 20 ℃ and the convection coefficient at the outer tube surface is 11W/m2 .K. Estimate the heat loss per unit length of tube
ANALYSIS: The rate equation, for a unit length of the pipe, can be written as m qco where the thermal resistance is comprised of two elements R ;D horD TD hi he convection coefficient for intemal flow, h, must be estimated from an appropriate correlation From practical considerations, we recognize that the oil flow rate cannot be large enough to achieve turbulent flow conditions. Hence, the flow is laminar, and if the pipe is very long, the flow will be fully developed. The appropriate correlation is hE D NuD=--=36 h;= Nup k/d=36601310030m162Wm2K mK he heat rate per unit length of the pipe is (50-20)C onV 今3=803Wm 丌(0030m)(162 W COMMENTS: This problem requires making a judgment that the oil flow will be laminar rather than turbulent. Why is this a reasonable assumption? Recognize that the correlation applies to a constant surface temperature condition. Heat Transfer Su Yongkang School of Mechanical Engineering
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