HEAT TRANSFER CHAPTER 7 External flow #1 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 7 External flow
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Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Looking for a job?
External Flow:Other Shapes Topic of the Day oven #3 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 3 External Flow: Other Shapes Topic of the Day oven
External Flow:Other Shapes Where we've been...... Empirical correlations and analytical solutions Nux= 0.332 Re2 Pr Where we're going: Applications to other shapes(cylinders and spheres) Brief discussion on multiple objects(tube bundles)and jet impingement. ·Internal flow next Textbook Sections 7.4-7.8 #4 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 4 External Flow: Other Shapes Where we’ve been …… • Empirical correlations and analytical solutions Where we’re going: • Applications to other shapes (cylinders and spheres) • Brief discussion on multiple objects (tube bundles) and jet impingement. • Internal flow next ……….. Textbook Sections §7.4-7.8 3 1 2 1 0.332 Re x Pr k h x Nu x x
Historical Example Cooling of lead shot Molten lead #5 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Historical Example • Cooling of lead shot Molten lead
Background-Flow Considerations Wake Stagnation point Separation point Boundary layer Favorable Adverse pressure gradient pressure gradient aP 0 Ox #6 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Background – Flow Considerations Favorable pressure gradient 0 x P Adverse pressure gradient 0 x P Stagnation point Separation point Wake
Background-Flow Considerations (Cont'd) Boundary layer transition Laminar Laminar Transition- Turbulent boundary boundary boundary layer layer layer V Ren≤2x105 Ren≥2×105 Separation Separation Momentum of fluid in a turbulent boundary layer is greater,and thus separation occurs further along the object. Example How fast must a soccer ball travel to expect a turbulent boundary layer? ReDV2×105×15.89×10-6 =14.4 m D 0.22 S But other factors also involved (surface roughness, wind,ball spin,etc.) #7 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Background – Flow Considerations (Cont’d) • Boundary layer transition • Momentum of fluid in a turbulent boundary layer is greater, and thus separation occurs further along the object. Example How fast must a soccer ball travel to expect a turbulent boundary layer? But other factors also involved (surface roughness, wind, ball spin, etc.) s m D V D 14.4 0.22 Re 2 10 15.89 10 5 6
Convection heat transfer for cylinder Complicated physics makes necessary using empirical (experimental)correlations of heat transfer coefficient and flow conditions. Local Nusselt number 800 700 600 Rep=2.19×10 500 1.86×105 1.70×105 星401 1.40×10 1.01×105 300 0.71×105 200 100 0 40 80 120 160 Anguiar coordinate,0 #8 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Convection heat transfer for cylinder • Complicated physics makes necessary using empirical (experimental) correlations of heat transfer coefficient and flow conditions. Local Nusselt number
Convection heat transfer for cylinder(Cont'd) Generally want the overall average Nusselt number for heat transfer with the entire object. As with a flat plate,correlations developed from experimental data to compute Nu as a f(Rem,Prm) Overall Average Nusselt number hD 1/4 Pr Nup k CRe PrV/3 二( Prs 「0.7<Pr<500 Valid for: 1<Rep <106 All properties are evaluated at the freestream temperature,except Prs which is evaluated at the surface temperature. #9 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Convection heat transfer for cylinder (Cont’d) • Generally want the overall average Nusselt number for heat transfer with the entire object. • As with a flat plate, correlations developed from experimental data to compute Nu as a f(Rem ,Pr n) Overall Average Nusselt number • All properties are evaluated at the freestream temperature, except Prs which is evaluated at the surface temperature. 6 1 4 1 3 1 Re 10 0.7 Pr 500 Valid for : Pr Pr Re Pr D s m D C D k hD Nu
Ren C m Values for C and m 1-40 0.75 0.4 40-1000 051 05 103-2×10° 0.26 0.6 2×10-10r 0.076 0.7 Expect accuracy within 20%with these correlations The empirical correlation due to Hilpert NuD≡ hD=CRepPr Values of C and m are listed in Table 7.2. All properties are evaluated at the film temperature #10 Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 10 • Values for C and m • Expect accuracy within 20% with these correlations • The empirical correlation due to Hilpert • Values of C and m are listed in Table 7.2. • All properties are evaluated at the film temperature. 1/3 Re Pr m D C D k hD Nu