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Water

Example 8.3. L = 6 m. D = 50 mm. Water. Find: Average convection heat transfer coefficient. L = 6 m. D = 50 mm. Water. Convection Correlations. Laminar Flow in Fully Developed Region. in the cylindrical coordinate system ( r , x ). for fully developed flow . Then,. When .

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Water

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  1. Example 8.3 L = 6m D = 50 mm Water Find: Average convection heat transfer coefficient

  2. L = 6m D = 50 mm Water

  3. Convection Correlations Laminar Flow in Fully Developed Region in the cylindrical coordinate system (r,x) for fully developed flow

  4. Then, When Scaling

  5. Thus, or Constant surface heat flux condition boundary conditions

  6. const. from overall energy balance : Integrating energy equation with boundary conditions

  7. Assume Constant surface temperature condition

  8. Example 8.4 water Conditions: absorber tube concentrator Find: 1) Length of tube L to achieve required heating 2) Surface temperature Ts,o at the outlet section, x = L Assumptions: 1) Incompressible flow with constant properties 2) Fully developed conditions at tube outlet

  9. 1) From energy balance Conditions: 2) surface temperature at the outlet → laminar flow fully developed condition

  10. Laminar Flow in the Entry Region Thermal entry length Ts= constant, properties at

  11. Combined entry length (hydrodynamic + thermal) Ts= constant properties at

  12. Gz: Gratez number

  13. Turbulent flow in circular tubes Fully developed region • Dittus-Boelter equation (smooth wall) moderate temperature difference properties at Tm

  14. Sieder & Tate (1936) large temperature difference properties at Tm

  15. Gnielinski (1976) properties at Tm • Petukhov (1970) f from Moody diagram properties at Tm

  16. Liquid metals fully developed turbulent flow constant Ts = constant Entry region since For short tubes :

  17. Convection Correlations: Noncircular Tube hydraulic diameter : Ac : flow cross-sectional area P : wetted perimeter

  18. Nusselt numbers and friction factors for fully developed laminar flow in tubes of different cross section

  19. Concentric Tube Annulus inner wall : outer wall : Nusselt numbers

  20. For fully developed laminar flow • One surface insulated and the • other at constant temperature

  21. 2) Uniform heat flux maintained at both surfaces

  22. Heat Transfer Enhancement Internal flow heat transfer enhancement schemes Coil-spring wire insert Twisted tape insert Longitudinal fins Helical ribs

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