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INTERNAL FLOW

INTERNAL FLOW. Hydrodynamic Considerations Thermal Considerations Overall Energy Balance Convection Correlations: Circular & Non-Circular Tubes Concentric Tube Annulus Heat Transfer Enhancement. hydrodynamic entrance region. fully developed region.

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INTERNAL FLOW

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  1. INTERNAL FLOW • Hydrodynamic Considerations • Thermal Considerations • Overall Energy Balance • Convection Correlations: • Circular & Non-Circular Tubes • Concentric Tube Annulus • Heat Transfer Enhancement

  2. hydrodynamic entrance region fully developed region Hydrodynamic Considerations u r ro x hydrodynamic entrance region flow acceleration inertia force ~ pressure force ~ viscous force

  3. u r ro ro x hydrodynamic entrance region fully developed region hydrodynamically fully developed region no acceleration (inertia force = 0) pressure force ~ viscous force constant pressure gradient fully developed condition :

  4. r ro u(r,x) r dr x Characteristic Velocity mean velocity over the cross-sectional area

  5. Reynolds number : critical Reynolds number : hydrodynamic entry length:

  6. r ro constant or Velocity Profile in Fully Developed Region momentum eq: boundary conditions:

  7. Friction Coefficient friction coefficient Moody friction factor

  8. thermal entrance region fully developed region Thermal Considerations u r ro ro x hydrodynamic entrance region fully developed region Ts Ti r ro x Thermal entry length :

  9. Mixed Mean Temperature (bulk fluid temperature, mixing-cup temperature) r ro u(r,x), T(r,x) dr x heat transfer coefficient :

  10. Suppose alone Thermally Fully Developed Condition experimental observation: in the far downstream region, h =const. for a given fluid and tube diameter = constant (not function of x) = constant

  11. thermally fully developed condition

  12. const. const. const. Constant surface heat flux condition Constant surface temperature condition

  13. Velocity profile ro r Temperature profile ro r Example 8.1 Ts ro Flow slug flow: liquid metal, Pr << 1 Find: Nusselt number at the prescribed location Assumptions: Incompressible, constant property flow

  14. Thus

  15. x dx Overall Energy Balance D perimeter:P = pD

  16. D x dx or

  17. const. Constant surface heat flux condition = constant in fully developed region

  18. or Constant surface temperature condition

  19. For a tube of length L

  20. Let then Log Mean Temperature Difference (LMTD)

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