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Internal Forced Convection : Heat Transfer Correlations

Internal Forced Convection : Heat Transfer Correlations. Chapter 8 Sections 8.4 through 8.6. Fully Developed Flow. Uniform Surface Heat Flux : . Uniform Surface Temperature : . For a smooth surface and fully turbulent conditions , the

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Internal Forced Convection : Heat Transfer Correlations

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  1. Internal Forced Convection :Heat Transfer Correlations Chapter 8 Sections 8.4 through 8.6

  2. Fully Developed Flow • Uniform Surface Heat Flux : • Uniform Surface Temperature : • For a smooth surface and fully turbulent conditions ,the Dittus – Boelter equation may be used as a first approximation: • The effects of wall roughness and transitional flow conditions may be considered by using the Gnielinski correlation: Fully Developed Flow • Laminar Flow in a Circular Tube: The local Nusselt number is a constant throughout the fully developed region, but its value depends on the surface thermal condition. • Turbulent Flow in a Circular Tube:

  3. Turbulent Flow: As a first approximation, the Dittus-Boelter or Gnielinski correlation may be used with the hydraulic diameter, irrespective of the surface thermal condition. Surface of roughness : The local Nusselt number is a constant whose value (Table 8.1) depends on the surface thermal condition and the duct aspect ratio. Fully Developed (cont.) Smooth surface: • Noncircular Tubes: • Use of hydraulic diameter as characteristic length: • Since the local convection coefficient varies around the periphery of a tube, approaching zero at its corners, correlations for the fully developed region are associated with convection coefficients averaged over the periphery of the tube. • Laminar Flow:

  4. Effect of the Entry Region Entry Region • The manner in which the Nusselt decays from inlet to fully developed conditions • for laminar flow depends on the nature of thermal and velocity boundary layer • development in the entry region, as well as the surface thermal condition. Laminar flow in a circular tube. • Combined Entry Length: Thermal and velocity boundary layers develop concurrently from uniform profiles at the inlet.

  5. Such a condition may also be assumed to be a good approximation for a uniform inlet velocity profile if Entry Region (cont) • Thermal Entry Length: Velocity profile is fully developed at the inlet, and boundary layer development in the entry region is restricted to thermal effects. Why? • Average Nusselt Number for Laminar Flow in a Circular Tube with Uniform • Surface Temperature: • Combined Entry Length: • Thermal Entry Length:

  6. For longtubes : • For shorttubes : depends strongly on aspect ratio, as well as entry region and surface thermal conditions. See references 11 and 12. Entry Region (cont) • Average Nusselt Number for Turbulent Flow in a Circular Tube : • Effects of entry and surface thermal conditions are less pronounced for turbulent flow and can be neglected. • Noncircular Tubes: • Laminar Flow:

  7. When determining for any tube geometry or flow condition, all • properties are to be evaluated at • Turbulent Flow: As a first approximation, correlations for a circular tube may be used with D replaced by . Entry Region (cont) Why do solutions to internal flow problems often require iteration?

  8. The Concentric Tube Annulus • Surface thermal conditions may be characterized by • uniform temperature or uniform heat flux . Annulus • Fluid flow through • region formed by • concentric tubes. • Convection heat transfer • may be from or to inner • surface of outer tube and • outer surface of inner tube. • Convection coefficients are associated with each surface, where

  9. Nusselt numbers depend on and surface thermal conditions (Tables 8.2, 8.3) Correlations for a circular tube may be used with replaced by . Annulus (cont) • Fully Developed Laminar Flow • Fully Developed Turbulent Flow

  10. Problem: Gas Turbine Vane Problem 8.43: For an air passage used to cool a gas turbine vane, calculate the air outlet temperature and heat removed from the vane.

  11. Problem: Gas Turbine Vane (cont)

  12. Problem: Gas Turbine Vane (cont)

  13. Problem: Oven Exhaust Gases Problem 8.52: Determine effect of ambient air temperature and wind velocity on temperature at which oven gases are discharged from a stack.

  14. Problem: Oven Exhaust Gases (cont)

  15. Problem: Oven Exhaust Gases (cont)

  16. Problem: Oven Exhaust Gases (cont)

  17. Problem: Oven Exhaust Gases (cont)

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