Internal Flow: Heat Transfer Correlations

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Internal FlowHeat Transfer Correlations

• Chapter 8
• Sections 8.4 through 8.8

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Fully Developed Flow
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

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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

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Entry Region
Effect of the 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.
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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

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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

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Entry Region (cont)
Why do solutions to internal flow problems often
require iteration?
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Annulus
The Concentric Tube 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

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Annulus (cont)

• Fully Developed Laminar Flow

• Fully Developed Turbulent Flow

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Problem Solar Collector
Problem 8.30 Determine the effect of flow rate
on outlet temperature and heat rate for water
flow through the tube of a flat-plate solar
collector.
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Problem Solar Collector (cont)
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Problem Solar Collector (cont)
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Problem Solar Collector (cont)
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Problem Oven Exhaust Gases
Problem 8.54 Determine effect of ambient air
temperature and wind velocity on temperature at
which oven gases are discharged from a stack.
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Problem Oven Exhaust Gases (cont)
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Problem Oven Exhaust Gases (cont)
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Problem Oven Exhaust Gases (cont)
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Problem Oven Exhaust Gases (cont)