Chapter 8 Internal Forced convection

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Chapter 8 Internal Forced convection

• 8.1 Introduction
• The laminar turbulent flows in channels
• The developing fully developed regions
• The heat transfer rate under two boundary
  conditions
• - Constant heat flux
• - Constant surface temperature
• Method to select a cooling fan

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The laminar turbulent in ducts

• The critical Reynolds number
• Similar to the case of external flow, the
  flow in a duct can be laminar or turbulent. The
  critical Reynolds number is
• Dh is called hydraulic diameter which is
  defined as 4A/P, P is the wetted perimeter A is
  the cross-sectional area of the duct, and ? is
  the kinematic viscosity of the coolant.
• For a duct of rectangular cross-sectional
  area

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• The developing and fully developed regions
• The flow in a duct can be divided into two
  regions
• Near the inlet of the duct, the boundary
  layer starts developing from both sides of the
  channel increases along the flow direction. At
  the point x where the two boundaries meet at the
  center and they cannot increase anymore. From the
  inlet to the meeting point is called developing
  region. Down stream of the developing region is
  called developed or fully developed region.
• - For laminar flow, the thermal boundary
  layer developing length is
• and the velocity boundary developing
  length is
• - For turbulent flow the developing length
  for both thermal and velocity
• boundary layers is

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• The Nussult number and heat transfer coefficient
• At any location in the duct, the Nussult
  number heat flux can be expressed
• h convection heat transfer coefficient
• Tsx Local surface temperature of the duct
• Tmx local mean fluid temperature
• It was found experimentally as well as
  theoretically that, for a given channel, the
  convection heat transfer coefficient is constant
  in the developed region. Near the inlet, where
  the boundary layer thickness increases from zero
  to half height of the duct. Both the temperature
  gradient and the heat transfer coefficient are
  very large at the leading edge and decrease along
  the flow direction and then meet the constant
  values in the developed region, as shown in
  figure above and values of heat transfer
  coefficients for various forms of channels are
  shown in Table 8-3
• The channel surface temperature is,

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8-3 the Nusselt correlation equations

• Nusselt number correlation equations for laminar
  flow

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8-3 the Nusselt correlation equations

• Nusselt number for turbulent flow and the
  transitional region
• 
  (for Re is
  greater than 2300)
• The average bulk mean temperature is used to get
  the properties of the coolant.
• The total heat transfer rate
• The distribution of the surface temperature of
  the duct depends on the boundary conditions.

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8-4 Internal forced convection with constant heat
flux

• The distribution of surface and bulk mean fluid
  temperatures
• The distribution of buck mean
• fluid temperature is linear

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8-4 Internal forced convection with constant heat
flux

• The variation of Tsx is also linear in the fully
  developed region
• The rate of heat transfer is equal to the rate of
  heat absorbed by the coolant
• The maximum surface temperature

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8-5 Internal convection heat transfer--Constant
surface temperature

• The energy balance on a elemental control volume
  (Ts is larger than Tm)
• Integrating from the entrance (x 0),
  where the inlet fluid mean temperature is Tmi, to
  any point x along the duct, where the mean fluid
  temperature is equal to Tmx
• The fluid temperature at any point x is

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8-5 constant surface temperature

• The maximum fluid temperature is at x L or the
  outlet fluid temperature
• The heat transfer rate
• logarithmic mean temperature difference

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Cooling of a hollow PCB

• Given Hollow PCB 12cm x 18cm, total heat
  dissipation 40W
• Tmi 20oC, air volume flow
  rate at inlet section 0.72litre/s
• channel cross-sectional area
  0.3cm x12cm
• Find (a) Tmo, (b) Tsmax
• Solution
• - Assumptions
• 1, Pressure at 1 atm.
• 2. Smooth inner surface
• 3. Steady state operation
• - the inlet condition

12cm
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Cooling of a hollow PCB
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Cooling of a constant surface temperature hollow
PCB

• Given Board 12cm x 20cm, flow rate
  0.72x10-3m3/s, channel 0.3cm x 12cm, Tmi 20oC,
  Ts 60oC
• Find Tmo , Heat dissipation rate
• Solution Assumptions 1. Steady state
  operation
• 
  2. Air behaves as ideal gas
• 
  3. pressure is equal to 1 atm.
• 
  4. Assume Tmo to be 50oC

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Method to select a cooling fan

• Characteristic curves
• - The static pressure developed by a given
  fan depends on its rpm and the flow rate of the
  fluid which it propels. The fan curve is usually
  provided by the manufacturers.
• - The system curve is the total pressure
  loss verses flow rate or velocity of
• a given flow system
• - The intersection of the two curves is the
  operation point of the fan

P1
p2
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Installation considerations

• Inlet or outlet of the duct
• - Preferred position is at the inlet
  positive pressure
• inside the cabinet to prevent air
  infiltration into the
• box from cracks or other openings and the
  air is
• denser and cooler at the position of the
  fan.
• - Heat generated by the motor is forced into
  the system. The inlet air temperature is higher.
• Do not used forced convection if nature
  convection is adequate
• Critical electronics should be mounted near the
  inlet where the coolant
• temperature is lower
• Air velocity should be less than 7m/s, otherwise
  noise will be too large.
• Arrange the system to use nature convection to
  help forced convection
• Series operation helps to increase the pressure
  head and parallel operation helps to increase the
  flow rate.
• Arrange the openings on the side surfaces, not on
  the top surface
• The maximum air temperature at the exit port
  should be less than 70oC
• Make a good arrangement of the boards for small
  flow resistance
• Consider the effect of air pressure change due to
  altitude effect

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• Parallel double the flow rate
• Series double the pressure difference

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• Heat transfer coefficient
• The actual average heat transfer coefficient is
  larger than the following
• developed value. For a given inlet coolant
  temperature, the surface
• temperature is smaller. Then the device
  temperature mounted on the surface is
• Smaller than that calculated by following
  developed h value.

h
x x
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• The following pages will not be taught

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8-5 Internal convection heat transfer--Constant
surface temperature

• The energy balance on a elemental control volume
  (Ts is larger than Tm)
• Integrating from the entrance (x 0),
  where the inlet fluid mean temperature is Tmi, to
  any point x along the duct, where the mean fluid
  temperature is equal to Tmx
• The fluid temperature at any point x is

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Forced convection- internal flow

• The mean film temperature, if one of the
  temperature is unknown, assume one.
• Properties of the coolant
• Calculate the Reynolds number
• - Re 2300, the flow is laminar
• - Re 2300, treat the flow as turbulent
• Select the Nusselt correlation equation
• - The boundary conditions constant
  surface or constant surface heat flux
• - Flow conditions laminar or turbulent
  flow
• Calculate the Nusselt number and heat transfer
  coefficient
• Calculate the heat transfer rate or the unknown
  temperature or both or the area
• Compare the assumed temperature and the
  calculated one. If the different is large,
  re-assume a temperature and repeat the process.

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The pressure loss in a flow system

• The total pressure in a flow system is
  represented by
• Pressure loss can be written in terms of loss
  of velocity head
• pressure loss
• k is called loss factor and it is
  dimensionless. Its value depends on the type of
  obstructions
• Type of obstruction k
• Inlet loss 0.5
• outlet loss 1.0
• channel
• L length of the channel and Dh is the
  hydraulic diameter
• f friction factor For fully developed
  flow is shown in Table 8 1
  

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8-2 The velocity and temperature fields in a duct

• The mass flow rate
• um is the average velocity in the duct.
• The bulk mean fluid temperature
• The energy transport rate of the fluid in
  the duct
• Tm is the average or mean temperature in the
  duct

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Example Hollow PCB- continue

• Find the system or pressure loss curve of example
  .
• u (m/s)
• 0 0
• 0.5 0.246
• 1.0 0.94
• 1.5 2.07
• 2.0 3.65
  

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Example 15-13 continue

• Plot the system curve
  The characteristic of the fan
• Superimpose the two curves
• 
  For u 2m/s, the rpm of the fan
  is selected

rpm