Chapter 7: Conductances for Heat and Mass Transfer

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Chapter 7 Conductances for Heat and Mass
Transfer

• Continue with investigation of conductance
• Now consider methods for computing conductances
  themselves
• Return to two laws discussed in last chapter
• Ficks Law and Fouriers Law
• Need to manipulate equations to determine
  conductances

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Four Processes for Conductances

• Molecular Diffusion
• Random molecular movement
• Forced Convection
• Fluid moved passed surface by external force
• Free Convection
• Fluid flow generated by temperature gradients
• Turbulent Transport or Eddy Diffusion
• Wind over rough surfaces

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Determining a Conductance

• Consider the process
• Decide what is moving in the system
• Heat? H2O? CO2?
• Determine the scale of the process
• Molecular diffusion happens on a VERY SMALL SCALE
• Forced and free convection are a leaf level
  process
• Turbulent transport is a field level process
• Select correct equation from Table 7.6
• If it is molecular diffusion, use equation for
  specific movement (planar, cylindrical,
  spherical)

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Process 1 Molecular Diffusion

• Occurs on a very small scale
• Molecules move along by random collisions along a
  potential gradient
• No Bulk Flow of Fluid
• Examples
• Air-filled pores in soils
• Stomatal cavities of leaves
• Animal coats
• Where hair/feathers makes up a small of total
  volume

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Process 1 Molecular Diffusion

• Ficks Law for Steady State Diffusion

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Process 1 Molecular Diffusion
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Process 1 Molecular Diffusion
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Process 1 Molecular Diffusion
A(z)
A(zs)
zs
za
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Process 1 Molecular Diffusion
A(z)
A(zs)
zs
za
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Process 1 Molecular Diffusion

• Finding molar density and Diffusivity
• Temperature and pressure dependent
• Use Table A.1
• For the diffusivity of gas j in air

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• Example The finger of a wool glove has a
  diameter of 3 cm. The diameter of a persons
  finger inside the glove is 2 cm. If wool acts as
  a layer of still air around the finger, what is
  the conductance of the glove finger at 20o C and
  100 kPa? What if it was a mitten instead?

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Process 2 Turbulent Transport

• Diffusion of eddy packets of air on a grand scale
• Similar to diffusion molecular diffusion because
• Packets are passively moving from one place to
  another
• The turbulent movement of heat and mass is a
  topic for an entire course
• We do not have time for that
• Read 7.4 to 7.6 on your own

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Stability in the Atmosphere

• Hear this term on the news
• Stable conditions
• Heat flux is negative
• Air temperature gt surface temperature
• Air is stratified
• We see this when smoke rises then seems to move
  horizontally

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Instability in the Atmosphere

• Unstable conditions
• Heat flux, H, is positive
• Surface temperature gt Air temperature
• Heat moving from surface up into the atmosphere
• Creates thermal turbulence
• Packets rising because they have lower density

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Calculating Turbulent Transport Fluxes

• Combine mechanical and thermal turbulence into
  one equation
• When atmosphere is at neutral stability, in
  between stable and unstable, ignore Ym and YH

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Using Stability Factors, Y

• Typically, when u gt 3 m/s, Y can be ignored
• Must use them when
• Wind speed is low
• Night time stable conditions

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• Example Consider a flat surface with snow on it
  where air temperature is 10o C, hr is 100, u(2m)
  10 m/s, and Pa 92 kPa. Find the water vapor
  and heat flux from the surface. (zm comes from
  Table 5.1, 0.002 m)

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Process 3 Forced Convection

• Intermediate scale
• ltmm to m/km for atmospheric fluxes
• Typically mm to m scale
• Leaf, flat plate, etc.
• Calculations involve empirical formulae
• Taken from Fluid Dynamics and Heat/Mass Transfer
• Use dimensionless numbers that relate relevant
  numbers to each other
• Reynolds number, Prandtl number, etc.
• Found in Table 7.3

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Dimensionless Numbers

• Reynolds number
• Relates inertial forces to viscous forces
• Determines laminar or turbulent conditions
• Value of 5 x 105 is typical difference between
  laminar and turbulent flow for an average plate
• Calculated

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Calculating Forced Convection Conductance
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Natural Turbulent Flow Correction Factor
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Free Convection

• Similar principle but uses different
  dimensionless numbers
• Laminar free convection for air

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Example Leaf in wind
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Forced vs. Free Convection

• Often you have both forces in the same problem
• How do you separate?
• If it gtgt than 1 then it is free convection
• If it is ltlt than 1 then it is forced
• In between Both must be considered

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Example Find Gr and ratio for the leaf
conductance example
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Evaluating Conductance 4 Basic Types
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Calculating Conductances

• Once you have determined the process
• Find Characteristic Dimension from Table 7.5
• Use equations for heat and mass transport in
  Table 7.6