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 energy and mass transport from
object to bulk fluid (atmosphere)

• 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 leaf level
  processes
• 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
• By re-arranging Ficks law, integrating, and
  solving for specific situations, we can construct
  equations for those situations

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Molecular diffusion, planar source
zs is the position of the point where the
concentration is measured
zs is the position of the source plane
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Molecular diffusion, spherical source
A(z)
A(zs)
zs
za
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Molecular diffusion, cylindrical source
zs
za
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Diffusive conductance through the integument

• Integument covering that reduces water loss to
  atmosphere
• Three types
• Still air
• Ex. leaf hairs, animal coat
• Calculate gv with equations just presented
  (diffusion in air)
• Hydrophobic cuticle
• Ex. Leaf cuticle, skin, other membranes
• To calculate gv, must use Dv through hydrophobic
  material, not through air
• More common to measure flux and vapor gradient,
  and calculate gv and Dv from that. tend to be
  conservative

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Diffusive conductance through the integument

• Three types
• Pores in cuticle
• Ex. Leaf stomata
• Equation available to calculate gv if you know
  area of individual pores and density
• Easier, and more common to just measure gvs
  well do it in lab

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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

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Using Stability Factors, Y

• When atmosphere is at neutral stability, in
  between stable and unstable, ignore Ym and YH
• 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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Process 3 Forced Convection

• Intermediate scale
• 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
  forces to each other
• Reynolds number, Prandtl number, etc.
• Found in Table 7.3

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Dimensionless Numbers

• Reynolds number
• Ratio of 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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Process 4 Free Convection

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

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Characteristic dimension

• Describes effective surface length of an object

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Forced vs. Free Convection

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

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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 (if
  forced or free convection)
• Use equations for heat and mass transport in
  Table 7.6