Conductances
for Heat and
Mass Transfer 7
This chapter continues the discussion of transport, and focuses on methods for computing the conductances and resistances needed for the
calculations in Ch. 6. We first discuss conductances on the smallest spatial scale; molecular diffusion. It is by this process that heat and mass are
transported in still air or water, such as in parts of the lungs of animals,
in soils, in the substomatal cavities of leaves, and in animal coats. The
equations for turbulent transport of heat and mass on larger scales in the
atmosphere are similar to those for molecular diffusion, so those equations
are discussed following the molecular diffusion equations. After diffusion processes are discussed, we consider an intermediate scale; namely,
convective heat and mass transfer theory as it applies to fluids moving
over plates, cylinders, and spheres (simulating leaves, stems, fruits, and
animals).
7.1 Conductances for Molecular Diffusion
To determine a conductance for molecular transport, we return to Fick's
law for steady diffusion of some component j (Eq. (6.5)):
where D j is the diffusivity and dCj/dz is the concentration gradient.
Assume that all of the material that diffuses across an imaginary boundary
at z originated at a surface with area A(z,) where the flux density is F (zs),
which is assumed to be constant, then:
where A(z) is the area of the surface at z. Integration of Eq. (7.2),
combining the result with Eq. (6.7), and solving for conductance gives:
where za is at the outer edge of the layer for which the diffusive conductance is being computed. Equation (7.3) is easily solved for several