100
Conductances for Heat and Mass Transfer
TABLE 7.3. Some dimensionless groups for heat and mass transfer.
Name
Equation
Reynolds number Re = $
Grashof number
Gr = gd33ST
-TJr
Prandtl number
Pr = -41- DH
Schmidt number Sc = 2
Dl
Nusselt number
Nu = gH" PDH
Explanation
Ratio of inertial
viscous forces
Ratio of a buoyant
force times an inertial
force to the the square
of a viscous force
Ratio of kinematic
viscosity to thermal
diffusivity
Ratio of kinematic
viscosity to mass
diffusivity
Dimensionless
conductance
Symbols
u free stream
fluid velocity
v kinematic
viscosity
d characteristic
dimension
g gravitational
constant
ST Temperature
difference
T kelvin
temperature
DH thermal
diffusivity
Dj molecular
diffusivity of
species j
p molar density
g~ boundary
layer
conductance
groups of the variables have been formed and correlated empirically. By
using these dimensionless groups, the results of a study on, say, heat
transfer to water by a rod with a diameter of 1 cm, can be used to calculate heat transfer from a person's arm to air. It is therefore convenient to
relate conductances to the appropriate dimensionless groups. Once this is
done, the relationships between the dimensionless groups for describing
the transport processes can be obtained directly from the engineering literature. The dimensionless groups that we use are given in Table 7.3. The
Reynolds number, besides being useful for correlation of data on heat and
mass transport, also gives an indication of whether the flow is laminar or
turbulent. At low Re viscous forces predominate and the flow is laminar.
At high Re, inertial forces predominate and the flow becomes turbulent.
The critical Re at which turbulence starts is around 5 x lo5 for a smooth,
flat plate under "average" conditions.
Forced convection refers to the condition in which a fluid is moved
past a surface by some external force (the analysis would be the same
for a surface moving through a stationary fluid). Free convection, on the
other hand, refers to fluid motion brought about by density gradients in the
Conductances for Heat and Mass Transfer
TABLE 7.3. Some dimensionless groups for heat and mass transfer.
Name
Equation
Reynolds number Re = $
Grashof number
Gr = gd33ST
-TJr
Prandtl number
Pr = -41- DH
Schmidt number Sc = 2
Dl
Nusselt number
Nu = gH" PDH
Explanation
Ratio of inertial
viscous forces
Ratio of a buoyant
force times an inertial
force to the the square
of a viscous force
Ratio of kinematic
viscosity to thermal
diffusivity
Ratio of kinematic
viscosity to mass
diffusivity
Dimensionless
conductance
Symbols
u free stream
fluid velocity
v kinematic
viscosity
d characteristic
dimension
g gravitational
constant
ST Temperature
difference
T kelvin
temperature
DH thermal
diffusivity
Dj molecular
diffusivity of
species j
p molar density
g~ boundary
layer
conductance
groups of the variables have been formed and correlated empirically. By
using these dimensionless groups, the results of a study on, say, heat
transfer to water by a rod with a diameter of 1 cm, can be used to calculate heat transfer from a person's arm to air. It is therefore convenient to
relate conductances to the appropriate dimensionless groups. Once this is
done, the relationships between the dimensionless groups for describing
the transport processes can be obtained directly from the engineering literature. The dimensionless groups that we use are given in Table 7.3. The
Reynolds number, besides being useful for correlation of data on heat and
mass transport, also gives an indication of whether the flow is laminar or
turbulent. At low Re viscous forces predominate and the flow is laminar.
At high Re, inertial forces predominate and the flow becomes turbulent.
The critical Re at which turbulence starts is around 5 x lo5 for a smooth,
flat plate under "average" conditions.
Forced convection refers to the condition in which a fluid is moved
past a surface by some external force (the analysis would be the same
for a surface moving through a stationary fluid). Free convection, on the
other hand, refers to fluid motion brought about by density gradients in the