T t
ð Þ ¼ T 0
ð Þ þ ut
ð6:115Þ
so that from solving Eq. (6.110) the change of the mean temperature of the system
will be governed by the following equation:
T 0 ðtÞ ¼ Tð0Þ þ ut À utð1 À expðÀt=sÞ
ð 6:116Þ
and thus, the heating rate of the surface will be
@T 0
@t
¼ uð1 À expðÀt=sÞÞ
ð6:117Þ
so that the rate of heating of the system will be nil in the beginning and will increase
to u in one later instant t much higher than the time constant. When the ratio ðÀt=sÞ
exceeds 3, the exponential term in Eq. (6.116) can be neglected and this equation
becomes
T 0 t
ð Þ ¼ T 0
ð Þ þ uðt À sÞ
ð 6:118Þ
so that the system heats at the same rate as the environmental temperature with a
time lag s, corresponding to a temperature lag of uT. Monteith and Unsworth
(2013) mentioned for forest canopies that a ramp change regime could command
the condensation rate in trunks of trees although imperceptible due to an eventual
roughness of the surface. In this context, Unsworth et al. (2004) reported that
saturated air in the forest canopies of Douglas fir became saturated in summer
mornings shortly after sunrise, defending that condensation on tree trunks could be
determinant for bark-dwelling organisms.
6.5 Mass Transfer
6.5.1 Gases and Water Vapor Transfer
In the free atmosphere, turbulent diffusion controls the circulation of gases and
water vapor by convective processes like those of heat convection, with less
influence on ground surfaces on calm nights. The turbulent transfer of water vapor
and carbon dioxide is of utmost relevance for the biosphere and forest canopies. For
example, the amount of carbon dioxide absorbed by a green crop canopy is roughly
of the same order of magnitude as all the carbon dioxide existing up to a height of
30 m above the canopy.
Although the daily concentration of carbon dioxide changes in the boundary
surface layer due to the photosynthesis dynamics, the amount of removed carbon
dioxide is of a maximum of 15% of the diurnal mean CO 2 concentration in the
208
6 Heat and Mass Transfer Processes
ð Þ ¼ T 0
ð Þ þ ut
ð6:115Þ
so that from solving Eq. (6.110) the change of the mean temperature of the system
will be governed by the following equation:
T 0 ðtÞ ¼ Tð0Þ þ ut À utð1 À expðÀt=sÞ
ð 6:116Þ
and thus, the heating rate of the surface will be
@T 0
@t
¼ uð1 À expðÀt=sÞÞ
ð6:117Þ
so that the rate of heating of the system will be nil in the beginning and will increase
to u in one later instant t much higher than the time constant. When the ratio ðÀt=sÞ
exceeds 3, the exponential term in Eq. (6.116) can be neglected and this equation
becomes
T 0 t
ð Þ ¼ T 0
ð Þ þ uðt À sÞ
ð 6:118Þ
so that the system heats at the same rate as the environmental temperature with a
time lag s, corresponding to a temperature lag of uT. Monteith and Unsworth
(2013) mentioned for forest canopies that a ramp change regime could command
the condensation rate in trunks of trees although imperceptible due to an eventual
roughness of the surface. In this context, Unsworth et al. (2004) reported that
saturated air in the forest canopies of Douglas fir became saturated in summer
mornings shortly after sunrise, defending that condensation on tree trunks could be
determinant for bark-dwelling organisms.
6.5 Mass Transfer
6.5.1 Gases and Water Vapor Transfer
In the free atmosphere, turbulent diffusion controls the circulation of gases and
water vapor by convective processes like those of heat convection, with less
influence on ground surfaces on calm nights. The turbulent transfer of water vapor
and carbon dioxide is of utmost relevance for the biosphere and forest canopies. For
example, the amount of carbon dioxide absorbed by a green crop canopy is roughly
of the same order of magnitude as all the carbon dioxide existing up to a height of
30 m above the canopy.
Although the daily concentration of carbon dioxide changes in the boundary
surface layer due to the photosynthesis dynamics, the amount of removed carbon
dioxide is of a maximum of 15% of the diurnal mean CO 2 concentration in the
208
6 Heat and Mass Transfer Processes