186
Animals and their Environment
where Rabs is the flux density of absorbed radiation, Lo, is the flux density
of outgoing, emitted radiation from the surface, M is the rate of metabolic
heat production per unit surface area, h E is the latent heat loss from
evaporation of water, H is the rate of sensible heat loss, G is the rate of
heat loss to the substrate by conduction, and q is the rate of heat storage
in the animal per unit surface area.
Initially, we concern ourselves only with steady-state conditions for
which the heat storage rate q is zero. The rate of heat storage is equal to
the heat capacity of the animal multiplied by the rate of change of body
temperature, so if the heat storage rate is zero, the rate of change of body
temperature must also be zero. For simplicity, we also assume G = 0.
The emitted radiation [Lo, = E,~T;] and sensible heat [H =
cpgH(T, - T,)] terms both involve the surface temperature of the animal. It is always possible to set a value for surface temperature which
balances Eq. (12. I), but that temperature may be too high or too low for
the animal to remain alive. If body temperature and metabolic rate are
specified, then Eq. (12.1) can be used to find environments that are energetically acceptable (Rabs and Ta that will balance the energy budget). On
the other hand, we could measure or estimate Rabs, Ta, and Tb and compute M. Knowing M, we can specify food needs for thermoregulation in
a given climate.
Equation (12.1) is not very useful as it stands because of its strong
dependence on surface temperature, a quantity that is hard to estimate,
or even to measure. Body temperature, at least for endotherms, is easily
estimated since it is under tight metabolic control. This fact can be used
to eliminate surface temperature from the energy balance equation. Figure 12.1 shows the assumptions we make about the source (M) and sink
(hE) of heat, and the resistances to heat flow from the body core to the
environment. In a nonsweating animal, much of the latent heat loss is
through breathing, or panting, and the remainder is from beneath the
coat, which generally has a much higher resistance than the tissues. It is
therefore justified to lump latent heat loss with metabolic heat production
and place them at the body core. Later we do a more complete analysis
which does not restrict the location of the latent heat loss. It is often useful
to combine coat and tissue conductance into a whole body conductance:
Since all of the heat from the body core flows through g ~ b ,
we can
write
where c, is the specific heat of air. Equation (12.1) can now be rewritten
explicitly showing the surface temperature dependence:
Animals and their Environment
where Rabs is the flux density of absorbed radiation, Lo, is the flux density
of outgoing, emitted radiation from the surface, M is the rate of metabolic
heat production per unit surface area, h E is the latent heat loss from
evaporation of water, H is the rate of sensible heat loss, G is the rate of
heat loss to the substrate by conduction, and q is the rate of heat storage
in the animal per unit surface area.
Initially, we concern ourselves only with steady-state conditions for
which the heat storage rate q is zero. The rate of heat storage is equal to
the heat capacity of the animal multiplied by the rate of change of body
temperature, so if the heat storage rate is zero, the rate of change of body
temperature must also be zero. For simplicity, we also assume G = 0.
The emitted radiation [Lo, = E,~T;] and sensible heat [H =
cpgH(T, - T,)] terms both involve the surface temperature of the animal. It is always possible to set a value for surface temperature which
balances Eq. (12. I), but that temperature may be too high or too low for
the animal to remain alive. If body temperature and metabolic rate are
specified, then Eq. (12.1) can be used to find environments that are energetically acceptable (Rabs and Ta that will balance the energy budget). On
the other hand, we could measure or estimate Rabs, Ta, and Tb and compute M. Knowing M, we can specify food needs for thermoregulation in
a given climate.
Equation (12.1) is not very useful as it stands because of its strong
dependence on surface temperature, a quantity that is hard to estimate,
or even to measure. Body temperature, at least for endotherms, is easily
estimated since it is under tight metabolic control. This fact can be used
to eliminate surface temperature from the energy balance equation. Figure 12.1 shows the assumptions we make about the source (M) and sink
(hE) of heat, and the resistances to heat flow from the body core to the
environment. In a nonsweating animal, much of the latent heat loss is
through breathing, or panting, and the remainder is from beneath the
coat, which generally has a much higher resistance than the tissues. It is
therefore justified to lump latent heat loss with metabolic heat production
and place them at the body core. Later we do a more complete analysis
which does not restrict the location of the latent heat loss. It is often useful
to combine coat and tissue conductance into a whole body conductance:
Since all of the heat from the body core flows through g ~ b ,
we can
write
where c, is the specific heat of air. Equation (12.1) can now be rewritten
explicitly showing the surface temperature dependence: