| \(A\) |
Area |
m2 |
L2 |
| \(A_b\) |
Area of cylinder representing animal’s body, measured inside fat |
m2 |
L2 |
| \(A_c\) |
Area in contact with substrate |
m2 |
L2 |
| \(A_e\) |
Area of emittance |
m2 |
L2 |
| \(A_h\) |
Area of cylinder representing animal’s body, measured at fleece tips |
m2 |
L2 |
| \(A_i\) |
Percent of total surface area exposed to radiation source \(i\) |
dimensionless |
— |
| \(A_s\) |
Area of cylinder representing animal’s body, measured at the skin |
m2 |
L2 |
| \(a\) |
Absorptivity |
dimensionless |
— |
| \(a_l\) |
Average absorptivity to long-wave radiation |
dimensionless |
— |
| \(a_s\) |
Average absorptivity to short-wave radiation |
dimensionless |
— |
| \(a(\lambda)\) |
Absorptivity at wavelength \(\lambda\) |
dimensionless |
— |
| \(B\) |
Sky thermal radiation |
W m-2 |
H L-2 |
| \(Br\) |
Breathing rate |
min-1 |
T-1 |
| \(b\) |
Wien constant |
2.8978 \(\times\) 10-3 m K |
Lθ |
| \(C\) |
Total heat exchanged by conduction between animal and environment |
W |
H |
| \(C\) |
Convection |
W m-2 |
M T-1 |
| \(C\) |
Heat capacity |
J K-1 |
H θ-1 |
| \(C_a\) |
Water vapor concentration of the air |
kg m-1 |
M L-1 |
| \(C_e\) |
Water vapor concentration of exhaled air |
kg m-1 |
M L-1 |
| \(C_o\) |
Water vapor concentration at the surface of the organism |
kg m-1 |
M L-1 |
| \(C_S\) |
speed of sound |
3.50 \(\times\) 102 m s-1 |
L T-1 |
| \(C_V\) |
Specific heat of air at constant volume |
20.79 J K-1 mol-1 |
L2 T-2 θ-1 |
| \(c\), \(c_L\) |
Speed of light |
3 \(\times\) 108 m s-1 |
L T-1 |
| \(c, c_p\) |
specific heat |
J kg-1 K-1 |
L2 T-2 θ-1 |
| \(c_v\) |
Volumetric specific heat |
J m-3 K-1 |
H L-3 θ^-1 |
| \(D\) |
Distance |
m |
L |
| \(D\) |
Leaf dimension parallel to the wind direction |
M |
L |
| \(D, L\) |
Characteristic length |
m |
L |
| \(DD\) |
Degree days |
K day |
θ T |
| \(d\) |
Diameter of cylinder representing animal’s body |
m |
L |
| \(_sd_a\) |
Saturation density of the air |
kg m-3 |
M L-3 |
| \(_sd_l\) |
Saturation density of the leaf |
kg m-3 |
M L-3 |
| \(d_i\) |
ith difference term |
dimensionless |
— |
| \(d_b\) |
Fat thickness |
m |
L |
| \(d_f\) |
Fur or feather thickness |
m |
L |
| \(E\) |
Rate of heat exchange between animal and environment by evaporation |
W |
H |
| \(E\) |
Total power |
J s-1 |
M L2 T-3 |
| \(E\) |
Water loss |
kg s-1 m-2 |
M T-1 L-2 |
| \(E\) |
Transpiration rate |
kg m-2 s-1 |
M L-2 T-1 |
| \(E_E\) |
power flow at earth’s surface |
J m-2 s-1 |
M T-3 |
| \(E_b\) |
Body water losses |
W m-2 |
H L-2 T-1 |
| \(E_{ex}\) |
Respiratory water loss |
W m-2 |
H L-2 T-1 |
| \(E_f\) |
Radiation flux per unit frequency |
J m-2 |
H L-2 |
| \(E_k\) |
Kinetic energy |
W |
H |
| \(E_n\) |
Radiation emittance |
J m-2 s-1 |
M T-3 |
| \(E_{sw}\) |
Cutaneous water loss |
W m-2 |
H L-2 T-1 |
| \(E_r\) |
Rate of loss of heat by respiratory mechanisms |
W |
H |
| \(E_r\) |
Surface water loss |
W m-2 |
H L-2 T-1 |
| \(E_s\) |
Rate of loss of heat by sweating |
W |
H |
| \(E_s\) |
Power flow at sun’s surface |
J m-3 s-1 |
M T-3 |
|
|
|
|
| \(E_{\lambda}\) |
Radiation flux per unit wavelength |
J m-3 s-1 |
H L-3 T-1 |
| \(E(\lambda)\) |
Energy density as a function of wavelength |
J m-4 |
M L-2 T-2 |
| \(E(\nu)\) |
Energy density as a function of frequency |
J m-3 s |
M L -1 T-1 |
| \(e\) |
Vapor pressure of atmosphere |
millibar |
M L-1 T-2 |
| \(e\) |
Energy in a photon |
J |
H |
| \(e_x\) |
Net energy gained in period \(x\) |
W |
H T-1 |
| \(F_H\) |
Heat flux |
J s-1 m-2 |
M T-3 |
| \(F_x\) |
Food captured in period \(x\) |
W |
H T-1 |
| \(f\) |
frequency |
m-1 |
L-1 |
| \(f_L\) |
Frequency at listener |
s-1 |
T-1 |
| \(f_s\) |
Frequency at source |
s-1 |
T-1 |
| \(G\) |
Conduction |
W m-2 |
M T-1 |
| \(G\) |
Heat flux density |
W m-2 |
H T-1 L-2 |
| \(Gr\) |
Grashof number |
dimensionless |
— |
| \(g\) |
gravity |
m s-2 |
L T-2 |
| \(H\) |
Rate of heat exchange by convection between animal and environment |
W |
H |
| \(h\) |
height |
m |
L |
| \(h\) |
Planck’s constant |
6.63 \(\times\) 10-34 J s |
H T |
| \(h\) |
Heat transfer coefficient |
J s-1 m-2 K-1 |
M T-3 θ-1 |
| \(h_c\) |
Convection coefficient |
W K-1 |
H T-1 θ-1 |
| \(K\) |
von Karmen’s constant |
|
|
| \(K, K_M\) |
Eddy viscosity |
m2 s-1 |
L2 T-1 |
| \(K_0, K_n\) |
Conductance |
W m-2 K-1 |
H L-2 T-1 θ-1 |
| \(K_b\) |
Boltzmann’s constant |
1.38 \(\times\) 10-23 J K-1 |
H θ-1 |
| \(K_g\) |
Thermal conductance |
W K-1 |
H θ-1 T-1 |
| \(K_H\) |
Eddy diffusivity for heat |
m2 s-1 |
L2 T-1 |
| \(k\) |
Thermal conductivity coefficient |
W m-1 K-1 |
H L-1 θ-1 |
| \(k_a\) |
Thermal conductivity of air |
W m-1 K-1 |
H L-1 θ-1 |
| \(k_c\) |
Constant for convection coefficient of a cylinder |
W m-2 K-1 |
H L-2 θ-1 T-1 |
| \(k_f\) |
Thermal conductivity of fur or feathers |
W m-1 K-1 |
H L-1 θ-1 T-1 |
| \(k_d, k_f\) |
Thermal conductivity of fat |
W m-1 K-1 |
H L-1 θ-1 |
| \(k_h\) |
Thermal conductivity of hair (fleece) |
W m-1 K-1 |
H L-1 θ-1 |
| \(k_s\) |
Constant for convection coefficient of a sphere |
W m-2 K-1 |
H L-2 θ-1 T-1 |
| \(L\) |
Length of cylinder representing the body length of the animal |
m |
L |
| \(L\) |
Latent heat of evaporation |
J kg-1 |
L2 T-2 |
| \(M\) |
Metabolism |
W m-2 |
H L-2 T-1 |
| \(M_b\) |
Body mass |
kg |
M |
| \(M_{fx}\) |
Metabolic cost of foraging in period \(x\) |
W |
H T-1 |
| \(M_{rx}\) |
Metabolic cost while resting in period \(x\) |
W |
H T-1 |
| \(m\) |
mass |
kg |
M |
| \(m\) |
molecular weight |
g mol-1 |
M |
| \(Nu\) |
Nusselt number |
dimensionless |
— |
| \(n\) |
number of moles |
mol |
— |
| \(n\) |
Wave number |
m-1 |
L-1 |
| \(P\) |
Photosynthesis |
W m-2 |
H L-2 T-1 |
| \(\overline{P}\) |
Mean air pressure |
kg m-1 s-2 |
M L-1 T-2 |
| \(p\) |
pressure |
kg m-1 s-2 |
M L-1 T-2 |
| \(Q\) |
Rate of heat loss |
W |
H |
| \(Q\) |
Heat energy |
W m-2 |
H L-2 T-1 |
| \(Q_a\) |
Absorbed radiation |
W |
H T-1 |
| \(Q_a\) |
Abnormal radiation |
W m-2 |
H L-2 T-1 |
| \(Q_e\) |
Emitted radiation |
W m-2 |
H L-2 T-1 |
| \(Q_h\) |
Rate of loss of heat across hair (fleece) |
W |
H |
| \(Q_f\) |
Rate of loss of heat across fat |
W |
H |
| \(Q_H\) |
Rate of heat loss from fleect tips by convection |
W |
H |
| \(Q_{n}\) |
Radiation factor |
W m-2 |
H L-2 T-1 |
| \(Q_{NR}\) |
Net Radiation |
W m-2 |
H L-2 T-1 |
| \(q\) |
Rate of heat loss per unit area |
W m-2 |
H L-2 |
| \(R\) |
ideal gas constant |
J kg-1 mol-1 |
M L2 T-2 |
| \(R\) |
Radiation conductance |
W m-2 K-1 |
H L-2 T-1 θ-1 |
| \(R\) |
Black body radiation |
W m-2 |
H L-2 T-1 |
| \(R_+\) |
Total long- and short-wave radiation absorbed by the animal per unit time |
W |
H |
| \(R_−\) |
Total long-wave radiation emitted by the animal per unit time |
W |
H |
| \(R_a\) |
Thermal radiation originating in atmosphere |
W m-2 |
H L-2 |
| \(Re\) |
Reynolds number |
dimensionless |
— |
| \(R_g\) |
Thermal radiation originating from earth’s surface (including vegetation) |
W m-2 |
H L-2 |
| \(R_{Nh}\) |
Net radiation absorbed or emitted at hair tips |
W |
H |
| \(R_{Na}\) |
Net radiation absorbed or emitted at hair tips if temperature of hair tips were the same as that of the air |
W |
H |
| \(R_p\) |
short-wave radiation from the sun and sky |
W m-2 |
H L-2 T-1 |
| \(R_v\) |
Respiration rate |
m3 s-1 |
L3 T-1 |
| \(r\) |
radius |
m |
L |
| \(r\) |
Reflectivity |
dimensionless |
— |
| \(r\) |
Distance along a radius of a cylinder measured from its center |
m |
L |
| \(r_E\) |
Mean distance from earth to sun |
1.5 \(\times\) 1011 m |
L |
| \(r_a\) |
Resistance to water diffusion across the boundary layer of air |
s m-1 |
T L-1 |
| \(r_b\) |
Body radius (not including fat) |
m |
L |
| \(r_e\) |
Resistance to water vapor loss |
s m-1 |
T L-1 |
| \(r_l\) |
Internal resistance of leaf |
s m-1 |
T L-1 |
| \(r_s\) |
Skin radius |
m |
L |
| \(r_s\) |
Radius of sun |
7.1 \(\times\) 108 m |
L |
| \(r_h\) |
Hair (fleece-tip) radius |
m |
L |
| \(r. h.\) |
Relative humidity |
dimensionless |
— |
| \(r(\lambda)\) |
Reflectivity at wavelength \(\lambda\) |
dimensionless |
— |
| \(S\) |
Direct solar radiation |
W m-2 |
H L-2 T-1 |
| \(S\) |
Sky radiation |
W m-2 |
H L-2 T-1 |
| \(SA\) |
Surface area |
m2 |
L2 |
| \(s\) |
Sky (scattered and reflected solar) radiation per unit area impinging on animal |
W m-2 |
H |
| \(T\) |
Temperature |
K |
θ |
| \(T_a\) |
Air temperature |
K |
θ |
| \(T_{amax}\) |
Maximum daily air temperature |
K |
θ |
| \(T_{amin}\) |
Minimum daily air temperature |
K |
θ |
| \(T_B\) |
Boundary temperature |
K |
θ |
| \(T_b\) |
Body temperature of animal |
K |
θ |
| \(T_e\) |
Effective temperature, operative temperature |
K |
θ |
| \(T_f\) |
Fruit temperature |
K |
θ |
| \(T_g\) |
Ground temperature |
K |
θ |
| \(T_h\) |
Surface, "radiant or hair (fleece-tip) temperature of animal |
K |
θ |
| \(T_l\) |
Leaf temperature |
K |
θ |
| \(T_o\) |
Temperature of organism |
K |
θ |
| \(T_o, T_r, T_S\) |
Surface temperature |
K |
θ |
| \(T_s\) |
Skin temperature of animal |
K |
θ |
| \(T_s\) |
Surface temperature of sun |
K |
θ |
| \(T_t\) |
Threshold temperature |
K |
θ |
| \(T_w\) |
Wall temperature |
K |
θ |
| \(t\) |
time |
s |
T |
| \(t(\lambda)\) |
Transmittance at wavelength \(\lambda\) |
dimensionless |
— |
| \(U\) |
iternal energy |
J |
M L2 T-2 |
| \(V\) |
volume |
m3 |
L3 |
| \(V\) |
Fluid velocity |
m s-1 |
L T-1 |
| \(V_L\) |
Volume of the lungs |
m3 |
L3 |
| \(V_L\) |
Listener velocity |
m s-1 |
L T-1 |
| \(V_s\) |
Source velocity |
m s-1 |
L T-1 |
| \(v\) |
velocity |
m s-1 |
L T-1 |
| \(v, w\) |
Wind speed |
m s-1 |
L T-1 |
| \(v\) |
volume |
m3 |
L3 |
| \(W\) |
work |
kg m2 s-2 = J |
M L2 T-2 |
| \(W\) |
Leaf dimension transverse to the wind |
m |
L |
| \(W_x\) |
Metabolic cost of waiting through period \(x\) |
W |
H T-1 |
| \(w\) |
Weight per unit height |
kg s-2 |
M T-2 |
| \(x\) |
Boundary layer thickness |
m |
L |
| \(X_a\) |
Volume fraction - air |
dimensionless |
— |
| \(X_m\) |
Volume fraction - minerals |
dimensionless |
— |
| \(X_o\) |
Volume fraction - organics |
dimensionless |
— |
| \(X_w\) |
Volume fraction - water |
dimensionless |
— |
| \(Z_f\) |
“Impedance” to flow of heat through fat |
s K J-1 |
θ W-1 |
| \(Z_h\) |
“Impedance” to flow of heat through hair |
s K J-1 |
θ W-1 |
| \(z\) |
Depth |
m |
L |
| \(\alpha\) |
“Conductance” associated with radiation and convection |
W K-1 |
W-1 |
| \(\alpha\) |
angle |
radians |
— |
| \(\beta\) |
“Conductance” associated with animal’s insulation (fat and hair) |
W K-1 |
W-1 |
| \(\gamma\) |
Thermal diffusivity |
m2 s-1 |
L2 T-1 |
| \(\delta\) |
Boundary layer thickness |
m |
L |
| \(\varepsilon\) |
Emissivity |
dimensionless |
— |
| \(\phi\) |
Energy flux |
W m-2 |
H L-2 T-1 |
| \(\eta\) |
Small scale eddy size |
m |
L |
| \(\lambda\) |
wavelength |
m |
L |
| \(\lambda_B\) |
Wavelength behind source |
m |
L |
| \(\lambda_F\) |
Wavelength in front of source |
m |
L |
| \(\lambda_m\) |
wavelength at which black-body spectrum has maximum energy density |
m |
L |
| \(\lambda_{max}\) |
Wavelength of maximum radiation |
m |
L |
| \(\mu\) |
Fluid viscosity |
kg m-1 s-1 |
M L T-1 |
| \(\nu\) |
Kinematic viscosity |
m2 s-1 |
L2 T-1 |
| \(\nu\) |
frequency |
s-1 |
T-1 |
| \(\rho\) |
Density |
kg m-3 |
M L-3 |
| \(\sigma\) |
Stefan-Boltzmann constant |
5.67 \(\times\) 10-8 W m-2 K-4 |
H L-2 θ-4 |
| \(\tau\) |
Shear stress |
kg m-1 s-2 |
M L-1 T-2 |
| \(\tau_t\) |
Shear stress attributed to turbulence |
kg m-1 s-2 |
M L-1 T-2 |