Chapter 17 List of Symbols

Symbol	Quantity	Unit	Dimension
$A$	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