onelump: One-lump Transient Heat Budget for Constant Environment

In mrke/NicheMapR: R implementation of Niche Mapper software for biophysical modelling

One-lump Transient Heat Budget for Constant Environment

Description

Transient, 'one-lump', heat budget for computing rate of change of temperature under a constant environment Michael Kearney, Raymond Huey and Warren Porter developed this R function and example in September 2017.

Usage

onelump(t, Tc_init, Ww_g, geom, Tair, Trad, vel, Qsol, Zen, ...)

Arguments

t	= seq(1,3600,60), time intervals (s) at which output is required
Tc_init	= 5, initial temperature (°C)
Ww_g	= 500, animal weight (g)
geom	= 2, organism shape, 0-5, Determines whether standard or custom shapes/surface area/volume relationships are used: 0=plate, 1=cyl, 2=ellips, 3=lizard (desert iguana), 4=frog (leopard frog), 5=custom (see parameter 'shape_coefs')
Tair	= 30, air temperature (°C)
Trad	= 30, radiant temperature (°C), averaging ground and sky
vel	= 0.1, wind speed (m/s)
Qsol	= 500, solar radiation (W/m2)
Zen	= 20, zenith angle of sun (90 is below horizon), degrees
k_flesh	= 0.5, thermal conductivity of flesh (W/mK, range: 0.412-2.8)
q	= 0, metabolic heat production rate W/m3
c_body	= 3073, specific heat of flesh J/(kg-K)
emis	= 0.95, emissivity of animal (0-1)
rho_body	= 932, animal density (kg/m3)
alpha	= 0.85, solar absorptivity, decimal percent
shape_coefs	= c(10.4713,.688,0.425,0.85,3.798,.683,0.694,.743), custom shape coefficients. Operates if geom=5, and consists of 4 pairs of values representing the parameters a and b of a relationship AREA=a*Ww_g^b, where AREA is in cm2 and Ww_g is in g. The first pair are a and b for total surface area, then a and b for ventral area, then for silhouette area normal to the sun, then silhouette area perpendicular to the sun
shape_b	= 1/5, proportionality factor (-) for going from volume to area, represents ratio of width:height for a plate, length:diameter for cylinder, b axis:a axis for ellipsoid
shape_c	= 1/5, proportionality factor (-) for going from volume to area, represents ratio of length:height for a plate, c axis:a axis for ellipsoid
posture	= 'n' pointing normal 'n', parallel 'p' to the sun's rays, or 'a' in between?
orient	= 1, does the object orient toward the sun? (0,1)
fatosk	= 0.4, configuration factor to sky (-) for infrared calculations
fatosb	= 0.4, configuration factor to substrate for infrared calculations
alpha_sub	= 0.2, substrate solar reflectivity, decimal percent
pdif	= 0.1, proportion of solar energy that is diffuse (rather than direct beam)
fluid	= 0, fluid type, air (0) or water (1)
press	= 101325, air pressure (Pa)

Value

Tc Core temperature (°C)

Tcf Final (steady state) temperature (°C), if conditions remained constant indefinitely

tau Time constant (s)

dTc Rate of change of core temperature (°C/s)

Examples

library(NicheMapR)

# compare heating rates of a variety of different-sized objects

t=seq(1,3600*2,60) # times (in seconds) to report back values - every minute for 2 hrs
tmins <- t/60

par(mfrow = c(1,2))
Ww_g <- 5 # body weight, g
Tc_init <- 20 # initial body temperature, °C
geom <- 2 # shape (2 = ellipsoid)
Tair <- 20 # air temperature, °C
Trad <- Tair # radiant temperature, °C
vel <- 1 # wind speed, m/s
Qsol <- 500 # horizontal plane solar radiation, W/m2
Zen <- 20 # zenith angle of sun, degrees
alpha <- 0.85 # solar absorptivity, -

Tbs<-onelump(t=t, alpha = alpha, Tc_init = Tc_init, Ww_g = Ww_g,
  geom = geom, Tair = Tair, Trad = Trad, vel = vel, Qsol = Qsol, Zen = Zen)
plot(Tbs$Tc ~ tmins, type= 'l' ,col = 1, ylim = c(20, 30), ylab = 'Temperature, °C',xlab='time, min', las = 1)
text(80, 27, "    500 g")
text(80, 24.5, "5 g")
text(90, 20.5, "Tair for both sizes", col = "blue")
text(90, 26, "   vel = 1.0 m/s")
text(90, 23.5, "     vel = 1.0 m/s")

Ww_g <- 500 # body weight, g
Tbs<-onelump(t=t, alpha = alpha, Tc_init = Tc_init, Ww_g = Ww_g,
  geom = geom, Tair = Tair, Trad = Trad, vel = vel, Qsol = Qsol, Zen = Zen)
points(Tbs$Tc~tmins,type='l',lty = 2, col=1)
abline(Tair,0, lty = 1, col = 'blue')
abline(h = Tair + .1, lty = 2, col = 'blue')

Ww_g <- 5 # body weight, g
Tair <- 25 # air temperature, °C
vel <-0.5 # wind speed, m/s

Tbs<-onelump(t=t, alpha = alpha, Tc_init = Tc_init, Ww_g = Ww_g,
  geom = geom, Tair = Tair, Trad = Trad, vel = vel, Qsol = Qsol, Zen = Zen)
plot(Tbs$Tc~tmins,type='l',col=1,ylim=c(20,30),ylab='Temperature, °C',xlab='time, min', las = 1)
abline(h = Tair, lty = 1, col = 'blue')

Ww_g <- 500 # body weight, g
Tair <- 20 # air temperature, °C
vel <-1 # wind speed, m/s

Tbs<-onelump(t=t, alpha = alpha, Tc_init = Tc_init, Ww_g = Ww_g,
  geom = geom, Tair = Tair, Trad = Trad, vel = vel, Qsol = Qsol, Zen = Zen)
points(Tbs$Tc~tmins,type='l',lty = 2, col=1)
abline(h = Tair, lty = 2, col = 'blue')

text(65, 29.65, "5 g")
text(85, 27, "500 g")
text(90, 20.5, "Tair for large animal", col = "blue")
text(90, 25.4, "Tair for small animal", col = "blue")
text(80, 28.65, "vel = 0.5 m/s")
text(93, 26, "vel = 1.0 m/s")

mrke/NicheMapR documentation built on Jan. 13, 2025, 9:11 p.m.