Heat transfer, heat production
and temperature regulation in
animals
Physics Spring 2012
Lou Armentano
learment@wisc.edu
263-3490
Why does temperature matter?
• chemical reactions of metabolism are
slower at low temperatures
– rate approximately doubles per 10o C rise
• proteins (enzymes, structural proteins),
DNA and RNA denature at high
temperatures
• lipids in membrane require temperature to
maintain fluidity for function
– fatty acid profile can differ depending on
species habitat temperature
All animals produce heat
• First law of thermodynamics, about the
conservation of energy:
• Second law of thermodynamics, about
entropy
• so they all must lose heat to
environment or will cook themselves to
death
• if they lose heat faster than they generate
it, body temperature falls
• and vice-versa
Heat transfer
• Conduction
• Convection
– forced or natural
• Radiation
• Evaporation
– heat loss only
• in all cases surface
area is important
Conduction
• heat transfer between non-moving matter
• within on matter or between two touching
matters
• solid to solid, solid to unmoving fluid,
unmoving fluid to unmoving fluid
• fluid is liquid (like water) or gas (like air)
Conduction and heat of fusion
Convection
• movement between a body and a moving fluid
• fluid movement can be generated by heat
– natural or passive convection
• fluid movement can be forced
– water pump forcefully moves engine coolant through
engine convecting heat from cylinders to coolant and
carrying it to radiator where it convects out of coolant
to solid radiator and convects off of radiator to air
– cooling fan and car movement forcefully convect air
through radiator
– heart forces blood from body core to surface
– fans cool (or heat) body by forced convection
Conduction (+ some Convection) to liquid
Evaporation when emerges from pond
Forced
convection
Reducing
convective
loss with
animal fibers
Radiation
• electro magnetic transfer of heat
• can operate through a vacuum
• long distance (sun)
P = rate of heat transfer, A = area, T = temperature
Radiation
Avoiding
heat gain
Seeking heat
gain – notice
surface area
exposure and
shape change
Evaporation
• latent heat of vaporization of water
– 540 kcal/kg water evaporated
– 2260 joule/g water evaporated
• can cool animal when environmental
temperature exceeds body temperature
• cannot cool animal if air is saturated with water
(100% relative humidity at skin temperature)
• THI (temperature humidity index)
– “its not the heat its the humidity”
– its both
• air movement replaces more water saturated air
with fresh drier air
Evaporation
Forced convection with evaporation
Note flattened tongue
to increase surface
area
Heat can transfer into animal
Radiation
Forced Convection (pumps active)
Conduction (pumps off, people still)
Conduction
• heat loss between unmoving matter (solids or
still fluids)
• Q/time = conductance (k)/depth (L) * area *
temperature difference
• heat loss/area at fixed temp difference = k / L
• L is ‘depth’ of solid
• k (conductance) is proportional to density
– Insulating materials (styrofoam, fiberglass blankets,
down jackets) are all low density to resist heat
– One reason why loosing heat to air requires
convection
American goldfinch
In this species feathers change
with season (bright yellow in
summer mating season)– but
piloerection allows
instantaneous adaptation to hot
and cold temperatures (and
sitting vs. flying)
Conduction
• heat loss between unmoving matter (solids or
still fluids)
• Q/time = heat loss
• heat loss/area = k / L * temperature difference
• l is ‘depth’ of solid
• k is proportional to density
• creating an unmoving layer of low density air
= smaller k
• increasing L reduces rate of heat transfer
• fluffy hair, fur or feathers do both!
• Offsets increased delta T in winter
Convection
• Rate of heat transfer by convection =
h*A*(Ts - Tb)
Ts=surface temperature (at interface of solid
and fluid)
Tb = temperature somewhere far enough from
the surface so its the average temperature of
the mass of fluid (think air temperature)
A is the contact area
Camels
Temperature can
vary by 6 degrees C
in camels deprived
of water – slows heat
gain by convection
during day, increase
loss at night
Heat transfer depends on
• temperature difference
determines direction and rate
• area
• how does area relate to animal mass?
Not all animals share
same shape
volume (or mass) vs. area
sphere
Volume = 4/3  r3
Surface = 4  r2
cylinder
Volume =  r2 x height
Surface = 2  rh + 2  r2
cube
Volume =L3
Surface = 6 * L2
square-cube law
Area increases
by square of
“length”
Volume increases
by cube of
“length”
even if shape described by multiple ‘lengths’ (like radius and
height of a cylinder) all “lengths” increase proportionally to
maintain shape (cylinder gets bigger or smaller but not
relatively skinner or fatter)
same
shaped
cylinders
(r = x*h)
different “shaped” cylinders (have
different “B”-see following slides)
Power function and log-log
transform
Y = B * Xz
log Y = log B + Z * log X
2/3
2/3
power rule: area = B * mass
B varies (slightly) with shape
log surface area
5
y = 0.6667x + 0.6845
4
y = 0.6667x + 0.7432
y = 0.6667x + 0.7782
3
sphere
2
cylinder, h=2r
1
cube
0
0
1
2
3
4
log volume (or mass at constant density)
5
6
Same basic shape – markedly different size
Giant and miniature Schnauzers
Size variation exists in nature too – think asses vs. horses, foxes
vs. wolves
but variation has been exaggerated by artificial selection in
domestic species
Relationship of heat production and
mass in adult homeotherms
log(10)BMR (kcal/d) = 1.83 + .756*log BW in kg
BMR = 67.6 * BW.756
BMR = 69 * BW .75
Kleiber, Fire of life
Not just homeotherms
Jack rabbits ears – blood flow increases
(internal forced convection) when
radiation/convection from ears allows cooling
Animal is really a collection of shapes
piloerection (physiological
response) and flocking
(behavioral response) both
decrease convection
note fluffier down type
feathers in chick
Shape and surface area important
for functions other than heat
• chicks don’t swim or fly so drag not
important
– have a relatively fixed solution in downy
feathers
• adult birds must be able to keep warm
when still but resist drag when swimming
or flying
– piloerection allows a flexible solution
rete mirabile – counter current for heat
exchange (forced convection + conduction)
Penquin feet: Counter
current circulation keeps feet
just above 0 C – venous
blood extracts heat from
arteries going to feet (feet
conduct heat to ice)
rete mirabile and sinus
evaporation
Brain (site of thermoregulation) remains cooler than
body during heat stress
Exercise 1
• What is heat loss by 70 kg homeotherm?
• If reduce heat loss by 10% what is
‘excess’ heat?
• how much will this raise body temperature
in a day?
• how much water would you need to
evaporate to restore balance?
• how much ice water would you need to
drink to restore balance
Solution
• Daily heat produced = heat lost = 69*70.75
= 1670 kcal/d
• 10% reduction in loss = 167 extra kcal
• this heats a mass of 70 kg water by 167/70 =
2.4oC
• 167/539 = .31 kg or L of water evaporated
• 167/37 = 4.5 L water heated from 0 to 37oC