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 differencedetermines direction and rate

• area

• how does area relate to animal mass?

Not all animals share same shape

volume (or mass) vs. area

sphereVolume = 4/3 r3

Surface = 4 r2

cylinder

Volume = r2 x heightSurface = 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 power rule: area = B * mass2/3

B varies (slightly) with shape

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 kgBMR = 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

note fluffier down type feathers in chick

piloerection (physiological response) and flocking

(behavioral response) both decrease convection

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