Question

2) (40 pts) An alligator that has been warming in the sun swims into cold water. Calculate the following parameters, if the alligator temperature (underneath the scales) is 33 °C and the water temperature is 15 °C. Assume the pathway for heat transport is through the thick scales (with conductance of 0.5 mol m-2 s -1 ) and then through a thin boundary layer in the water (with conductance of 1 mol m-2 s -1 ). Ignore radiative effects and view factor considerations, and assume there is no fluid movement, just diffusion (ie, no forced or free convection).

a) What is the total conductance to heat loss?

b) What is the convective heat loss in Watts per square meter?

c) Now imagine that a python swallows the alligator whole, and that the python has a resistance to heat loss of 3 m2 s mol-1 . What is the new total conductance of the alligator-python combination to heat loss? (hint – this just adds a third series element to the conductances – assume the boundary layer conductance still applies and does not change).

d) What is the new convective heat loss from the alligator to the water (through the python)?

e) How would your answer to c) change if the python’s resistance was a parallel combination of 3 m2 s mol-1 through the spots, and 15 m2 s mol-1 through the spot-free areas?

f) What is the convective heat loss in e)?

Answer 1

2) (40 pts) An alligator that has been warming in the sun swims into cold water. Calculate the following

parameters, if the alligator temperature (underneath the scales) is 33 °C and the water temperature is 15

°C. Assume the pathway for heat transport is through the thick scales (with conductance of 0.5 J m-2 s -1

K) and then through a thin boundary layer in the water (with conductance of 1 J m-2 s -1 K). Ignore

radiative effects and view factor considerations, and assume there is no fluid movement, just diffusion

(ie, no forced or free convection).

a) What is the total conductance to heat loss?

thick scales conductance, hc1 = 0.5 J m-2 s-1 K
Resistance, R1 = 1/(hc1*A)
thin boundary layer in the water conductance, hc2 = 1 J m-2 s-1 K
Resistance, R2 = 1/(hc2*A)
Total resistance, Rtotal = R1+R2 = 1/(0.5*A)+1/(1*A) = 3/A   J-1 s K
Total conductance , hc = 1/(Rtotal*A) = 1/(3/A*A) = 1/3 = 0.33 J m-2 s-1 K

b) What is the convective heat loss in Watts per square meter?
Q/A = hc*dT=0.33*(33-15)= 6 J m-2 s-1 = 6 W m-2

c) Now imagine that a python swallows the alligator whole, and that the python has a resistance to heat

loss of 3 m2 s mol-1 . What is the new total conductance of the alligator-python combination to heat loss?

(hint – this just adds a third series element to the conductances – assume the boundary layer conductance

still applies and does not change).

python resistance to heat loss, Rpython*A = 3 m2 s J-1
Rpython = 3/A
Total resistance, Rtotal = R1+R2+Rpython = 1/(0.5*A)+1/(1*A)+3/A = 6/A
Total conductance , hc = 1/(Rtotal*A) = 1/(6/A*A) = 1/6 = 0.167 J m-2 s-1 K

d) What is the new convective heat loss from the alligator to the water (through the python)?
Q/A = hc*dT=0.167*(33-15)= 3 J m-2 s-1 = 3 W m-2

e) How would your answer to c) change if the python’s resistance was a parallel combination of 3 m2 s

mol-1 through the spots, and 15 m2 s mol-1 through the spot-free areas?

Rpython1 = 3/A s J-1
Rpython2 = 15/A s J-1
1/Rpython = 1/Rpython1+1/Rpython2= A/3+A/15 = 0.4*A
Rpython = 1/(0.4*A)= 2.5/A
Total resistance, Rtotal = R1+R2+Rpython = 1/(0.5*A)+1/(1*A)+2.5/A = 5.5/A
Total conductance , hc = 1/(Rtotal*A) = 1/(5.5/A*A) = 1/5.5 = 0.18 J m-2 s-1 K

f) What is the convective heat loss in e)?
Q/A = hc*dT=0.18*(33-15)= 3.27 J m-2 s-1 = 3.27 W m-2