thermal conductivity

Vanessa23

1. The problem statement, all variables and given/known data
A mountain climber wears a goose down jacket 3.28 cm thick with total surface area 1.10 m2. The temperature at the surface of the clothing is -19.3°C and at the skin is 36.0°C. Determine the rate of heat flow by conduction through the jacket assuming it is dry and the thermal conductivity, k, is that of down.
Part 2:
Determine the rate of heat flow by conduction through the jacket assuming the jacket is wet, so k is that of water and the jacket has matted down to 0.462 cm thickness.


2. Relevant equations
thermal conductivity of goose down is .025 J/(mKs)
thermal conductivity of water is .561W/(mKs)

phi dot = KA (delta T/delta X)

K is goose down (.025 j/smk)
A is area
T is temperature
x is distance heat flows

Part 2
The rate of heat flow= (the rate of heat flow you found in
part 1) x (k water/ k goose down) x (thickness of goosedown/
thickness of wet jacket)

3. The attempt at a solution
.025*(.0328*1.10)*(36+19.3/.0328)

I get the rate is 1.52 W, yet it is the wrong answer. If I had that answer I could use it to get part 2 where I would do the following
rate=rate1*(.561/.025)*(.0328/.00462)

Please let me know what I am doing wrong! Thank you!

Shooting Star

Why is the distance between the two surfaces in the numerator? Delta_x should be in the bottom.