Question

The doctor is trying to decide what type of “feather” material to give his creations so that they keep warm while sleeping in the winter. Given the following data calculate the conductive heat flux (W) for the different “feather” materials. Material “A” has a K of 0.036 W/mK and increases the bird’s x by 2.769 x 10^-3 m. Material “B” has a K of 0.17 W/mK and increases the bird’s x by 1.308 x 10^-2 m. The bird’s internal temperature is 311.0 K (we are assuming that they are endothermic) and the temperature of the ground is 260.0 K. The distance from the exterior of the bird’s skin to its core is 0.75 m. When the animal is sleeping the surface area of the bird that touches the ground is 1.76 m². Which of these materials results in the smallest loss of heat due to conduction?     

Answer 1

For Material A , K = 0.036 W/mK and X = 2.769 × m

For Material B ,. K = 0.17 W /mK and X = 1.308 × m

Given the birds internal temperature = 311.0K and

temperature of the ground   = 260.0 K

∆T = 311.0K -260.0 K = 51 K

The distance from the exterior of the bird’s skin to its core d = 0.75 m

the surface area of the bird = 1.76

For Material A ,

The heat loss of a system through conduction (Q)

Q= K A ∆T / 3.412 × X W /hr

= 0.036 × 1.76 × 51/ 3.421× 2.769×

= 341.1216 W/hr

For Material B ,

The heat loss of a system through conduction (Q)

Q = K A ∆T /3.412 × X W/hr

= 0.17 × 1.76 × 51 / 3.412 × 1.308 ×

= 340.8587 W/hr

Material B results in the smallest loss of heat due to conduction.