Question

Suppose 150W of heat flows by conduction from the blood capillaries beneath the skin to the body's surface area of 1.5 m^2. If the temperature difference is 0.50 ºC, estimate the average distance of capillaries below the skin surface. Use 'mm' as your units.

Answer 1

Answer:

$l =1mm$

Explanation:

Given:

Rate of heat transfer, P = 150 W

Body surface Area, A = 1.5 m²

Temperature difference, ΔT = 0.50°C

Also,

The rate of heat transfer, P is given as:

$P = \frac{kA\Delta T}{l}$

Where,

l =length of material (or here it isaverage distance of the capillaries below the skin surface)

k = Thermal conductivity

Here the transfer of heat is through the skin. Thus, k for human tissue is given as 0.2

substituting the values in the above equation, we get

$150 = \frac{0.2\times 1.5\times 0.50}{l}$

or

$l = \frac{0.2\times 1.5\times 0.50}{150}$

or

$l = 1\times 10^{-3}m=1mm$