Heat Transfer - Conduction and Radiation

[sinthreck]

Homework Statement

An animal has a core body temperature of 37^oC and a skin temperature of 34^oC while in surrounding of an air temperature of 25^oC. If the skin temperature fell, what would happen to:
(i) the rate of heat transfer via conduction through body tissue?
(ii) the rate of heat loss via radiation

Homework Equations

Q = h * A * [change in temp]

Q_net = e * (boltzsman) * (T_surface⁴ - T_environment⁴)

The Attempt at a Solution

(i) the rate of transfer due to conduction will increase because the change in temperature has increased. e.g. (37 - 30) > (37 -34)

(ii) the rate of transfer due to radiation will decrease because the T_surface⁴ has decreased.

Whilst my solution seems ok, doesn't the heat transfer need to be conserved?

ie. my textbook says the following:
" Heat must be transferred away from the outer surface at the same rate as it arrives there"

So I take this to mean, if one increases the other must increase and vice versa, If one decreases, the other must decrease.

With my solution, I have conduction increasing but radiation decreasing...

 

[Mapes]

Solution looks good to me. And I agree with your argument about energy conservation; in fact, that's why skin temperature is maintained at an equilibrium level that remains stable unless one of the other parameters changes also.