Heat conduction between 2 objects

[fahraynk]

Can someone tell me if my logic is correct here.

I am trying to figure out how the cross sectional area to make the heat transfer from one object be the maximum amount of heat transfer with the minimal amount of area... I know the thermal transfer coefficient is watts per (meter*kelvin).
I find this to be odd. So firstly can someone explain to me why its watts per meter kelvin instead of watts per square meter? If it is longer heat transfers slower even in steady state?
Secondly, if it IS watts per meter Kelvin... Then what if one object is a weird shape? What if one object is say, a human body with a heat sink on your foot. What would the thickness of the human be (Assuming a thermal coefficient "average" for the human of 0.3)
And third, assuming all the above, is the below calculation correct?

Object 1 is at 37K (Kelvin), Length 15M, transfer coefficient of 0.3 W/(M*K)
Object 2 is at 0K, Length : L2 , thermal transfer: 400 W/(M*K)

$$\frac{400*A1*37K}{15}=\frac{0.3*A2*37K}{L2}$$
$$\frac{A2}{A1}=\frac{400*0.3*L2}{15}$$

 

[lewando]

I know the thermal transfer coefficient is watts per (meter*kelvin)

That is true but when used with Fourier's law of heat conduction:

q = k * A * ΔT / L

q: heat transfer [W]
k: thermal transfer coefficient of the conductor/insulator [W/(mK)]
A: contact area [m²]
ΔT: temperature difference from heat source to heat sink [K]
L: length of material between heat source and heat sink [m]

the units will be consistent. And hopefully make more intuitive sense.

Fourier's law applies to a 3-object system (ideal heat source, conductor/insulator, and ideal heat sink). A 2-object system is a different matter.
https://en.wikipedia.org/wiki/Thermal_contact_conductance

 

[fahraynk]

When I think of it as dT/dx it makes a bit more sense. I guess if L is large the temperature gradient has more time to change and thus changes slower, so that will slow down heat transfer since the difference in temperature would be lower between any differential distance.

That link you gave is interesting... for the purposes of sanity I will ignore interstitial materials and pressure and just assume thermal paste between the junction!