Heat conduction between 2 objects

In summary, the cross sectional area of an object is important in determining how much heat can be transferred from one object to another. If one object is a weird shape, its thermal transfer coefficient will be lower.
  • #1
fahraynk
186
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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)

$$\frac{400*A1*37K}{15}=\frac{0.3*A2*37K}{L2}$$
$$\frac{A2}{A1}=\frac{400*0.3*L2}{15}$$
 
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  • #2
fahraynk said:
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
 
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  • #3
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!
 
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1. What is heat conduction?

Heat conduction is the transfer of thermal energy between two objects that are in direct contact with each other. It occurs when there is a difference in temperature between the two objects, and the thermal energy flows from the hotter object to the colder one.

2. How does heat conduction occur between two objects?

Heat conduction occurs through the vibration and movement of molecules in the objects. When two objects are in contact, the molecules with higher kinetic energy (higher temperature) will transfer their energy to the molecules with lower kinetic energy (lower temperature).

3. What factors affect heat conduction between two objects?

The rate of heat conduction between two objects is affected by several factors, including the temperature difference between the two objects, the type of materials the objects are made of, the distance between the objects, and the surface area of contact between the objects.

4. How is heat conduction different from convection and radiation?

Heat conduction is the transfer of thermal energy through direct contact between objects. Convection, on the other hand, is the transfer of heat through the movement of fluids (liquids or gases). Radiation is the transfer of heat through electromagnetic waves, such as infrared radiation from the sun.

5. How can heat conduction be controlled or manipulated?

Heat conduction can be controlled by changing the temperature difference between the two objects, using insulating materials to reduce the rate of heat transfer, or increasing the surface area of contact between the objects. It can also be manipulated by using materials with different thermal conductivities or by altering the distance between the objects.

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