1. TEM - Lecture 4
Thermal Resistance

3. Heat Transfer Equation
Stationary, 1D, no heat generation:
At the walls one has convective transfer:

4. Thermal Resistance (1/3)
In case of Electricity one has:

5. Thermal Resistance (2/3)

6. Thermal Resistance (3/3)

7. Or

8. Example (1/3)
Hypothesis a): Isothermal along yy direction:

9. Example (2/3) Hypothesis b): Adiabatic along YY/2:
Results a) and b) are different.
None is exact!!!

10. Example (3/3) Hypotheses c): Numerical solution, the more accurate.4 5 6
Hypotheses c): Numerical solution, the more accurate.
For simplicity let us consider the case
of (KE =KF= KH )> KG.
And plot a graph of the temperature
evolutions along the lower and
upper borders.
There is a yy temperature gradient
and the problem is 2D.
A numerical method is needed

11. Contact Resistance

13. Porous Media

15. This would be the maximum value of the conductivity.
For Small porosities, the extrapolation of Maxwell’s solution of electrical conductivity would give:
What about the soil?

16. Heat Transport in the Soil
In the soil there is continuity between the porous.
Usually there is a water movement as well.
Heat conduction is a rough approximation.
A better solution is got considering the water movement.
Soil is important for:
Water distribution in freezing regions;
As a heat reservoir for winter “heat pumping”