TEM - Lecture 10 Thermal Resistance

Heat flux is driven by temperature gradients (temperature differences) and controlled by resistances to the flux.

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

Thermal Resistance/Analogy with Electricity In case of heat, one has: In case of Electricity, one would have: The analogy is:

Equivalent/Total Thermal Resistance

Overall heat transfer coefficient (U) U - overall heat transfer coefficient, W/m2K

Composite Wall

Contact Resistance

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

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

Example (3/3) Hypotheses c): Numerical solution, the most accurate. 4 5 6 Hypotheses c): Numerical solution, the most 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

Porous Media This hypotheses gives minimum conductivity This Hypotheses gives maximum conductivity

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?

Heat Transport in the Ground 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”

Advantages/Disadvantages of the Resistance and Overall Heat Transfer Coefficient concepts The resolution of the equations system is embedded into them. One has to know the expression of the coefficient. It eases the inclusion of surface resistance into calculations It eases the calculation of heat flux into composite materials. It is great for people that has to work regularly on heat transfer!!!