In thermal domain, there are basic definitions like thermal conductivity k(W/m*k), thermal resistance R(W/m^{2}*k) whose meanings are confusing to beginners. Recently, I read an article about thermal electrical analogy, which make them easy to understand.

**1. Definitions analogy**

Voltage ** U <————> ****ΔT (k)** Temperature difference

Current ** I <————> q ** Heat flow rate

Electrical Resistance **R <————> Rth(K/W) **Absolute thermal resistance

Electrical Resistance unit area **<———–> R (K*m ^{2}/W)** Thermal resistance

Electrical conductivity **σ <———–> k (W/m*k)** Thermal conductivity

Electrical resistivity **ρ <———–> R**

_{λ (K·m)/W Specific thermal resistivity }

Among the four definitions about thermal resistance, absolute thermal resistance **Rth** is a property of a specific component just like a resistor and the other three are constant property of material or a kind of component. Thermal resistance **R** is per unit area, thermal conductivity **k** is per unit area and unit length, and specific thermal resistivity ** Rλ** is the reciprocal of

**k**.

**2. Equations analogy**

Rt is the absolute thermal resistance of the component, q is heat flow rate and *ΔT is temperature difference.*

K is the thermal conductivity which is reciprocal of thermal resistivity, thus in the oposite position with electrical resistivity ρ.

These two equations are the main equations used to calculate the thermal conducivity of the material. The first one is used to calculate the performance of the specific sample and the second one is used to calculate the performance of material per unit area and length.

Here is the reference link:

http://www.egr.msu.edu/~raguin/ME812/FinalProjects/Lindberg_FinalProject.htm

I have some questions. When can you say that a material has a good thermal and electrical resistance? And can you say if the voltage rises, the temperature rises propartional to the voltage?

We can say a material has a good thermal resitance when it has a low heat flow rate at the same temperature difference and same dimension.

A good electrical resistance wehn it has a low current at the same voltage difference and same dimension.

You can’s say temperature rises proportional to the voltage. Because it’s only analogy, but not numericaly related to. Temperature rises proportionaly to heat flow rate.

I find it fascinating how certain properties in nature can be so alike.

Did this thermal-electrical analogy provide you some inspiration for your thesis research?

It helps me a lot in understanding the definitions and relations of the thermal domain.