# Analogy between thermal and electrical

In thermal domain, there are basic definitions like thermal conductivity k(W/m*k), thermal resistance R(W/m2*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*m2/W)   Thermal resistance

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

Electrical resistivity            ρ       <———–>       Rλ (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.

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