Thermtest is happy to introduce the new Thermal Resistance in Series Calculator. After inputting the thermal resistance and thickness of the material, the calculator outputs the thermal resistance of the composite.

What is Thermal Resistance?

As the name suggests, thermal resistance is a material’s ability to resist the flow of heat. This thermal property greatly depends on the area, thickness, and thermal conductivity of a material. Resistance increases by increasing the thickness of the material, and decreasing its area and thermal conductivity. Often times, heat flow and temperature can be determined from thermal resistance. This becomes useful in construction applications, when heat loss from electronics must be accounted for in building designs. 

Figure 1. A structure composed of two materials with different resistances, where the heat flux through them (Q) is considered constant.

Calculating Thermal Resistance in Series

When the heat flux through multiple mediums is assumed constant, the thermal resistance “in series” can be determined. Thermal resistance can be compared to an electrical circuit model. In this case, heat flow is represented by current, temperatures are substituted with voltages, and resistances are expressed as resistors.

Figure 2. Thermal resistance represented as an electrical circuit. Current is replaced by heat flow (Q), voltages are represented as temperatures (T), and resistors are substituted for resistances (R).

The heat flow, or boundary temperatures of the system, can also be determined when an object’s resistance is known. In series, the heat flux through a composite material is considered constant, and the different series are equivalent to:

\[R = R_{1} + R_{2}\]

When the temperatures on each side of the composite material are known (\(T_{L}\) and \(T_{R}\)), the heat transfer rate is expressed as:

\[\dot{Q}=\frac{T_{L} {-} T_{R}}{R} = \frac{T_{L} {-} T_{R}}{R_{1} {+} R_{2}}\]

This resistance equation can be applied to the “in series” composites, such as a wall surrounded by insulation, because \(\dot{Q}\) is constant across each component. The heat transfer of a composite material can be determined with the following equation:  

\[{Q}=\frac{T_{ \infty 1} {-} T_{1}}{R_{conv1}} = \frac{T_{1} {-} T_{2}}{R_{wall}}= \frac{T_{2} {-}T_{ \infty 2}}{R_{conv1}}\]

Figure 3. The thermal resistances (R) and temperatures (T) of a wall surrounded by insulation (left), modelled as an electrical current (right).

From which, the resistances of each component, \(R_{conv1}\), \(R_{wall}\), and \(R_{conv2}\) can be calculated using:

\[R_{total}=R_{conv1}+R_{wall}+R_{conv2}\]

After the total resistance of the system is known, the heat flow through the composite can be calculated from the heat flow equation. This includes the known boundary temperatures, as seen in the following equation. 

\[Q = \frac{T_{ \infty 1}{-}T_{ \infty 2}}{R_{total}}\]

The Resistance in Series Calculator is capable of easily determining the thermal resistance of composite materials. The calculator can also be used  combination with Thermtest’s materials database, which includes the thermal properties of more than 1000 materials. This newly designed calculator provides a fast, simple, and accurate way to calculate the thermal resistance in series.  

References

https://neutrium.net/heat_transfer/thermal-resistance/

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node118.html