How To Calculate Thermal Conductivity

In terms of physics, thermal conductivity refers to the property of materials to conduct heat and thermal energy. Thermal conductivity is a useful concept because of a variety of applications. Objects with high thermal conductivity can be used for transmitting heat or allowing heat to remain in a given object. Copper, for instance, has high thermal conductivity, which is why this type of metal is considered as one of the best materials for pots and pans. On the other hand, low thermal conductivity is effective for insulation, either to keep an object warm at a constant temperature over long periods of time, or cold over long periods of time. Here’s how you can calculate for the thermal conductivity of an object.

  1. Partial derivative. There are two main data that you need to obtain first before calculating the thermal conductivity of a given substance or material. The first is the partial derivative, and the second is the heat flux. The partial derivative is the value of a given variable when the other variables are held at a constant rate. This can be done by using a uni-directional heat and temperature distribution, where x is the variable whose partial derivative you are looking for. Keep in mind, however, that this is effective only when looking for partial derivatives in planes. Other types of distribution, such as spherical or radial distributions, will have coordinates whose partial derivatives will be calculated via various other types of methods.
  2. Heat flux. Next, take the heat flux. In school, the heat flux is usually given in equations, which will allow you to proceed to the next step. In laboratories and when conducting experiments, however, you will need to obtain the heat flux yourself. Getting the value for the heat flux can be done by using the guarded hot plate. This is a device that will heat flow for a given material with a certain thickness. The guarded hot plate apparatus is also very useful in simplifying the heat flux, since it can only measure heat flux in terms of one dimensional and steady heat flow. This means that the heat flux becomes linear, which is easier to measure.
  3. Fourier’s Law. With the heat flux and the partial derivative ready, you can now use Fourier’s law to compute for a material’s thermal conductivity. The formula for Fourier’s law is q”=-kdT/dx. To compute for the value of thermal conductivity, you will need to replace the q variable with the heat flux value. Replace the dT/dX value with the partial derivative value, and you should be able to get the value for k, which is the thermal conductivity, through simple division and mathematical transposition.

Keep in mind that there are also other ways to measure the thermal conductivity of a given object. The type of measurement and formulas that you will use will vary depending on the materials that you use and the accuracy level that you are aiming for. Apart from Fourier’s law using the heat flux and the partial derivative, you can also measure the thermal conductivity of a given object by using the disc method, formulated by Lee, and the bar method by Searle’s.


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