Furthermore, these principles find applications in a multitude of fields, including materials science, mechanical engineering, electronics, and energy management.

Knowledge of these principles is crucial in various scientific, engineering, and everyday applications, from designing efficient temperature control, thermal insulation, and thermal management in industrial processes to optimizing the performance of electronic devices.

Conversely, thermal resistance (R) measures the opposition to the heat current in a material or system.

It is essential to optimize the building insulation, evaluate the efficiency of electronic devices, and enhance the performance of heat sinks in various applications.

Objects made of insulators like rubber tend to have very high resistance and low conductance, while objects made of conductors like metals tend to have very low resistance and high conductance.

However, the nature of a material is not the only factor as it also depends on the size and shape of an object because these properties are extensive rather than intensive.

It quantifies how effectively a material can resist the transfer of heat through conduction, convection, and radiation.

The thermal resistance of materials is of great interest to electronic engineers because most electrical components generate heat and need to be cooled.

Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.

Electrical engineers are familiar with Ohm's law and so often use it as an analogy when doing calculations involving thermal resistance.

Mechanical and structural engineers are more familiar with Hooke's law and so often use it as an analogy when doing calculations involving thermal resistance.

The diagram shows an equivalent thermal circuit for a semiconductor device with a heat sink.

Consider a component such as a silicon transistor that is bolted to the metal frame of a piece of equipment.

The transistor's manufacturer will specify parameters in the datasheet called the absolute thermal resistance from junction to case (symbol:

For simplicity, let us assume that the designer decides to bolt the transistor to a metal surface (or heat sink) that is guaranteed to be less than

Let us substitute some sample numbers: The result is then: This means that the transistor can dissipate about 18 watts before it overheats.

A cautious designer would operate the transistor at a lower power level to increase its reliability.

From Fourier's law for heat conduction, the following equation can be derived, and is valid as long as all of the parameters (x and k) are constant throughout the sample.

where: In terms of the temperature gradient across the sample and heat flux through the sample, the relationship is: where: A 2008 review paper written by Philips researcher Clemens J. M. Lasance notes that: "Although there is an analogy between heat flow by conduction (Fourier's law) and the flow of an electric current (Ohm’s law), the corresponding physical properties of thermal conductivity and electrical conductivity conspire to make the behavior of heat flow quite unlike the flow of electricity in normal situations.

This is because a material that is considered an insulator in electrical terms is about 20 orders of magnitude less conductive than a material that is considered a conductor, while, in thermal terms, the difference between an "insulator" and a "conductor" is only about three orders of magnitude.

[4] (A more sophisticated way of expressing the same fact is saying that junction-to-ambient thermal resistance is not Boundary-Condition Independent (BCI).

A JEDEC standard for measuring the junction-to-board thermal resistance (relevant for surface-mount technology) has been published as JESD51-8.

[5] A JEDEC standard for measuring the junction-to-case thermal resistance (JESD51-14) is relatively newcomer, having been published in late 2010; it concerns only packages having a single heat flow and an exposed cooling surface.

Similarly to electrical circuits, the total thermal resistance for steady state conditions can be calculated as follows.

[9] Spherical and cylindrical systems may be treated as one-dimensional, due to the temperature gradients in the radial direction.

as a variable becomes evident when the rate at which energy is conducted across a cylindrical surface, this is represented as Where

In order to determine the temperature distribution in the cylinder, equation 4 can be solved applying the appropriate boundary conditions.

and substituting into the general solution, we obtain The logarithmic distribution of the temperature is sketched in the inset of the thumbnail figure.

Assuming that the temperature distribution, equation 7, is used with Fourier's law in equation 5, the heat transfer rate can be expressed in the following form Finally, for radial conduction in a cylindrical wall, the thermal resistance is of the form 10.

“Interfacial thermal resistance engineering for polyaniline (C3N)-graphene heterostructure”, The Journal of Physical Chemistry, 2020.