Conduction of Thermal Energy
Heat naturally flows from hot objects to cold objects. This calculator specifically measures Conduction, which is the transfer of heat through a solid material via direct microscopic collisions of particles and movement of electrons within a body.
Fourier's Law of Heat Conduction states that the rate of heat transfer (the Power, measured in Watts) through a material is directly proportional to the temperature difference and the cross-sectional area, but inversely proportional to the thickness of the material.
Thermal Insulation and Heat Sinks
- Home Insulation: The walls of your house are filled with fiberglass or foam. These materials have a terrible thermal conductivity ($k$). Furthermore, the walls are thick ($d$). According to the formula, minimizing $k$ and maximizing $d$ brutally chokes the flow of heat, keeping your house warm in the winter and cool in the summer.
- Computer Processors: A CPU generates a massive amount of heat in a tiny area. Engineers use Copper or Aluminum because they have an incredibly high thermal conductivity ($k$). The heatsink is designed with hundreds of thin fins to absolutely maximize the surface area ($A$), ensuring the heat transfers out of the metal and into the air as fast as possible.
- Double-Pane Windows: Glass conducts heat relatively well. By putting two panes of glass together with a thick layer of trapped Argon gas between them (Argon has a terrible thermal conductivity), window manufacturers can drastically slash the heat transfer out of your home.
The Formula
Example Calculation
You have a solid copper plate that is $0.1 , \text{m}^2$ in area and $0.02 , \text{meters}$ thick. One side is touching boiling water ($100^\circ\text{C}$), the other side is touching ice water ($0^\circ\text{C}$), making $\Delta T = 100 , \text{K}$. The thermal conductivity of copper is $385 , \text{W/(m}\cdot\text{K)}$.
- Multiply $k \cdot A \cdot \Delta T$: $385 \cdot 0.1 \cdot 100 = 3,850$.
- Divide by thickness ($d$): $3,850 / 0.02 = 192,500 , \text{Watts}$.
An absolutely staggering $192,500 , \text{Joules}$ of thermal energy is blasting through that copper plate every single second.