Thermal Conductivity

Heat moves through a solid by conduction: fast-vibrating atoms on the hot side jostle their neighbors, passing energy along without the atoms themselves traveling. Some materials do this well, metals especially, because their free electrons carry energy quickly. Others, like wool or air, do it badly. Wool is not warm itself, it just slows the escape of the heat your body already made. That is why it feels warm: it is a bad conductor, so your body heat leaks out slowly and builds up in a thin warm layer against your skin instead of racing away.

The rate of that leak follows one equation: Q/t = kA(dT)/d, where k is the thermal conductivity of the material, A is the cross-sectional area heat passes through, dT is the temperature difference between the two sides, and d is the thickness the heat must cross. More area gives heat more paths to escape, so flow rises with A. A bigger temperature difference pushes harder, so flow rises with dT. A thicker wall makes the trip longer, so flow drops as d grows. Doubling thickness and area together cancels out, since one doubles the rate and the other halves it, leaving the leak unchanged.

This equation is built the same way as Ohm's law for circuits. Temperature difference plays the role of voltage, the driving push. Thickness divided by conductivity and area acts like resistance, the thing that resists the flow. Heat flow rate plays the role of current. That parallel lets you reuse circuit intuition: thin, wide, high-conductivity walls are like low-resistance wires, letting heat flow fast, while thick, narrow, low-conductivity walls behave like high-resistance wires that choke the flow down.