Thermal conduction

Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy until an object has the same kinetic energy throughout. Thermal conductivity, represented by k, is a property that relates the rate of heat loss per unit area to its rate of change of temperature. It accounts for any property that could change the way a material conducts heat. Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached.

Every process involving heat transfer takes place by one of three methods:

• Conduction: heat transfer by physical contact. (The matter is stationary on a macroscopic scale—thermal motion affects atoms and molecules at any temperature above absolute zero.) Heat transferred between the electric burner of a stove and the bottom of a pan is transferred by conduction.
• Convection: heat transfer by the macroscopic movement of a fluid. Examples: a forced-air furnace and in weather systems.
• Radiation: heat transfer by microwaves, infrared radiation, visible light, or other electromagnetic radiation. An obvious example is the warming of the Earth by the Sun. A less obvious example is thermal radiation from the human body.

A hotter region experiences greater molecular agitation. When a hotter object touches a cooler surface, the molecules from the hot object bump the molecules of the cooler surface, transferring kinetic energy, heating the colder object. Mathematically, thermal conduction works via diffusion. As temperature difference goes up, the distance traveled gets shorter, or the area goes up, thermal conduction increases:

${\displaystyle {\dot {Q}}={\frac {\kappa A\Delta T}{\ell }}}$

where

• ${\displaystyle {\dot {Q}}}$ is the thermal conduction or power (the energy transferred per unit time over some distance between the two temperatures),
• ${\displaystyle \kappa }$ is the thermal conductivity of the material,
• ${\displaystyle A}$ is the cross-sectional area of the object,
• ${\displaystyle \Delta T}$ is the difference in temperature from one side to the other,
• ${\displaystyle \ell }$ is the distance over which the heat is transferred.

Conduction is the main mode of heat transfer for solid materials because the strong inter-molecular forces allow the vibrations of particles to be easily transmitted, in comparison to liquids and gases. Liquids have weaker inter-molecular forces and more space between the particles, which makes the vibrations of particles harder to transmit. Gases have even more space, and therefore infrequent particle collisions. This makes liquids and gases poor conductors of heat.

Thermal contact conductance is heat conduction between solid bodies in contact. A temperature drop is often observed at the interface between the two surfaces. This phenomenon is a result of a thermal contact resistance between the contacting surfaces. Interfacial thermal resistance is an interface's resistance to thermal flow. This resistance differs from contact resistance, as it exists even at atomically perfect interfaces. Understanding the thermal resistance at the interface between two materials is of primary significance in the study of thermal properties. Interfaces often contribute significantly to the observed properties of the materials.

Inter-molecular energy transfer could be primarily by elastic impact, as in fluids, or by free-electron diffusion, as in metals, or phonon vibration, as in insulators. In insulators, the heat flux is carried almost entirely by phonon vibrations.

Metals (e.g., copper, platinum, gold, etc.) are typically good conductors. This is due to the way that metals bond chemically: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons that transfer thermal energy rapidly. The electron fluid of a conductive metallic solid conducts heat flux through the solid. Phonon flux is present, but carries less energy. Electrons conduct electric current through conductive solids, and the thermal and electrical conductivities of most metals have about the same ratio. A good electrical conductor, such as copper, conducts heat well. Thermoelectricity is caused by the interaction of heat flux and electric current. Heat conduction within a solid is directly analogous to diffusion of particles within a fluid, absent fluid currents.

In gases, heat transfer occurs through collisions of gas molecules. Without convection, which relates to a fluid or gas phase, thermal conduction through a gas phase is dependent on the composition and pressure of this phase, and in particular, the mean free path of gas molecules relative to the size of the gas gap, as given by the Knudsen number ${\displaystyle K_{n}}$.

To quantify the ease with which a particular medium conducts, engineers measure thermal conductivity, also known as the conductivity constant or conduction coefficient, k. In thermal conductivity, k is defined as "the quantity of heat, Q, transmitted in time (t) through a thickness (L), in a direction normal to a surface of area (A), due to a temperature difference (ΔT) [...]". Thermal conductivity is a material property that is primarily dependent on the medium's phase, temperature, density, and molecular bonding. Thermal effusivity is derived from conductivity, which is a measure of its ability to exchange thermal energy with its surroundings.