Physics: Fourier's law of heat conduction

Nuclear & Particle Thermodynamics

Fourier's law of heat conduction Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact.

Commentary

Fourier's law of heat conduction Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. Why does Fourier's law of heat conduction matter? This principle is one of the building blocks physicists use to explain the world. Without it, a whole class of phenomena would have no mathematical description. Engineers, chemists, and astronomers all rely on it. 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: Background: Fourier's law of heat 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: Q ˙ = κ A Δ T ℓ {\displaystyle {\dot {Q}}={\frac {\kappa A\Delta T}{\ell }}}

Sources: Wikipedia