Heat conduction Heat conduction (or thermal conduction) is the movement of heat from one object to another one that has different temperature when they are touching each other. For example, we can warm our hands by touching hot-water bottles. When the cold hands touch the hot-water bottle, heat flows from the hotter object (hot-water bottle) to the colder one (hand). People make things with different thermal conductivity, for example cookware to heat things or insulated containers to keep hot things hot or cold things cold. Other ways to transfer heat are by thermal radiation and/or convection. Usually more than one of these processes happen at the same time. Microscopic explanation In the atomic theory solids, liquids and gases are made of tiny particles called "atoms". The temperature of the material measures how fast the atoms are moving and the heat measures the total amount of energy due to the vibration of the atoms. Conduction can happen when one part of a material is heated. The atoms in this part vibrate faster and are more likely to hit their neighbors. The collisions cause those atoms also to move faster, passing the heat energy to them. 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. 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 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 K n {\displaystyle K_{n}} . If changes in external temperatures or internal heat generation changes are too rapid for the equilibrium of temperatures in space to take place, then the system never reaches a state of unchanging temperature distribution in time, and the system remains in a transient state. An example of a new source of heat "turning on" within an object, causing transient conduction, is an engine starting in an automobile. In this case, the transient thermal conduction phase for the entire machine is over, and the steady-state phase appears, as soon as the engine reaches steady-state operating temperature. In this state of steady-state equilibrium, temperatures vary greatly from the engine cylinders to other parts of the automobile, but at no point in space within the automobile does temperature increase or decrease. After establishing this state, the transient conduction phase of heat transfer is over. New external conditions also cause this process: for example, the copper bar in the example steady-state conduction experiences transient conduction as soon as one end is subjected to a different temperature from the other. Over time, the field of temperatures inside the bar reaches a new steady-state, in which a constant temperature gradient along the bar is finally set up, and this gradient then stays constant in time. Typically, such a new steady-state gradient is approached exponentially with time after a new temperature-or-heat source or sink, has been introduced. When a "transient conduction" phase is over, heat flow may continue at high power, so long as temperatures do not change. An example of transient conduction that does not end with steady-state conduction, but rather no conduction, occurs when a hot copper ball is dropped into oil at a low temperature. Such a state never occurs in this situation, but rather the end of the process is when there is no heat conduction at all. The analysis of non-steady-state conduction systems is more complex than that of steady-state systems. If the conducting body has a simple shape, then exact analytical mathematical expressions and solutions may be possible (see heat equation for the analytical approach). However, most often, because of complicated shapes with varying thermal conductivities within the shape (i.e., most complex objects, mechanisms or machines in engineering) often the application of approximate theories is required, and/or numerical analysis by computer. Compared required to point to trace specified Biot number on the nomogram. == Applications == === Splat cooling === Splat cooling is a method for quenching small droplets of molten materials by rapid contact with a cold surface. The particles undergo a characteristic cooling process, with the heat profile at t = 0 {\displaystyle t=0} for initial temperature as the maximum at x = 0 {\displaystyle x=0} and T = 0 {\displaystyle T=0} at x = − ∞ {\displaystyle x=-\infty } and x = ∞ {\displaystyle x=\infty } , and the heat profile at t = ∞ {\displaystyle t=\infty } for − ∞ ≤ x ≤ ∞ {\displaystyle -\infty \leq x\leq \infty } as the boundary conditions.

in metals, or phonon vibration, as in insulators. In insulators, the heat flux is carried almost entirely by phonon vibrations. Metals (e.g., copper 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 distribute 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 ar Dur… 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. 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 K n {\displaystyle K_{n}} . If changes in external temperatures or internal heat generation changes are too rapid for the equilibrium of temperatures in space to take place, then the system never reaches a state of unchanging temperature distribution in time, and the system remains in a transient state. An example of a new source of heat "turning on" within an object, causing transient conduction, is an engine starting in an automobile. In this case, the transient thermal conduction phase for the entire machine is over, and the steady-state phase appears, as soon as the engine reaches steady-state operating temperature. In this state of steady-state equilibrium, temperatures vary greatly from the engine cylinders to other parts of the automobile, but at no point in space within the automobile does temperature increase or decrease. After establishing this state, the transient conduction phase of heat transfer is over. New external conditions also cause this process: for example, the copper bar in the example steady-state conduction experiences transient conduction as soon as one end is subjected to a different temperature from the other. Over time, the field of temperatures inside the bar reaches a new steady-state, in which a constant temperature gradient along the bar is finally set up, and this gradient then stays constant in time. Typically, such a new steady-state gradient is approached exponentially with time after a new temperature-or-heat source or sink, has been introduced. When a "transient conduction" phase is over, heat flow may continue at high power, so long as temperatures do not change. An example of transient conduction that does not end with steady-state conduction, but rather no conduction, occurs when a hot copper ball is dropped into oil at a low temperature. Such a state never occurs in this situation, but rather the end of the process is when there is no heat conduction at all. The analysis of non-steady-state conduction systems is more complex than that of steady-state systems. If the conducting body has a simple shape, then exact analytical mathematical expressions and solutions may be possible (see heat equation for the analytical approach). However, most often, because of complicated shapes with varying thermal conductivities within the shape (i.e., most complex objects, mechanisms or machines in engineering) often the application of approximate theories is required, and/or numerical analysis by computer. {\displaystyle q_{x}=-\kappa {\frac {dT}{dx}}.} In an isotropic medium, Fourier's law leads to the heat equation ∂ T ∂ t = α ( ∂ 2 T ∂ x 2 + ∂ 2 T ∂ y 2 + ∂ 2 T ∂ z 2 ) {\displaystyle {\frac {\partial T}{\partial t}}=\alpha \left({\frac {\partial ^{2}T}{\partial x^{2}}}+{\frac {\partial ^{2}T}{\partial y^{2}}}+{\frac {\partial ^{2}T}{\partial z^{2}}}\right)} with a fundamental solution famously known as the heat kernel. Compared required to point to trace specified Biot number on the nomogram. == Applications == === Splat cooling === Splat cooling is a method for quenching small droplets of molten materials by rapid contact with a cold surface. The particles undergo a characteristic cooling process, with the heat profile at t = 0 {\displaystyle t=0} for initial temperature as the maximum at x = 0 {\displaystyle x=0} and T = 0 {\displaystyle T=0} at x = − ∞ {\displaystyle x=-\infty } and x = ∞ {\displaystyle x=\infty } , and the heat profile at t = ∞ {\displaystyle t=\infty } for − ∞ ≤ x ≤ ∞ {\displaystyle -\infty \leq x\leq \infty } as the boundary conditions.

Radiant Heat .—It is assumed that heat and light traverse space in “waves” or vibrations of the ether. Positive knowledge is confined to the fact that heat is