Thermal conduction

src: i.ytimg.com

Thermal conduction is the heat transfer (internal energy) by particle microscopic collision and movement of electrons in the body. The microscopic collision objects, which include molecules, atoms, and electrons, transfer unorganized microscopic kinetic and potential energy, together known as internal energy. Conduction takes place in all phases of matter including solids, liquids, gases and waves. The rate at which energy is performed as heat between two bodies is a function of the temperature difference (temperature gradient) between two objects and the properties of the conductive medium through which heat is transferred. Thermal conduction was originally called diffusion. Conduction: heat transfer through direct contact.

The heat spontaneously flows from the hotter to the colder body. For example, the heat is carried from the hotplate of the electric stove to the bottom of the pot in contact with it. In the absence of an opposing source of external drive energy, within the body or between bodies, the temperature difference will decay over time, and the heat balance is approached, the temperature becomes more uniform.

In conduction, the heat flow is within and through the body itself. Conversely, in heat transfer by thermal radiation, transfers occur frequently between bodies, which may be spatially separated. It may also be a heat transfer with a combination of conduction and thermal radiation. In convection, internal energy is carried between the body by a moving material carrier. In solids, conduction is mediated by a combination of vibration and collision of molecules, propagation and collision [phonon], and diffusion and collision of free electrons. In gases and liquids, conduction is caused by collisions and diffusion of molecules during their random motion. Photons in this context do not collide with each other, and heat transport by electromagnetic radiation is conceptually different from heat conduction by microscopic diffusion and particle and phonon particle collisions. But the difference is often not easily observed, unless the material is semi-transparent.

In engineering science, heat transfer involves the process of heat radiation, convection, and sometimes mass transfer. Usually, more than one process occurs in certain situations. The conventional symbol for thermal conductivity is k .

Video Thermal conduction

Overview

On a microscopic scale, conduction takes place in bodies that are regarded as stationary; this means that the kinetic energy and potential energy of the body mass movement are separately taken into account. Internal energy diffuses as atoms and molecules that move or vibrate quickly interact with neighboring particles, transferring a portion of their kinetic energy and microscopic energy, this quantity is determined relative to most of the bodies regarded as stationary. Heat is transferred by conduction when adjacent atoms or molecules collide, or because some electrons move back and forth from atom to atom in an irregular fashion so as not to form macroscopic electric currents, or as photons collide and scatter. Conduction is the most significant means of heat transfer in solid or between solids in thermal contact. Conduction is larger in solids because the relatively close spatial linkage network between atoms helps to transfer energy between them with vibration.

Thermal contact conductance is the study of the heat conduction between the contacted solids. A temperature drop is often observed at the interface between two touching surfaces. This phenomenon is said to be the result of the contact of the thermal resistance present between the touching surfaces. Interfacial thermal resistance is a measure of interface resistance to thermal flow. This heat resistance is different from the contact resistance, because there is even an atomically perfect interface. Understanding the heat resistance at the interface between the two materials is of primary significance in the study of thermal properties. Interfaces often contribute significantly to the observed material properties.

The transfer of energy between molecules can be mainly by elastic effects, such as in fluids, or by free electron diffusion, as in metals, or phononic vibrations, as in isolators. In the insulator, the heat flux is performed almost entirely by phonon vibrations.

Metals (eg, copper, platinum, gold, etc.) are usually good thermal energy conductors. This is because of the way metal bonds chemically: metal bonds (as opposed to covalent or ionic bonds) have free-moving electrons that rapidly transfer heat energy through metal. The electron fluid of conductive metal metallic conducts most of the heat flux through solids. Phonon flux is still there, but it lacks energy. Electrons also conduct electric current through conductive solids, and the thermal and electrical conductivity of most metals has the same ratio. Good electrical conductors, such as copper, also do heat well. Thermoelectricity is caused by the interaction of heat flux and electric current. Heat conduction in solids is directly analogous to the diffusion of particles in a liquid, in situations where there is no fluid flow.

To measure the ease with which certain media, engineers use thermal conductivity, also known as constant conductivity or conduction coefficient, k . In thermal conductivity, k is defined as "quantity of heat, Q , transmitted in time ( t ) through thickness ( L ), in the normal direction to the surface area ( A ), due to the temperature difference (? T ) [...] ". Thermal conductivity is the material property which depends mainly on the phase medium, temperature, density, and molecular bonds. Thermal sensitivity is the quantity derived from conductivity, which is a measure of its ability to exchange heat energy with its environment.

Steady-state conduction

Steady state conduction is a form of conduction that occurs when the temperature difference (s) of driving conduction is constant, so that (after equilibrium time), the spatial distribution of temperature (temperature field) in the conductor object does not change further.. Thus, all partial derivatives of the to space temperature may be zero or have non-zero values, but all derivatives of temperature at any point with respect to time are zero uniform. In steady state conduction, the amount of heat entering any region of an object is equal to the amount of heat coming out (otherwise, the temperature will rise or fall, because heat energy is tapped or trapped in a region).

For example, the bar may be cold at one end and heat at the other end, but once steady state conduction is achieved, the temperature spatial gradient along the bar does not change again, over time. In contrast, the temperature at a particular part of the rod remains constant, and this temperature varies linearly in space, along the direction of heat transfer.

In steady state conduction, all direct current electrical conduction laws can be applied to "heat currents". In such a case, it is possible to take "thermal resistance" as analogous to the electrical resistance. In such a case, the temperature plays the role of voltage, and the heat transferred per unit of time (heat power) is the analog of the electric current. The steady state system can be modeled by the network of thermal barriers such as series and in parallel, in the proper analogy for power lines of resistors. Refer to pure resistive thermal circuits for such tissue samples.

Temporary conduction

During each period in which the temperature changes in time in any place within an object, the heat energy flow mode is called transient conduction. Another term is a "non-steady state" conduction, referring to the time dependence of the temperature field in an object. The non-steady-state situation arises after a forced temperature change at the boundary of an object. They can also occur with temperature changes within an object, as a result of a new source or sinking of heat suddenly introduced in an object, causing a near-source temperature or sink to change in time.

When a new disturbance of this type of temperature occurs, the temperature inside the system changes in time to a new equilibrium with new conditions, provided this does not change. After equilibrium, the heat flow into the system is once again equal to the outflow of heat, and the temperature at each point in the system no longer changes. After this happens, the transient conduction ends, although steady-state conduction may continue if the heat flow continues.

If external temperature changes or internal heat changes are too fast for the temperature equilibrium in the space that occurs, then the system never reaches a state of unchanged temperature distribution in time, and the system remains in a transient state.

An example of a new heat source "lit" inside an object, causing temporary conduction, is a machine that starts in the car. In this case, the transient thermal conduction phase for the whole machine is completed, and the steady state phase appears, as soon as the engine reaches the steady-state operating temperature. In a steady-state equilibrium state, the temperature varies greatly from engine cylinder to other parts of the car, but there is no point in the space in the car whether the temperature increases or decreases. After establishing this state, the transfer transfers conduction phase ends.

New external conditions also cause this process: for example a copper rod in a steady-state conduction sample undergoes transient conduction immediately after one end experiences temperature different from the other. Over time, the temperature field inside the bar reaches a new steady state, where a constant temperature gradient along the bar is finally set, and this gradient then remains constant in space. Typically, the new steady-state gradient is approximated exponentially with time after a new source or hot-or-hot source has been introduced. When the "temporary conduction" phase ends, the heat flow may still continue at high power, as long as the temperature does not change.

An example of a transient conduction that does not end with steady-state conduction, but no conduction, occurs when a hot copper ball falls into the oil at low temperatures. Here, the temperature field within the object begins to change as a function of time, since heat is removed from the metal, and its interest lies in analyzing the spatial changes of this temperature in objects over time, until all the gradients disappear completely (the ball has reached the same temperature as the oil ). Mathematically, this condition is also approached exponentially; in theory it takes unlimited time, but in practice it is over, for all intents and purposes, in a much shorter time. At the end of this process without the heat sink but the internal part of the ball (which is limited), there is no heat conduction stable state to achieve. Such a situation never happens in this situation, but the end of the process is when there is no heat conduction at all.

Analysis of the non-steady state conduction system is more complex than the steady-state system. If the organizing body has a simple form, then an appropriate analytical and analytical expressions may be possible (see heat equation for the analytical approach). However, most often, due to intricate forms with various thermal conductivities in shape (ie, most complex objects, mechanisms or machines in engineering) often the approximate theoretical applications are required, and/or numerical analysis by the computer. One popular graphical method involves the use of Heisler Charts.

Sometimes, the problem of transient conduction can be greatly simplified if the area of ​​a heated or cooled object can be identified, for which the thermal conductivity is so much greater than that for the hot path leading to the region. In this case, areas with high conductivity can often be treated in a centralized capacitance model, as "clods" of material with a simple thermal capacitance comprising its aggregate heat capacity. Such areas are warm or cool, but do not show significant temperature variations throughout the process (as compared to other systems). This is because their conductance is much higher. During temporary conduction, therefore, temperatures in all conductive regions change uniformly in space, and as simple exponentially in time. Examples of such systems are those that follow Newton's cooling law during temporary cooling (or vice versa during heating). The equivalent thermal circuit consists of a simple capacitor in series with the resistor. In such cases, the rest of the system with high heat resistance (relatively low conductivity) plays the role of resistors in the circuit.

Relativistic conduction

The relativistic heat conduction theory is a model compatible with the special theory of relativity. For much of the last century, it was recognized that Fourier's equations conflict with the theory of relativity because it recognizes the infinite speed of propagation of the heat signals. For example, according to the Fourier equation, the heat rate at the origin will be instantly unlimited. The propagation speed of information is faster than the speed of light in a vacuum, which is physically unacceptable within the framework of relativity.

Quantum conduction

The second sound is a phenomenon of quantum mechanics in which heat transfer occurs by wave-like motions, rather than by more general diffusion mechanisms. Heat takes place of pressure on normal sound waves. This causes very high thermal conductivity. It is known as the "second voice" because the motion of a heat wave is similar to the spread of sound in the air.

Maps Thermal conduction

Fourier's Law

The heat conduction law, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in temperature and to the region, at a right angle to the gradient, through which heat flows. We can express this law in two equivalent forms: the integral form, in which we see the amount of energy flowing into or out of the body as a whole, and the differential form, where we see the flow rate or the flux of energy locally.

Newton's cooling law is a discrete analogy of Fourier's law, while Ohm's law is the electrical analog of Fourier's law.

Differential form

Bentuk diferensial hukum Fourier tentang konduksi termal menunjukkan bahwa kerapatan fluks panas lokal, ${\ displaystyle {\ overrightarrow {q}}}  ÂÂ$ , sama dengan produk konduktivitas termal, ${\ displaystyle k}  ÂÂ$ , dan gradien temperatur lokal negatif, ${\ displaystyle - \ nabla T}  ÂÂ$ . Kerapatan fluksi panas adalah jumlah energi yang mengalir melalui area unit per satuan waktu.

${\ displaystyle {\ overrightarrow {q}} = - k {\ nabla} T}  ÂÂ$

di mana (termasuk unit SI)

${\ displaystyle {\ overrightarrow {q}}}  ÂÂ$ adalah kerapatan fluks panas lokal, WÂ · m ^-2

${\ displaystyle {\ big.} k {\ big.}}  ÂÂ$ adalah konduktivitas material, WÂ · m ^-1 Â · K ^-1 ,

${\ displaystyle {\ big.} \ nabla T {\ big.}}  ÂÂ$ adalah gradien suhu, K Â · m ^-1 .

Thermal conductivity, ${\ displaystyle k}$ , often treated as constants, though this is not always true. While the thermal conductivity of a material generally varies with temperature, the variation can be small above the temperature range that is significant for some common materials. In anisotropic materials, thermal conductivity usually varies with orientation; in this case ${\ displaystyle k}$ is represented by second-order tensor. In non-uniform material, ${\ displaystyle k}$ varies with spatial location.

Untuk banyak applicasi sederhana, hukum Fourier digunakan dalam bentuk satu dimensinya. Dalam x -direction,

${\ displaystyle q_ {x} = - k {\ frac {dT} {dx}}} Â Â$

Bentuk integral

Dengan mengintegrasikan bentuk diferensial di atas permukaan total material ${\ displaystyle S}  ÂÂ$ , kita sampai pada bentuk integral dari hukum Fourier:

${\ displaystyle {\ frac {\ partial Q} {\ partial t}} = - k}  ÂÂ$ ${\ displaystyle \ scriptstyle S}  ÂÂ$ ${\ displaystyle {\ nabla} T \ cdot \, dS}  ÂÂ$

di mana (termasuk unit SI):

• ${\ displaystyle {\ big.} {\ Frac {\ partial Q} {\ partial t}} {\ big.}} Â$ adalah jumlah panas yang ditransfer per satuan waktu (dalam W), dan
• ${\ displaystyle dS} Â$ adalah elemen area permukaan yang berorientasi (dalam m ² )

Persamaan diferensial di atas, ketika diintegrasikan untuk material homogen geometri 1-D antara dua titik akhir pada suhu konstan, memberikan laju aliran panas sebagai:

${\ displaystyle {\ big.} {\ frac {Q} {\ Delta t}} = - kA {\ frac {\ Delta T} {\ Delta x}}}  ÂÂ$

dimana

${\ displaystyle A}  ÂÂ$ adalah luas permukaan cross-sectional,

${\ displaystyle \ Delta T}  ÂÂ$ adalah perbedaan suhu antara ujungnya,

${\ displaystyle \ Delta x}  ÂÂ$ adalah jarak antara ujungnya.

This law forms the basis for the derivation of heat equations.

src: www.linseis.com

Conductance

Penulisan

${\ displaystyle {\ big.} U = {\ frac {k} {\ Delta x}}, \ quad} Â Â$

where U is conductance, in W/(m ² K).

Hukum Fourier juga dapat dinyatakan sebagai:

$            {\displaystyle                                                                   \frac{              \mathrm{?}              Q            }{              \mathrm{?}              t            }                =        U        A                (        -        \mathrm{?}        T        )        .      }        \{\backslash \; displaystyle\; \{\backslash \; big.\}\; \{\backslash \; frac\; \{\backslash \; Delta\; Q\}\; \{\backslash \; Delta\; t\}\}\; =\; UA\; \backslash ,\; (-\; \backslash \; Delta\; T).\}\;  ÂÂ$

Kebalikan dari konduktansi adalah resistensi, R, yang diberikan oleh:

${\ displaystyle {\ big.} R = {\ frac {1} {U}} = {\ frac {\ Delta x} {k}} = {\ frac { A \, (- \ Delta T)} {\ frac {\ Delta Q} {\ Delta t}}}.}  ÂÂ$

Perlawanan bersifat aditif ketika beberapa lapisan konduktor berada di antara daerah panas dan dingin, karena A dan Q adalah sama untuk semua lapisan. Dalam partisi multilayer, total konduktansi terkait dengan konduktansi lapisannya dengan:

${\ displaystyle {\ big.} {\ frac {1} {U}} = {\ frac {1} {U_ {1}}} {\ frac {1 } {U_ {2}}} {\ frac {1} {U_ {3}}} \ cdots}  ÂÂ$

Jadi, ketika berhadapan dengan partisi multilayer, rumus berikut biasanya digunakan:

$            {\displaystyle                                                                   \frac{              \mathrm{?}              Q            }{              \mathrm{?}              t            }                =                  \frac{              A                            (              -              \mathrm{?}              T              )            }{                              \frac{                    \mathrm{?}                    x_{                        1                      }                  }{k_{                      1                    }}                                                          \frac{                    \mathrm{?}                    x_{                        2                      }                  }{k_{                      2                    }}                                                          \frac{                    \mathrm{?}                    x_{                        3                      }                  }{k_{                      3                    }}                                          ?            }                .      }        \{\backslash \; displaystyle\; \{\backslash \; big.\}\; \{\backslash \; frac\; \{\backslash \; Delta\; Q\}\; \{\backslash \; Delta\; t\}\}\; =\; \{\backslash \; frac\; \{A\; \backslash ,\; (-\; \backslash \; Delta\; T)\}\; \{\; \{\backslash \; frac\; \{\backslash \; Delta\; x\_\; \{1\}\}\; \{k\_\; \{1\}\}\}\; \{\backslash \; frac\; \{\backslash \; Delta\; x\_\; \{2\}\}\; \{k\_\; \{2\}\}\}\; \{\backslash \; frac\; \{\backslash \; Delta\; x\_\; \{3\}\}\; \{\; k\_\; \{3\}\}\}\; \backslash \; cdots\}\}.\}\;  ÂÂ$

For heat conduction from one liquid to another through a barrier, it is sometimes important to consider the conductance of a thin film of a liquid that remains stationary beside the obstructions. This thin liquid film is difficult to calculate because its characteristics depend on complex turbulence and viscosity conditions - but when confronted with the thin high conductance resistance can sometimes be very significant.

Property-intensive representation

Persamaan konduktansi sebelumnya, ditulis dalam hal sifat yang luas, dapat dirumuskan kembali dalam hal sifat intensif. Idealnya, rumus untuk konduktansi harus menghasilkan kuantitas dengan dimensi independen jarak, seperti Hukum Ohm untuk hambatan listrik, ${\ displaystyle R = V/I \, \!}  ÂÂ$ , dan konduktansi, ${\ displaystyle G = I/V \, \!}  ÂÂ$ .

Dari rumus listrik: ${\ displaystyle R = \ rho x/A \, \!} Â Â$ , di mana ? adalah resistivitas, x adalah panjang, dan A adalah area cross-sectional, kami memilize ${\ displaystyle G = kA/x \, \!} Â Â$ , di mana G adalah konduktansi, k adalah behaviors, x panjang, dan A adalah area cross-sectional.

Untuk Panas,

${\ displaystyle {\ big.} U = {\ frac {kA} {\ Delta x}}, \ quad} Â Â$

where U is conductance.

Hukum Fourier juga dapat dinyatakan sebagai:

${\ displaystyle {\ big.} {\ dot {Q}} = U \, \ Delta T, \ quad}  ÂÂ$

analog denotes hookum Ohm, ${\ displaystyle I = V/R \, \!} Â$ atau $Â\; ÂÂ\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; ÂSayaÂ\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂVÂ\; Â\; Â\; Â\; Â\; Â\; ÂGÂ\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â}$

Source of the article : Wikipedia