Editing Heat transfer (section)

==Mechanisms==
[[File:Heat-transmittance-means2.jpg|thumb|250px|The four fundamental modes of  heat transfer illustrated with a campfire]]
The fundamental modes of heat transfer are:

;[[Advection]]
: Advection is the transport mechanism of a [[fluid]] from one location to another, and is dependent on [[Motion (physics)|motion]] and [[momentum]] of that fluid.
;[[Thermal conduction|Conduction]] or [[Heat conduction|diffusion]]
: The transfer of energy between objects that are in physical contact. [[Thermal conductivity]] is the property of a material to conduct heat and is evaluated primarily in terms of [[Heat conduction#Fourier's law|Fourier's law]] for heat conduction.
;[[Convection (heat transfer)|Convection]]
: The transfer of energy between an object and its environment, due to fluid motion. The average temperature is a reference for evaluating properties related to convective heat transfer.
;[[Thermal radiation|Radiation]]
: The transfer of energy by the emission of [[electromagnetic radiation]].

===Advection===
By transferring matter, energy—including thermal energy—is moved by the physical transfer of a hot or cold object from one place to another. This can be as simple as placing hot water in a bottle and heating a bed, or the movement of an iceberg in changing ocean currents. A practical example is [[thermal hydraulics]]. This can be described by the formula:
<math display="block">\phi_q = v \rho c_p \Delta T</math>
where
* <math>\phi_q</math> is [[heat flux]] (W/m<sup>2</sup>),
* <math>\rho</math> is density (kg/m<sup>3</sup>),
* <math>c_p</math> is heat capacity at constant pressure (J/kg·K),
* <math>\Delta T</math> is the difference in temperature (K),
* <math>v</math> is velocity (m/s).

===Conduction===
{{main|Thermal conduction}}
On a microscopic scale, heat conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring particles. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from one atom to another. Conduction is the most significant means of heat transfer within a solid or between solid objects in [[thermal contact]]. Fluids—especially gases—are less conductive. [[Thermal contact conductance]] is the study of heat conduction between solid bodies in contact.<ref name=Abbott>{{cite book |last1=Abbott |first1=J.M. |last2=Smith |first2=H.C. |last3=Van Ness |first3=M.M. |title=Introduction to Chemical Engineering Thermodynamics |year=2005 |publisher=McGraw-Hill |location=Boston, Montreal |isbn=0-07-310445-0 |edition=7th}}</ref> The process of heat transfer from one place to another place without the movement of particles is called conduction, such as when placing a hand on a cold glass of water—heat is conducted from the warm skin to the cold glass, but if the hand is held a few inches from the glass, little conduction would occur since air is a poor conductor of heat. Steady-state conduction is an idealized model of conduction that happens when the temperature difference driving the conduction is constant so that after a time, the spatial distribution of temperatures in the conducting object does not change any further (see [[Fourier's law]]).<ref>{{cite web |title=Heat conduction |url=https://www.thermalfluidscentral.org/encyclopedia/index.php/Heat_Conduction |work=Thermal-FluidsPedia |publisher=Thermal Fluids Central}}</ref> In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out, since the temperature change (a measure of heat energy) is zero.<ref name="Abbott"/> An example of steady state conduction is the heat flow through walls of a warm house on a cold day—inside the house is maintained at a high temperature and, outside, the temperature stays low, so the transfer of heat per unit time stays near a constant rate determined by the insulation in the wall and the spatial distribution of temperature in the walls will be approximately constant over time.

''Transient conduction'' (see [[Heat equation]]) occurs when the temperature within an object changes as a function of time. Analysis of transient systems is more complex, and analytic solutions of the heat equation are only valid for idealized model systems. Practical applications are generally investigated using numerical methods, approximation techniques, or empirical study.<ref name="Abbott"/>

===Convection===
{{main|Convective heat transfer}}
The flow of fluid may be forced by external processes, or sometimes (in gravitational fields) by buoyancy forces caused when thermal energy expands the fluid (for example in a fire plume), thus influencing its own transfer. The latter process is often called "natural convection". All convective processes also move heat partly by diffusion, as well. Another form of convection is forced convection. In this case, the fluid is forced to flow by using a pump, fan, or other mechanical means.

[[Convection (heat transfer)|Convective heat transfer]], or simply, convection, is the transfer of heat from one place to another by the movement of [[fluids]], a process that is essentially the transfer of heat via [[mass transfer]]. The bulk motion of fluid enhances heat transfer in many physical situations, such as between a solid surface and the fluid.<ref>{{cite book |last=Çengel |first=Yunus |year=2003 |title=Heat Transfer: A practical approach |url=https://books.google.com/books?id=nrbfpSZTwskC |edition=2nd |publisher=McGraw-Hill |location=Boston |isbn=978-0-07-245893-0}}</ref> Convection is usually the dominant form of heat transfer in liquids and gases. Although sometimes discussed as a third method of heat transfer, convection is usually used to describe the combined effects of heat conduction within the fluid (diffusion) and heat transference by bulk fluid flow streaming.<ref>{{cite web |title=Convective heat transfer |url=https://www.thermalfluidscentral.org/encyclopedia/index.php/Convective_Heat_Transfer |work=Thermal-FluidsPedia |publisher=Thermal Fluids Central}}</ref> The process of transport by fluid streaming is known as advection, but pure advection is a term that is generally associated only with mass transport in fluids, such as advection of pebbles in a river. In the case of heat transfer in fluids, where transport by advection in a fluid is always also accompanied by transport via heat diffusion (also known as heat conduction) the process of heat convection is understood to refer to the sum of heat transport by advection and diffusion/conduction.

Free, or natural, convection occurs when bulk fluid motions (streams and currents) are caused by buoyancy forces that result from density variations due to variations of temperature in the fluid. ''Forced'' convection is a term used when the streams and currents in the fluid are induced by external means—such as fans, stirrers, and pumps—creating an artificially induced convection current.<ref>{{cite web |title=Convection — Heat Transfer |url=http://www.engineersedge.com/heat_transfer/convection.htm |publisher=Engineers Edge |access-date=2009-04-20}}</ref>

====Convection-cooling====
{{See also |Nusselt number}}
Convective cooling is sometimes described as [[Convective heat transfer#Newton's law of cooling|Newton's law of cooling]]:
{{Blockquote|''The rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings''.}} However, by definition, the validity of Newton's law of cooling requires that the rate of heat loss from convection be a linear function of ("proportional to") the temperature difference that drives heat transfer, and in convective cooling this is sometimes not the case. In general, convection is not linearly dependent on [[temperature gradient]]s, and in some cases is strongly nonlinear. In these cases, Newton's law does not apply.

===Convection vs. conduction===
In a body of fluid that is heated from underneath its container, conduction, and convection can be considered to compete for dominance. If heat conduction is too great, fluid moving down by convection is heated by conduction so fast that its downward movement will be stopped due to its [[buoyancy]], while fluid moving up by convection is cooled by conduction so fast that its driving buoyancy will diminish. On the other hand, if heat conduction is very low, a large temperature gradient may be formed and convection might be very strong.

The [[Rayleigh number]] (<math>\mathrm{Ra} </math>) is the product of the Grashof (<math>\mathrm{Gr} </math>) and Prandtl (<math>\mathrm{Pr} </math>) numbers. It is a measure that determines the relative strength of conduction and convection.<ref>{{cite book |last1=Incropera |first1=Frank P. |display-authors=etal |year=2012 |title=Fundamentals of heat and mass transfer |page=603 |edition=7th |publisher=Wiley |isbn=978-0-470-64615-1}}</ref>

<math display="block"> \mathrm{Ra} = \mathrm{Gr} \cdot \mathrm{Pr} = \frac{g \Delta \rho L^3} {\mu \alpha} = \frac{g \beta \Delta T L^3} {\nu \alpha}</math>
where
* ''g'' is the acceleration due to gravity,
* ''ρ'' is the density with <math>\Delta \rho</math> being the density difference between the lower and upper ends,
* ''μ'' is the [[dynamic viscosity]],
* ''α'' is the [[Thermal diffusivity]],
* ''β'' is the volume [[thermal expansivity]] (sometimes denoted ''α'' elsewhere),
* ''T'' is the temperature,
* ''ν'' is the [[kinematic viscosity]], and
* ''L'' is characteristic length.

The Rayleigh number can be understood as the ratio between the rate of heat transfer by convection to the rate of heat transfer by conduction; or, equivalently, the ratio between the corresponding timescales (i.e. conduction timescale divided by convection timescale), up to a numerical factor. This can be seen as follows, where all calculations are up to numerical factors depending on the geometry of the system.

The buoyancy force driving the convection is roughly <math>g \Delta \rho L^3</math>, so the corresponding pressure is roughly <math>g \Delta \rho L </math>. In [[steady state]], this is canceled by the [[shear stress]] due to viscosity, and therefore roughly equals <math>\mu V/L = \mu / T_\text{conv} </math>, where ''V'' is the typical fluid velocity due to convection and <math>T_\text{conv}</math> the order of its timescale.<ref>{{Cite journal |last1=Wei |first1=Tao |last2=Zhang |first2=Mengqi |date=December 2020 |title=Rayleigh–Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour |url=https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/rayleightaylor-unstable-condensing-liquid-layers-with-nonlinear-effects-of-interfacial-convection-and-diffusion-of-vapour/0C205AA39E63190BB6D1D5B37A5B1136 |journal=Journal of Fluid Mechanics |language=en |volume=904 |doi=10.1017/jfm.2020.572 |bibcode=2020JFM...904A...1W |s2cid=225136577 |issn=0022-1120|url-access=subscription }}</ref> The conduction timescale, on the other hand, is of the order of <math>T_\text{cond} = L^2/ \alpha</math>.

Convection occurs when the Rayleigh number is above 1,000–2,000.

===Radiation===
[[File:Hot metalwork.jpg|thumb|left|Red-hot iron object, transferring heat to the surrounding environment through thermal radiation]]
Radiative heat transfer is the transfer of energy via [[thermal radiation]], i.e., [[Electromagnetic radiation|electromagnetic waves]].<ref name=Geankoplis /> It occurs across [[vacuum]] or any [[transparency (optics)|transparent]] [[Optical medium|medium]] ([[solid]] or [[fluid]] or [[gas]]).<ref>{{cite web |title=Radiation |url=https://www.thermalfluidscentral.org/encyclopedia/index.php/Radiation |work=Thermal-FluidsPedia |publisher=Thermal Fluids Central}}</ref> Thermal radiation is emitted by all objects at temperatures above [[absolute zero]], due to random movements of atoms and molecules in matter. Since these atoms and molecules are composed of charged particles ([[proton]]s and [[electron]]s), their movement results in the emission of [[electromagnetic radiation]] which carries away energy. Radiation is typically only important in engineering applications for very hot objects, or for objects with a large temperature difference.

When the objects and distances separating them are large in size and compared to the wavelength of thermal radiation, the rate of transfer of [[radiant energy]] is best described by the [[Stefan-Boltzmann equation]]. For an object in vacuum, the equation is:
<math display="block"> \phi_q=\epsilon \sigma T^4. </math>

For [[radiative transfer]] between two objects, the equation is as follows:
<math display="block"> \phi_q=\epsilon \sigma F (T_a^4 - T_b^4), </math>
where
* <math>\phi_q</math> is the [[heat flux]],
* <math>\epsilon </math> is the [[emissivity]] (unity for a [[black body]]),
* <math>\sigma </math> is the [[Stefan–Boltzmann constant]],
* <math>F</math> is the [[view factor]] between two surfaces a and b,<ref>{{cite book |last1=Howell |first1=John R. |last2=Menguc |first2=M.P. |last3=Siegel |first3=Robert |title=Thermal Radiation Heat Transfer |year= 2015 |publisher=Taylor and Francis}}</ref> and
* <math> T_a</math> and <math> T_b</math> are the absolute temperatures (in [[kelvin]]s or [[degrees Rankine]]) for the two objects.

The blackbody limit established by the [[Stefan-Boltzmann equation]] can be exceeded when the objects exchanging thermal radiation or the distances separating them are comparable in scale or smaller than the [[Wien's displacement law|dominant thermal wavelength]]. The study of these cases is called [[near-field radiative heat transfer]].

Radiation from the sun, or solar radiation, can be harvested for heat and power.<ref>{{cite journal |last1=Mojiri |first1=A |year=2013 |title=Spectral beam splitting for efficient conversion of solar energy—A review |journal=Renewable and Sustainable Energy Reviews |volume=28 |pages=654–663 |doi=10.1016/j.rser.2013.08.026|bibcode=2013RSERv..28..654M }}</ref> Unlike conductive and convective forms of heat transfer, thermal radiation – arriving within a narrow-angle i.e. coming from a source much smaller than its distance – can be concentrated in a small spot by using reflecting mirrors, which is exploited in [[concentrating solar power]] generation or a [[burning glass]].<ref>{{cite journal |last1=Taylor |first1=Robert A. |last2=Phelan |first2=Patrick E. |last3=Otanicar |first3=Todd P. |last4=Walker |first4=Chad A. |last5=Nguyen |first5=Monica |last6=Trimble |first6=Steven |last7=Prasher |first7=Ravi |title=Applicability of nanofluids in high flux solar collectors |url=http://digitalcommons.lmu.edu/cgi/viewcontent.cgi?article=1019&context=mech_fac |journal=Journal of Renewable and Sustainable Energy |date=March 2011 |volume=3 |issue=2 |pages=023104 |doi=10.1063/1.3571565|url-access=subscription }}</ref> For example, the sunlight reflected from mirrors heats the [[PS10 solar power tower]] and during the day it can heat water to {{convert|285|°C|°F}}.<ref>{{Cite web|title=Solar thermal power plants - U.S. Energy Information Administration (EIA)|url=https://www.eia.gov/energyexplained/solar/solar-thermal-power-plants.php|access-date=2022-01-28|website=www.eia.gov}}</ref>

The reachable temperature at the target is limited by the temperature of the hot source of radiation. (T<sup>4</sup>-law lets the reverse flow of radiation back to the source rise.) The (on its surface) somewhat 4000 K hot [[sun]] allows to reach coarsely 3000 K (or 3000&nbsp;°C, which is about 3273 K) at a small probe in the focus spot of a big concave, concentrating mirror of the [[Mont-Louis Solar Furnace]] in France.<ref>Megan Crouse: [https://www.manufacturing.net/news/2016/07/gigantic-solar-furnace-can-melt-steel This Gigantic Solar Furnace Can Melt Steel] manufacturing.net, 28 July 2016, retrieved 14 April 2019.</ref>

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