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 and
momentum of that fluid. ;
Conduction or
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
Fourier's law for heat conduction. ;
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. ;
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: \phi_q = v \rho c_p \Delta T where • \phi_q is
heat flux (W/m2), • \rho is density (kg/m3), • c_p is heat capacity at constant pressure (J/kg·K), • \Delta T is the difference in temperature (K), • v is velocity (m/s).
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. 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). 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. 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. 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.
Convection-cooling Convective cooling is sometimes described as
Newton's law of cooling: 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 gradients, 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 (\mathrm{Ra} ) is the product of the Grashof (\mathrm{Gr} ) and Prandtl (\mathrm{Pr} ) numbers. It is a measure that determines the relative strength of conduction and convection. \mathrm{Ra} = \mathrm{Gr} \cdot \mathrm{Pr} = \frac{g \Delta \rho L^3} {\mu \alpha} = \frac{g \beta \Delta T L^3} {\nu \alpha} where •
g is the acceleration due to gravity, •
ρ is the density with \Delta \rho 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 g \Delta \rho L^3, so the corresponding pressure is roughly g \Delta \rho L . In
steady state, this is canceled by the
shear stress due to viscosity, and therefore roughly equals \mu V/L = \mu / T_\text{conv} , where
V is the typical fluid velocity due to convection and T_\text{conv} the order of its timescale. The conduction timescale, on the other hand, is of the order of T_\text{cond} = L^2/ \alpha. Convection occurs when the Rayleigh number is above 1,000–2,000.
Radiation Radiative heat transfer is the transfer of energy via
thermal radiation, i.e.,
electromagnetic waves. 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 (
protons and
electrons), 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: \phi_q=\epsilon \sigma T^4. For
radiative transfer between two objects, the equation is as follows: \phi_q=\epsilon \sigma F (T_a^4 - T_b^4), where • \phi_q is the
heat flux, • \epsilon is the
emissivity (unity for a
black body), • \sigma is the
Stefan–Boltzmann constant, • F is the
view factor between two surfaces a and b, and • T_a and T_b are the absolute temperatures (in
kelvins 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
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. 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. For example, the sunlight reflected from mirrors heats the
PS10 solar power tower and during the day it can heat water to . The reachable temperature at the target is limited by the temperature of the hot source of radiation. (T4-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 °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. ==Phase transition==