Radiation
Main article: Thermal radiation

Radiation is the transfer of heat energy through empty space. All objects with a temperature above absolute zero radiate energy at a rate equal to their emissivity multiplied by the rate at which energy would radiate from them if they were a black body. No medium is necessary for radiation to occur, for it is transferred through electromagnetic waves; radiation works even in and through a perfect vacuum. The energy from the Sun travels through the vacuum of space before warming the earth.

Both reflectivity and emissivity of all bodies is wavelength dependent. The temperature determines the wavelength distribution of the electromagnetic radiation as limited in intensity by Planck’s law of black-body radiation. For any body the reflectivity depends on the wavelength distribution of incoming electromagnetic radiation and therefore the temperature of the source of the radiation. The emissivity depends on the wave length distribution and therefore the temperature of the body itself. For example, fresh snow, which is highly reflective to visible light, (reflectivity about 0.90) appears white due to reflecting sunlight with a peak energy wavelength of about 0.5 micrometres. Its emissivity, however, at a temperature of about -5°C, peak energy wavelength of about 12 micrometres, is 0.99.

Gases absorb and emit energy in characteristic wavelength patterns that are different for each gas.

Visible light is simply another form of electromagnetic radiation with a shorter wavelength (and therefore a higher frequency) than infrared radiation. The difference between visible light and the radiation from objects at conventional temperatures is a factor of about 20 in frequency and wavelength; the two kinds of emission are simply different "colours" of electromagnetic radiation.
[edit] Clothing and building surfaces, and radiative transfer

Lighter colors and also whites and metallic substances absorb less illuminating light, and thus heat up less; but otherwise color makes little difference as regards heat transfer between an object at everyday temperatures and its surroundings, since the dominant emitted wavelengths are nowhere near the visible spectrum, but rather in the far infrared. Emissivities at those wavelengths have little to do with visual emissivities (visible colors); in the far infrared, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit. The main exception to this is shiny metal surfaces, which have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions; an example of this is the multi-layer insulation used to insulate spacecraft. Low-emissivity windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light.
[edit] Physical Transfer

Finally it is possible to move heat by 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 your bed or the movement of an iceberg and changing ocean currents.
[edit] Newton's law of cooling

A related principle, Newton's law of cooling, states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. The law is

\frac{d Q}{d t} = h \cdot A( T_{\text{env}}- T(t)) = - h \cdot A \Delta T(t)\quad

Q = Thermal energy in joules
h = Heat transfer coefficient
A = Surface area of the heat being transferred
T = Temperature of the object's surface and interior (since these are the same in this approximation)
Tenv = Temperature of the environment
ΔT(t) = T(t) − Tenv is the time-dependent thermal gradient between environment and object

This form of heat loss principle is sometimes not very precise; an accurate formulation may require analysis of heat flow, based on the (transient) heat transfer equation in a nonhomogeneous, or else poorly conductive, medium. An analog for continuous gradients is Fourier's Law.

The following simplification (called lumped system thermal analysis and other similar terms) may be applied, so long as it is permitted by the Biot number, which relates surface conductance to interior thermal conductivity in a body. If this ratio permits, it shows that the body has relatively high internal conductivity, such that (to good approximation) the entire body is at the same uniform temperature throughout, even as this temperature changes as it is cooled from the outside, by the environment. If this is the case, these conditions give the behavior of exponential decay with time, of temperature of a body.

In such cases, the entire body is treated as lumped capacitance heat reservoir, with total heat content which is proportional to simple total heat capacity C , and T, the temperature of the body, or Q = C T. From the definition of heat capacity C comes the relation C = dQ/dT. Differentiating this equation with regard to time gives the identity (valid so long as temperatures in the object are uniform at any given time): dQ/dt = C (dT/dt). This expression may be used to replace dQ/dt in the first equation which begins this section, above. Then, if T(t) is the temperature of such a body at time t , and Tenv is the temperature of the environment around the body:

\frac{d T(t)}{d t} = - r (T(t) - T_{\mathrm{env}}) = - r \Delta T(t)\quad

where

r = hA/C is a positive constant characteristic of the system, which must be in units of 1/time, and is therefore sometimes expressed in terms of a characteristic time constant t0 given by: r = 1/t0 = ΔT/[dT(t)/dt] . Thus, in thermal systems, t0 = C/hA. (The total heat capacity C of a system may be further represented by its mass-specific heat capacity cp multiplied by its mass m, so that the time constant t0 is also given by mcp/hA).

Thus the above equation may also be usefully written:

\frac{d T(t)}{d t} = - \frac{1}{t_0} \Delta T(t)\quad


The solution of this differential equation, by standard methods of integration and substitution of boundary conditions, gives:

T(t) = T_{\mathrm{env}} + (T(0) - T_{\mathrm{env}}) \ e^{-r t}. \quad

Here, T(t) is the temperature at time t, and T(0) is the initial temperature at zero time, or t = 0.

If:

\Delta T(t) \quad is defined as : T(t) - T_{\mathrm{env}} \ , \quad where \Delta T(0)\quad is the initial temperature difference at time 0,

then the Newtonian solution is written as:

\Delta T(t) = \Delta T(0) \ e^{-r t} = \Delta T(0) \ e^{-t/t_0}. \quad

Uses: For example, simplified climate models may use Newtonian cooling instead of a full (and computationally expensive) radiation code to maintain atmospheric temperatures.
[edit] One dimensional application, using thermal circuits

A very useful concept used in heat transfer applications is the representation of thermal transfer by what is known as thermal circuits. A thermal circuit is the representation of the resistance to heat flow as though it were an electric resistor. The heat transferred is analogous to the current and the thermal resistance is analogous to the electric resistor. The value of the thermal resistance for the different modes of heat transfer are calculated as the denominators of the developed equations. The thermal resistances of the different modes of heat transfer are used in analyzing combined modes of heat transfer. The equations describing the three heat transfer modes and their thermal resistances, as discussed previously are summarized in the table below:
Thermal Circuits.png

In cases where there is heat transfer through different media (for example through a composite), the equivalent resistance is the sum of the resistances of the components that make up the composite. Likely, in cases where there are different heat transfer modes, the total resistance is the sum of the resistances of the different modes. Using the thermal circuit concept, the amount of heat transferred through any medium is the quotient of the temperature change and the total thermal resistance of the medium. As an example, consider a composite wall of cross- sectional area A. The composite is made of an L1 long cement plaster with a thermal coefficient k1 and L2 long paper faced fiber glass, with thermal coefficient k2. The left surface of the wall is at Ti and exposed to air with a convective coefficient of hi. The Right surface of the wall is at To and exposed to air with convective coefficient ho.
Thermal Circuits2.jpg

Using the thermal resistance concept heat flow through the composite is as follows:
Thermal Circuits3.jpg

"hi and h0 should be ki and k0 in Thermal_Circuits3.jpg"
[edit] Insulation and radiant barriers
Main articles: Thermal insulation and Radiant barrier

Thermal insulators are materials specifically designed to reduce the flow of heat by limiting conduction, convection, or both. Radiant barriers are materials which reflect radiation and therefore reduce the flow of heat from radiation sources. Good insulators are not necessarily good radiant barriers, and vice versa. Metal, for instance, is an excellent reflector and poor insulator.

The effectiveness of an insulator is indicated by its R- (resistance) value. The R-value of a material is the inverse of the conduction coefficient (k) multiplied by the thickness (d) of the insulator. The units of resistance value are in SI units: (K·m²/W)

{R} = {d \over k}

{C} = {Q \over m \Delta T}

Rigid fiberglass, a common insulation material, has an R-value of 4 per inch, while poured concrete, a poor insulator, has an R-value of 0.08 per inch.[7]

The effectiveness of a radiant barrier is indicated by its reflectivity, which is the fraction of radiation reflected. A material with a high reflectivity (at a given wavelength) has a low emissivity (at that same wavelength), and vice versa (at any specific wavelength, reflectivity = 1 - emissivity). An ideal radiant barrier would have a reflectivity of 1 and would therefore reflect 100% of incoming radiation. Vacuum bottles (Dewars) are 'silvered' to approach this. In space vacuum, satellites use multi-layer insulation which consists of many layers of aluminized (shiny) mylar to greatly reduce radiation heat transfer and control satellite temperature.
[edit] Critical insulation thickness
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To reduce the rate of heat transfer, one would add insulating materials i.e with low thermal conductivity (k). The smaller the k value, the larger the corresponding thermal resistance (R) value.
The units of thermal conductivity(k) are W·m-1·K-1 (watts per meter per kelvin), therefore increasing width of insulation (x meters) decreases the k term and as discussed increases resistance.

This follows logic as increased resistance would be created with increased conduction path (x).

However, adding this layer of insulation also has the potential of increasing the surface area and hence thermal convection area (A).

An obvious example is a cylindrical pipe:

* As insulation gets thicker, outer radius increases and therefore surface area increases.
* The point where the added resistance of increasing insulation width becomes overshadowed by the effects of surface area is called the critical insulation thickness. In simple cylindrical pipes:[8]

{R_{critical}} = {k \over h}

For a graph of this phenomenon in a cylidrical pipe example see: External Link: Critical Insulation Thickness diagram as at 26/03/09
[edit] Heat exchangers
Main article: Heat exchanger

A heat exchanger is a device built for efficient heat transfer from one fluid to another, whether the fluids are separated by a solid wall so that they never mix, or the fluids are directly contacted. Heat exchangers are widely used in refrigeration, air conditioning, space heating, power generation, and chemical processing. One common example of a heat exchanger is the radiator in a car, in which the hot radiator fluid is cooled by the flow of air over the radiator surface.

Common types of heat exchanger flows include parallel flow, counter flow, and cross flow. In parallel flow, both fluids move in the same direction while transferring heat; in counter flow, the fluids move in opposite directions and in cross flow the fluids move at right angles to each other. The common constructions for heat exchanger include shell and tube, double pipe, extruded finned pipe, spiral fin pipe, u-tube, and stacked plate.

When engineers calculate the theoretical heat transfer in a heat exchanger, they must contend with the fact that the driving temperature difference between the two fluids varies with position. To account for this in simple systems, the log mean temperature difference (LMTD) is often used as an 'average' temperature. In more complex systems, direct knowledge of the LMTD is not available and the number of transfer units (NTU) method can be used instead.
[edit] Boiling heat transfer
See also: boiling and critical heat flux

Heat transfer in boiling fluids is complex but of considerable technical importance. It is characterised by an s-shaped curve relating heat flux to surface temperature difference (see say Kay & Nedderman 'Fluid Mechanics & Transfer Processes', CUP, 1985, p. 529).

At low driving temperatures, no boiling occurs and the heat transfer rate is controlled by the usual single-phase mechanisms. As the surface temperature is increased, local boiling occurs and vapour bubbles nucleate, grow into the surrounding cooler fluid, and collapse. This is sub-cooled nucleate boiling and is a very efficient heat transfer mechanism. At high bubble generation rates the bubbles begin to interfere and the heat flux no longer increases rapidly with surface temperature (this is the departure from nucleate boiling DNB). At higher temperatures still, a maximum in the heat flux is reached (the critical heat flux). The regime of falling heat transfer which follows is not easy to study but is believed to be characterised by alternate periods of nucleate and film boiling. Nukleate boiling slowing the heat transfer due to gas phase {bubbles} creation on the heater surface, as mentioned, gas phase thermal conductivity is much lower than liquid phase thermal conductivity, so the outcome is a kind of "gas thermal barrier".

At higher temperatures still, the hydrodynamically quieter regime of film boiling is reached. Heat fluxes across the stable vapour layers are low, but rise slowly with temperature. Any contact between fluid and the surface which may be seen probably leads to the extremely rapid nucleation of a fresh vapour layer ('spontaneous nucleation').
[edit] Condensation heat transfer

Condensation occurs when a vapor is cooled and changes its phase to a liquid. Condensation heat transfer, like boiling, is of great significance in industry. During condensation, the latent heat of vaporization must be released. The amount of the heat is the same as that absorbed during vaporization at the same fluid pressure.

There are several modes of condensation:

* Homogeneous condensation (as during a formation of fog).
* Condensation in direct contact with subcooled liquid.
* Condensation on direct contact with a cooling wall of a heat exchanger-this is the most common mode used in industry:
o Filmwise condensation (when a liquid film is formed on the subcooled surface, usually occurs when the liquid wets the surface).
o Dropwise condensation (when liquid drops are formed on the subcooled surface, usually occurs when the liquid does not wet the surface). Dropwise condensation is difficult to sustain reliably; therefore, industrial equipment is normally designed to operate in filmwise condensation mode.

[edit] Heat transfer in education

Heat transfer is typically studied as part of a general chemical engineering or mechanical engineering curriculum. Typically, thermodynamics is a prerequisite to undertaking a course in heat transfer, as the laws of thermodynamics are essential in understanding the mechanism of heat transfer. Other courses related to heat transfer include energy conversion, thermofluids and mass transfer.

Heat transfer methodologies are used in the following disciplines, among others: