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## Heat transfer

Heat transfer, also known as heat flow, heat exchange, or transfer of thermal energy is the movement of heat from one place to another. When an object is at a different temperature from its surroundings, heat transfer occurs so that the body and the surroundings reach the same temperature at thermal equilibrium. Such spontaneous heat transfer always occurs from a region of high temperature to another region of lower temperature as required by the second law of thermodynamics.

In engineering, energy transfer by heat between objects is classified as either heat conduction, also called diffusion, of two objects in contact, by fluid convection, which is the mixing of hot and cold fluid regions, and by thermal radiation, the transmission of electromagnetic radiation described by black body theory.[1] However, engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve transfer of heat.

## Overview

This article deals with specific methods by which heat transfer occurs. Note that although the definition of heat implicitly means the movement of energy, the term "heat transfer" has acquired a traditional usage in engineering and other contexts (despite its literal redundancy).

Fundamental methods of heat transfer in engineering include conduction, convection, and radiation. Although separate physical laws have been discovered to describe the behavior of each of these methods, real systems may exhibit a complicated combination. Heat transfer methodologies are used in the numerous disciplines, such as automotive engineering, thermal management of electronic devices and systems, climate control, Insulation, materials processing, and power plant engineering.

Various mathematical methods have been developed to solve or approximate the results of heat transfer in systems. Heat transfer is a path function (or process quantity), as opposed to a state quantity, therefore the amount of heat transferred in a thermodynamic process which changes the state of a system depends on how that process occurs, not only the net difference between the initial and final states of the process. Heat flux is a quantitative, vectorial representation of the heat flow through a surface.

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.

There are some notable similarities in transport equations for heat, momentum, and mass transfer.[2] The equations Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are very similar. A great deal of effort has been devoted to developing analogies among these three transport processes so as to allow prediction of one from any of the others.

## Heat transfer mechanisms

There are a number of distinct, or fundamental, modes of heat transfer:

• Conduction or diffusion: Transfer of energy between objects in physical contact
• Convection: Transfer of energy between an object and its environment, due to fluid motion
• Radiation: Transfer of energy from or to a body by the emission or absorption of electromagnetic radiation
• Mass transfer: Movement of physical objects represents a movement of their internal energy

### Conduction

Fire test used to test the heat transfer through firestops and penetrants used in construction listing and approval use and compliance.

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 atoms. 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 (and especially gases) are less conductive. Thermal contact conductance is the study of heat conduction between solid bodies in contact.

Steady state conduction is a form of conduction which happens when the temperature difference driving the conduction is constant so that after an equilibration time, the spatial distribution of temperatures in the conducting object does not change any further. In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out.

Transient conduction occurs when the temperature within an object changes as a function of time. Analysis of transient systems is more complex and often calls for the application of approximation theories, and/or numerical analysis by computer.

### Convection

Convective heat transfer is the transfer of heat from one place to another by the movement of fluids. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid.[3] Convection is usually the dominant form of heat transfer in liquids and gases. Although often discussed as a third method of heat transfer, convection actually describes the combined effects of conduction and fluid flow.

Free or natural convection occurs when the fluid motion is caused by buoyancy forces that result from the density variations due to variations of temperature in the fluid. Forced convection is when the fluid is forced to flow over the surface by external sources such as fans, stirrers, and pumps, creating an artificially induced convection current.[4]

Convection is described by Newton's law of cooling, which states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings.

A red-hot iron rod from which heat transfer to the surrounding environment will be primarily through radiation.

Thermal radiation is the transfer of heat energy through empty space by electromagnetic waves. All objects with a temperature above absolute zero radiate energy. No medium is necessary for radiation to occur, for it is transferred by electromagnetic waves; radiation takes place even in and through a perfect vacuum. For instance, the energy from the Sun travels through the vacuum of space before warming the earth. Radiation is the only form of heat transfer that can occur in the absence of any form of medium (i.e., through a vacuum).

Thermal radiation is a direct result of the movements of atoms and molecules in a material. Since these atoms and molecules are composed of charged particles (protons and electrons), their movement results in the emission of electromagnetic radiation, which carries energy away from the surface. At the same time, the surface is constantly bombarded by radiation from the surroundings, resulting in the transfer of energy to the surface. Since the amount of emitted radiation increases with increasing temperature, a net transfer of energy from higher temperatures to lower temperatures results.

Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a tiny spot by using reflecting mirrors. Concentrating solar power takes advantage of this fact. For example, the sunlight reflected from mirrors heats the PS10 solar power tower, and during the day it can heat water to 285 °C (558.15 K) or 545 °F.

### Mass Transfer

In mass transfer, energy, including thermal energy, is moved 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 a bed or the movement of an iceberg and changing ocean currents. A practical example is thermal hydraulics.

### Convection vs. conduction

Consider a body of fluid where heat is produced or enters at its lower end and leaves at its upper end. Ignoring radiation, conduction and convection can be considered to "compete" for dominance. If heat conduction is too great, fluid moving down by convection will be heated by conduction so fast that its downward movement will be stopped due to its buoyancy, while fluid moving up by convection will be cooled by conduction so fast that its driving buoyancy will diminish. If, on the other hand, heat conduction is very low, a large temperature gradient will be formed and convection will be very strong.

The Rayleigh number (Ra) is a measure determining the result of this competition.

$Ra = \frac{g \Delta \rho L^3} {\mu \alpha} = \frac{g \beta \Delta T L^3} {\nu \alpha}$

where

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 gΔρL3 so the corresponding pressure is roughly gΔρL. In steady state, this is canceled by the shear stress due to viscosity and therefore roughly equals μV / L = μ / Tconv, where V is the typical fluid velocity due to convection and Tconv the order of its timescale. The conduction timescale, on the other hand, is of the order of Tcond = L2 / α.

Convection occurs when Rayleigh number is above 1000-2000. For example, the Earth's mantle, exhibiting non-stable convection, has Rayleigh number of the order of 103, and Tconv as calculated above is around 108 years.

## Heat transfer in phase changes

Transfer of heat through a phase transition in the medium such as water-to-ice or water-to-steam or steam-to-water or ice-to-water involves significant energy and is exploited in many ways: steam engine, refrigerator etc. (see latent heat of fusion). For example, the Mason equation is an approximate analytical expression for the growth of a water droplet based on the effects of heat transport on evaporation and condensation.

### Boiling

Heat transfer in boiling fluids is complex but of considerable technical importance. It is characterized 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. Nucleate 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').

### Condensation

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:
• Filmwise condensation (when a liquid film is formed on the subcooled surface, usually occurs when the liquid wets the surface).
• 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.

## Modelling approaches

A number of approaches to modelling complex heat transfer phenomena have been developed.

### Heat equation

The heat equation is an important partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time. In some cases, exact solutions of the equation are available; in other cases the equation must be solved numerically (see computational methods, below).

### Computational methods

For example, simplified climate models may use Newtonian cooling instead of a full (and computationally expensive) radiation code to maintain atmospheric temperatures.

### Lumped system analysis

Lumped system analysis is a common approximation in transient conduction which may be used whenever heat conduction within an object is much faster than heat conduction across the boundary of the object.

This is a method of approximation that reduces one aspect of the transient conduction system (that within the object) to an equivalent steady state system (that is, it is assumed that the temperature within the object is completely uniform, although its value may be changing in time).

In this method, a term known as the Biot number is calculated, which is defined as the ratio of the conductive heat resistance within the object to the convective heat transfer resistance across the object's boundary. For small Biot numbers, the approximation of spatially uniform temperature within the object can begin to be used, since it can be presumed that heat transferred into the object has time to uniformaly distribute itself, due to the lower resistance to doing so, as compared with the resistance to heat entering the object.

## Applications and techniques

Heat transfer has broad application to the functioning of numerous devices and systems. Objectives of studying and applying heat transfer principles may be to preserve, i.e. insulate, increase, or decrease temperature in a wide variety of circumstances.

Heat exposure as part of a fire test for firestop products.

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.[5]

The tog is a measure of thermal resistance, commonly used in the textile industry, and often seen quoted on, for example, duvets and carpet underlay.

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.

#### Critical insulation thickness

Low thermal conductivity (k) materials reduce heat fluxes. 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). Increasing thickness of insulation (d meters) increases the thermal resistance (R term as discussed above).

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

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 thickness becomes overshadowed by the effects of surface area is called the critical insulation radius. In simple cylindrical pipes:[6]
${R_{critical}} = {k \over h}$

For a graph of this phenomenon in a cylidrical pipe example see: External Link: Critical Insulation Thickness diagram as at 26/03/09

### Heat exchangers

A heat exchanger is a tool 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.

### Heat dissipation

#### Heat sinks

A heat sink is a term for a component that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator (also a heat exchanger) in a car. Heat sinks also help to cool electronic and optoelectronic devices, such as CPUs, higher-power lasers, and light emitting diodes (LEDs). A heat sink uses its extended surfaces to increase the surface area in contact with the cooling fluid, the air for example.

#### Buildings

In cold climates, houses with their heating systems form dissipative systems. In spite of efforts to insulate such houses to reduce heat losses to their exteriors, considerable heat is lost which can make their interiors uncomfortably cool or cold. For the comfort of the inhabitants, the interiors must be maintained out of thermal equilibrium with the external surroundings. In effect, these domestic residences are oases of warmth in a sea of cold and the thermal gradient between the inside and outside is often quite steep. This can lead to problems such as condensation and uncomfortable draughts (drafts) which, if left unaddressed, can cause cosmetic or structural damage to the property. Such issues can be prevented by use of insulation techniques for reducing heat loss.

Thermal transmittance is the rate of transfer of heat through a structure divided by the difference in temperature across the structure. It is expressed in watts per square metre per kelvin, or W/m²K. Well-insulated parts of a building have a low thermal transmittance whereas poorly-insulated parts of a building have a high thermal transmittance.

A thermostat is a device capable of starting the heating system when the house's interior falls below a set temperature, and of stopping that same system when another (higher) set temperature has been achieved. Thus the thermostat controls the flow of energy into the house, that energy eventually being dissipated to the exterior.

### Thermal energy storage

Thermal energy storage refers to a number of technologies that store energy in a thermal reservoir for later use. They can be employed to balance energy demand between day time and night time. The thermal reservoir may be maintained at a temperature above (hotter) or below (colder) than that of the ambient environment. Applications include later use in space heating, domestic or process hot water, or to generate electricity. Most practical active solar heating systems have storage for a few hours to a day's worth of heat collected.

### Evaporative cooling

Evaporative cooling is a physical phenomenon in which evaporation of a liquid, typically into surrounding air, cools an object or a liquid in contact with it. Latent heat describes the amount of heat that is needed to evaporate the liquid; this heat comes from the liquid itself and the surrounding gas and surfaces. The greater the difference between the two temperatures, the greater the evaporative cooling effect. When the temperatures are the same, no net evaporation of water in air occurs, thus there is no cooling effect. A simple example of natural evaporative cooling is perspiration, or sweat, which the body secretes in order to cool itself. An evaporative cooler is a device that cools air through the simple evaporation of water.

Radiative cooling is the process by which a body loses heat by radiation and is an important effect in the Earth's atmosphere. In the case of the earth-atmosphere system it refers to the process by which long-wave (infra red) radiation is emitted to balance the absorption of short-wave (visible) energy from the sun. Convective transport of heat and evaporative transport of latent heat both remove heat from the surface and redistributes it in the atmosphere, making it available for radiative transport at higher altitudes.

### Laser cooling

Laser cooling refers to a number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields. The most common method of laser cooling is Doppler cooling. In Doppler cooling, the frequency of light is tuned slightly below an electronic transition in the atom. Thus the atoms would absorb more photons if they moved towards the light source, due to the Doppler effect. If an excited atom then emits a photon spontaneously, it will be accelerated. The result of the absorption and emission process is to reduce the speed of the atom. Eventually the mean velocity, and therefore the kinetic energy of the atoms will be reduced. Since the temperature of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the atoms.

Sympathetic cooling is a process in which particles of one type cool particles of another type. Typically, atomic ions that can be directly laser cooled are used to cool nearby ions or atoms. This technique allows cooling of ions and atoms that can't be cooled directly by laser cooling.

### Magnetic cooling

Magnetic evaporative cooling is a technique for lowering the temperature of a group of atoms. The process confines atoms using a magnetic field. Collisions mean that over time, individual atoms will become much more energetic than the others, and will escape, removing energy from the system and reducing the temperature of the remaining group. This process is similar to the familiar process by which standing water becomes water vapor.

### Other

A heat pipe is a passive device that is constructed in such a way that it acts as though it has extremely high thermal conductivity. Heat pipes use latent heat and capillary action to move heat, and can carry many times as much heat as a similar-sized copper rod. Originally invented for use in satellites, they are starting to have applications in personal computers.

A thermocouple is a junction between two different metals that produces a voltage related to a temperature difference. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert heat into electric power.

A thermopile is an electronic device that converts thermal energy into electrical energy. It is composed of thermocouples. Thermopiles do not measure the absolute temperature, but generate an output voltage proportional to a temperature difference. Thermopiles are widely used, e.g., they are the key component of the infrared thermometers that are widely used to measure body temperature via the ear.

A thermal diode or thermal rectifier is a device that preferentially passes heat in one direction; a "one-way valve" for heat.

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