Heat Transfer

Heat transfer is the movement of thermal energy from a region of high temperature to a region of lower temperature. It is a core concept of thermodynamics and related aspects of classical physics.

Overview

Heat transfer is the movement of thermal energy from a region of high temperature to a region of low temperature. Specifically, it is the heat-transfer rate that is most often desired; that is, a prediction of how long it will take for thermal energy to transfer from one location to another. While thermodynamics is used to determine the final thermal conditions between systems in equilibrium, heat transfer predicts actual temperatures of regions over time before equilibrium is reached.

Heat is transferred by three mechanisms that are commonly known as "sensible" heat-transfer mechanisms. These include conduction heat transfer, convection heat transfer, and radiation heat transfer. Each of these mechanisms depends on a temperature difference at different positions in order for heat to be conveyed. A heat-transfer problem may include two or all three of these mechanisms.

Conduction heat transfer is the transfer of heat through a solid or group of solids in contact where a temperature difference exists between one point and another. The rate of conduction heat transfer is directly related to the material's thermal conductivity, which is a thermal property distinctive to each material. The greater a material's thermal conductivity, the faster heat will transfer through it. Pure metals such as copper and aluminum are materials with high thermal conductivities that transfer heat readily. Generally, materials that are good electrical conductors are good thermal conductors. Conduction is also directly related to the magnitude of temperature difference and the solid's area perpendicular to the direction of temperature difference. The conduction rate will be inversely related to the thickness or distance between points of different temperature, so as a solid becomes thicker, it will take longer for heat to flow through it.

The most important law associated with conduction heat transfer is Fourier's conduction law, which states that the heat-transfer rate through a solid by conduction is directly proportional to the temperature difference between two locations, the solid's thermal conductivity, and the area perpendicular to the direction of temperature difference, and inversely proportional to the solid's thickness. This law assumes a steady-state temperature difference; that is, the temperatures at two distinct points in the solid are different but remain constant over a given time period. An example of steady-state conduction is the heat transfer across the wall of a home. During a given period, the outdoor air temperature on one side of the wall may not change, and the heating or cooling system maintains the inside air temperature relatively constant. The conduction heat-transfer rate is directly proportional to the wall's height and length, the thermal conductivity of the wall materials, and the temperature difference between indoor and outdoor air, while it will be inversely related to the wall's thickness.

A common term associated with conduction heat transfer is a material's "thermal resistance." Thermal resistance, or R-value, is a material's ability to resist heat transfer. This is a particularly important concept related to the quality of thermal insulation materials, an important component of most buildings that is directly related to their energy use and efficiency. A material's thermal resistance is equal to its thickness in a direction of temperature difference divided by its thermal conductivity.

Materials with high thermal resistances are used as insulation, an important building component. Insulation's purpose is to reduce the expense and amount of fuel used to heat or cool a building's interior environment. Insulation's high thermal resistance is nearly always achieved by producing many small cells of still air or gas. Conduction depends on a solid's molecules coming into contact with one another to transport heat. Materials with pockets of still air deter this action and slow heat transfer, thus providing a good thermal insulation. Examples of good insulation are polystyrene board (with many small gas bubbles), fiberglass blankets, goose down, and sprayed foams.

Another important category of heat-transfer problem is that of time-dependent or transient conduction, in which temperatures at different points change over time. Transient conduction problems are more difficult to solve than steady-state problems. A well-known differential equation, the heat equation, relates transient temperatures, thermal and physical characteristics of the solid, and time. An important parameter associated with transient conduction is a material's thermal diffusivity. Thermal diffusivity is equal to a material's thermal conductivity divided by the product of its density and specific heat; this product is known as the material's "thermal capacity." Specific heat is a property unique to each material that describes the amount of heat needed to raise a unit mass of material by one degree of temperature. A material with a high thermal diffusivity will have temperatures that change more quickly over time when exposed to heating or cooling than a material with a lower thermal diffusivity. A simple example of transient conduction can be observed by placing a potato in a pot of boiling water. The temperature of the potato will change quickly over the ensuing minutes, with the temperature on its surface warming sooner than the temperature at the potato's center. Using a knowledge of heat transfer, the time needed to cook the potato can be determined.

Convection heat transfer is the transfer of heat between a moving fluid (gas or liquid) in contact with the surface of a solid when the solid and fluid are at different temperatures. When the fluid motion results from a fan or pump, the convection is known as "forced" convection. When a fluid increases in temperature, it becomes less dense, and it rises. This fluid motion, without a fan or pump, results in convection known as "free" or "natural" convection. The convection heat-transfer rate can be determined using Newton's cooling law, which states that this rate is directly proportional to the product of the solid's surface area in contact with the fluid and the temperature difference between the solid and fluid. The heat-transfer rate is also directly proportional to the convection coefficient, sometimes known as the "surface conductance" or "film coefficient," which relates a variety of factors, including fluid velocity, fluid viscosity, the surface roughness of the solid, and its general shape. A simple example of convection heat transfer can be experienced by placing one's face in front of a fan on a warm day to cool oneself.

Radiation heat transfer is the heat exchanged between surfaces that emit electromagnetic waves proportional to their surface temperature when the surface temperature is above absolute zero. Thermal electromagnetic waves are but one type of electromagnetic wave, having wavelengths between 0.1 and 100 micrometers.

Unlike conduction and convection heat transfer, radiation heat transfer does not need a solid or liquid transfer medium; it can occur in a vacuum. The net rate of radiation heat transfer depends upon the difference in the amount of electromagnetic waves leaving and impinging on a surface. A simple example of radiation heat transfer can be observed in a restaurant where food on a buffet is heated by lamps. The lamps are warmest, the surrounding surfaces of the restaurant (walls and ceiling) are likely coolest, and the heated food should have a temperature in between them. The food, because it is warmer, radiates heat to the surroundings but gains radiant heat from the heat lamps above it to maintain its temperature.

When radiation waves collide with a surface, they are either reflected away from the surface, absorbed into the surface, or transmitted through the surface. These three surface characteristics are defined as the reflectivity, absorbtivity, and transmissivity for each material's surface and are unique for each material's surface according to the surface color and texture and the wavelength of incoming radiation. A perfect absorbing surface has an absorbtivity of one and is known as a "black body." Thermal radiation will have shorter wavelengths as the temperature of the emitting surface increases. To simplify the analysis of a surface's reaction to thermal radiation, the thermal-radiation wavelengths can be reduced to two main types: solar radiation (short wave) and earthwave radiation (radiation emitted from surfaces on Earth that are much cooler than the Sun's surface temperature). This can be illustrated by remembering that a person who wears a white shirt outdoors on a sunny day will remain cooler than a person who wears a black shirt. White surfaces reflect 92 percent of solar radiation, while black surfaces absorb 95 percent (and reflect only 5 percent) of incoming solar radiation.

An important parameter relating the orientation of one surface radiating heat to another is the shape or view factor. The shape factor, expressed as a decimal value between zero and one, reveals the percentage of waves emitted by one surface that directly hit another surface. Shape factors have many practical applications, among them determination of how far a radiant-type heater must be situated from its target, as in the case of the radiant heaters used to warm food in restaurants. Shape factors have been experimentally determined for several geometric configurations and are available from graphs published in heat-transfer textbooks. Radiation heat transfer does not have a single simple equation to quantify it.

Applications

Heat transfer has a multitude of applications that affect everyday life. One of the most obvious is human thermal comfort. Nearly everyone assesses and comments on whether they are too hot, too cold, or comfortable. The following applications, although illustrating only one small segment of heat transfer, will focus on human thermal comfort.

An important influence on human thermal comfort in a home, school, or workplace is how the building is constructed and how the heating or cooling system is designed to maintain conditions in the space. There are many different heating and cooling systems used to condition air in enclosed spaces effectively so that occupants are comfortable. Since a large portion of the human body is typically exposed to the air while indoors, the two heat-transfer mechanisms influencing human thermal comfort the most are convection and radiation. Most heating and cooling systems distribute conditioned air from heating and cooling equipment to rooms using a fan to push air through ductwork. Ductwork, usually made of a metal with a high thermal conductivity, should be insulated so that heat does not quickly conduct through it into unconditioned spaces such as attics, basements, or crawlspaces; if it is not insulated, air emerging from the ductwork may no longer be warm or cold enough. Conditioned air emerges from ductwork through vent openings in the ceiling or floor and moves throughout the room. Occupants are cooled or heated by convection as the moving fluid (air) moves past body surfaces, assuming that the air and body surface temperatures are different.

Radiant floor-heating systems use radiation heat transfer to heat occupants. A heated fluid (liquid) is circulated through plastic tubing embedded in low-density concrete beneath the floor surface. Heat conducts through the tubing, concrete, and flooring material to heat the exposed floor surface and raise its temperature. As the floor surface temperature rises, it emits more thermal radiation. A portion of this radiation will be absorbed by and warm room occupants without heating air in the room. Heating air in large rooms frequently is ineffective, because warmed air becomes less dense and rises to near the ceiling, away from room occupants. Radiant floor heating is effective in large rooms because the heat is not used to heat air in the room; it is transferred directly from the floor to the occupants by radiation.

Thermal insulation to reduce heat transfer between the building envelope and outdoors is essential to maintain a cost-effective conditioning system and to achieve thermal comfort. Thermal insulations are materials with lower thermal conductivities that reduce conduction heat transfer. When a material has a lower thermal conductivity, its thermal resistance is increased. A properly insulated building slows the rate of heat gain or loss by conduction between indoors and outdoors, so that a given heating or cooling system can deliver heat or cooling as quickly or quicker than heat flows through the building boundaries to outdoors by conduction.

Lower conduction heat flow usually produces surface temperatures on interior surfaces that also reduce radiant heat transfer between the surfaces and humans. For example, if a building's walls are not insulated, during winter the interior wall surface temperature will be colder than insulated walls would be. A colder wall surface emits less thermal radiation, so the net exchange of radiation waves between uninsulated walls and humans will result in more radiant heat loss from humans. This is an example of why someone may feel cold in a room even though the air temperature is not cold.

A similar interesting example of radiation heat transfer explains why fruit such as oranges on trees in orchards might freeze even though the air temperature remains slightly above freezing. Air at temperatures near freezing circulating among the fruit cools it by convection to near freezing; on a clear, cold night, however, enough heat may radiate from the fruit to a cold sky so that the fruit freezes. Cloudy nights frequently result in warmer temperatures, because cloud cover tends to reflect thermal radiation from heated objects on the ground back toward the ground.

Thermally efficient windows use special films suspended between multiple glazings to reduce heat transfer by conduction and radiation between buildings and the outdoors. Films known as "low emissivity" coatings have a higher reflectivity to earthwave thermal radiation than untreated window glass. Normal window glass transmits nearly 85 percent of radiant heat, resulting in large amounts of heat loss from homes during cold weather. Double glazed windows, which create a layer of still air between glazings, will decrease conduction heat transfer by 50 percent compared to single glazed windows. Adding a suspended film with a low-emissivity coating to double glazed windows will reflect radiation waves and hold heat in a building, reducing heat loss by approximately 60 percent compared to single glazed windows. Thermally efficient windows will result in lower heating costs and a more comfortable interior environment.

Thermal comfort may sometimes be achieved by adjusting the velocity of air passing by one's body. In warm weather, fans are used to move air past bodies at higher velocity to provide cooling. During cold weather, air leaking through window and door frames can create uncomfortable drafts. Altering air velocity will effectively control convection heat transfer between humans and the surrounding air.

Increased convection heat loss from bodies outdoors under cold, windy conditions during winter is commonly expressed as "wind-chill" temperature. It often feels colder outdoors than the air temperature indicates because wind velocity increases convection heat transfer.

Clothing has long been designed to optimize thermal comfort. With the advent of synthetic clothing materials and production techniques, clothing can be designed to maintain body heat in cold weather without accumulating overwhelming weight. Cold-weather clothing utilizes the concept of creating many tiny pockets of still air to reduce heat transfer. This is achieved using lightweight, low-density materials such as goose down as opposed to a material basing its insulative value on bulk and thickness. For warm weather, fabrics have been developed that breathe and wick moisture away from body surfaces, thereby increasing heat transfer from the body surface. Athletic clothing is often made with synthetic fibers that draw perspiration away from body surfaces, allowing athletes to remain dry.

Context

The science of heat transfer is a division of applied thermodynamics. Heat transfer is nearly always concerned with the rate at which heat flows, while thermodynamics focuses on the total amount of heat involved with a process. Heat transfer is based on the first and second laws of thermodynamics. The first law states that for a closed system, an increase in energy is equal to the sum of net heat gain and net gain in work. The second law dictates that heat will flow from a location of high temperature to a location of lower temperature.

Knowledge of heat transfer has developed largely since 1700. Early contributions were made by famous scientists such as Sir Isaac Newton, Jean-Baptiste Biot, and Joseph Fourier. These men were mathematicians as well as physicists and were involved with several branches of science. In 1701, Newton developed his cooling law, which is the basic equation for convection heat transfer. Biot worked on the analysis of conduction heat transfer in 1802. Fourier developed a mathematical description of conduction heat transfer in 1822, ultimately resulting in the formulation of Fourier's conduction law.

A multitude of European scientists during the nineteenth and early twentieth centuries expanded the science of heat transfer dramatically. Among these scientists were Osborne Reynolds, Leo Graetz, and Ernst Nusselt who were pioneers in developing analytical techniques for convection heat transfer. Josef Stefan and his student Ludwig Boltzmann made significant contributions to help explain radiation heat transfer. Between 1879 and 1884, Stefan and Boltzmann were responsible for establishing the relationship between energy radiating from a black-body surface and that surface's temperature.

The development of the U.S. space program during the 1960's required important applications of heat transfer. More important, the space program helped to spawn computer technology and numerical techniques such as the finite-element method and the finite difference method, which were used to solve heat-transfer problems related to space flight.

Applications of heat transfer have influenced nearly every aspect of human life. These applications range from those necessary for human life to those that enhance human life. Thermal aspects of global climate and interaction with the Sun's radiant energy play an important role in sustaining life on Earth. Excessive weather-related phenomena such as heat, cold, rain, and drought as well as natural disasters such as tornadoes, hurricanes, volcanoes, and earthquakes are closely associated with heat transfer.

Heat transfer's impact extends to global pollution and influences ecology. Thermal inversions can adversely affect air quality in urban areas. Industrial and power generation facilities produce excessive heat that is usually dissipated by large amounts of water. Returning this warmer water to its source raises average water temperatures and often produces dramatic ecological changes.

Applications of heat transfer have made life much easier for humankind. Electrical power often involves conversion of heat to electrical energy. This has allowed air-conditioning and irrigation systems to transform unproductive areas into desirable locations. Heat transfer allows for food processing, sterilization, and packaging that not only provide a wide range of foods but also make them easy to prepare and safe to eat.

Principal terms

CONDUCTION: The transfer of heat through a solid or group of solids in contact in a direction where a temperature difference exists

CONVECTION: The transfer of heat between a moving fluid in contact with a solid surface at different temperatures

RADIATION: The transfer of heat by electromagnetic waves between surfaces at different temperatures

RADIATION SHAPE FACTOR: A parameter describing the percentage of thermal radiation leaving one surface and directly striking another surface; varies between value of zero and one

THERMAL CONDUCTIVITY: A property of a solid, liquid, or gas indicating how fast heat will conduct through it; the higher the conductivity, the faster heat will conduct

THERMAL INSULATION: A material with a low thermal conductivity or high thermal resistance used for energy conservation in buildings

THERMAL RESISTANCE: The ability of a material to resist heat transfer

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