Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer. All forms of heat transfer may occur in some systems (for example, in transparent fluids like the Earth's atmosphere) at the same time. Heat transfer only occurs because of a temperature-difference driving force and heat flows from the high to the low temperature region.^[1]

Heat conduction, also called diffusion, is the direct microscopic exchange of kinetic energy of particles through the stationary boundary between two systems. Heat conduction occurs between stationary masses where there is no movement to carry heat away. Heat transfer through the stationary air layer immediately adjacent to, say one millimeter or so from an interior wall, or from a warm pot placed on a counter, are examples of conductive heat transfer.

Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid. 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 sometimes 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 use of a pump, fan or other mechanical means.

The final major form of heat transfer is by radiation, which occurs in any transparent medium (solid or fluid) but may also even occur across vacuum (as when the Sun heats the Earth). Radiation is the transfer of energy through space by means of electromagnetic waves in much the same way as electromagnetic light waves transfer light. The same laws that govern the transfer of light govern the radiant transfer of heat.^[1]

Overview

Heat is defined in physics as the transfer of thermal energy across a well-defined boundary around a thermodynamic system. It is a characteristic of a process and is not statically contained in matter. In engineering contexts, however, the term heat transfer has acquired a specific usage, despite its literal redundancy of the characterization of transfer. In these contexts, heat is taken as synonymous to thermal energy. This usage has its origin in the historical interpretation of heat as a fluid (caloric) that can be transferred by various causes,^[2] and that is also common in the language of laymen and everyday life.

Fundamental methods of heat transfer in engineering include conduction, convection, and radiation. Physical laws describe the behavior and characteristics of each of these methods. Real systems often exhibit a complicated combination of them. Heat transfer methods are used in 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 that 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.^[3]

Heat transfer is typically studied as part of a general chemical engineering or mechanical engineering curriculum. Typically, thermodynamics is a prerequisite for heat transfer courses, as the laws of thermodynamics are essential to the mechanism of heat transfer.^[3] Other courses related to heat transfer include energy conversion, thermofluids, and mass transfer.

The transport equations for thermal energy (Fourier's law), mechanical momentum (Newton's law for fluids), and mass transfer (Fick's laws of diffusion) are similar^[4][5] and analogies among these three transport processes have been developed to facilitate prediction of conversion from any one to the others.^[5]

Mechanisms

The fundamental modes of heat transfer are:

Conduction or diffusion

The transfer of energy between objects that are in physical contact

Convection

The transfer of energy between an object and its environment, due to fluid motion

Radiation

The transfer of energy to or from a body by means of the emission or absorption of electromagnetic radiation

Mass transfer

The transfer of energy from one location to another as a side effect of physically moving an object containing that energy

Conduction

Main article: 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.^[6]

Steady state conduction (see Fourier's law) is a form of conduction that 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.^[7] In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out.^[6]

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 often calls for the application of approximation theories or numerical analysis by computer.^[6]

Convection

Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids. (In physics, the term fluid means any substance that deforms under shear stress; it includes liquids, gases, plasmas, and some plastic solids.) Bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid.^[8] 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.^[9]

Free, or natural, convection occurs when the fluid motion is caused by buoyancy forces that result from 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 means—such as fans, stirrers, and pumps—creating an artificially induced convection current.^[10]

Convective heating or cooling in some circumstances may be described by Newton's law of cooling: "The rate of heat loss of a body is proportional to the difference in temperatures 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 gradients, and in some cases is strongly nonlinear. In these cases, Newton's law does not apply.

Radiation

Main article: thermal radiation

A red-hot iron object, transferring heat to the surrounding environment primarily through thermal radiation.

Thermal radiation is energy emitted by matter as electromagnetic waves due to the pool of thermal energy that all matter possesses that has a temperature above absolute zero. Thermal radiation propagates without the presence of matter through the vacuum of space.^[11]

Thermal radiation is a direct result of the 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 energy away from the surface.

Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a small spot by using reflecting mirrors, which is exploited in concentrating solar power generation. For example, the sunlight reflected from mirrors heats the PS10 solar power tower and during the day it can heat water to 285 °C (545 °F).^{[citation needed]}

Mass Transfer

In mass transfer, energy—including thermal energy—is moved by the physical transfer of a hot or cold object from one place to another.^[12] 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.^{[citation needed]}

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 (Ra) is a measure determining the result of this competition.^{[citation needed]}

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

where

• g is acceleration due to gravity
• ρ is the density with Δρ 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 and
• ν is the kinematic viscosity.

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 / T_conv, where V is the typical fluid velocity due to convection and T_conv the order of its timescale.^{[citation needed]} The conduction timescale, on the other hand, is of the order of T_cond = L² / α.

Convection occurs when the Rayleigh number is above 1,000–2,000. For example, the Earth's mantle, exhibiting non-stable convection, has Rayleigh number of the order of 1,000, and T_conv as calculated above is around 100 million years.^{[citation needed]}

Phase changes

See also: latent heat of fusion

Transfer of heat through a phase transition in the medium—such as water-to-ice, water-to-steam, steam-to-water, or ice-to-water—involves significant energy and is exploited in many ways: steam engines, refrigerators, etc.^[13] 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.^{[14][further explanation needed]}

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 vapor 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, or DNB). At higher temperatures still, a maximum in the heat flux is reached (the critical heat flux, or CHF). The regime of falling heat transfer that follows is not easy to study, but is believed to be characterized by alternate periods of nucleate and film boiling. Nucleate boiling slows the heat transfer due to gas bubbles on the heater's 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".^{[citation needed]}

At higher temperatures still, the hydrodynamically-quieter regime of film boiling is reached. Heat fluxes across the stable vapor layers are low, but rise slowly with temperature. Any contact between fluid and the surface that may be seen probably leads to the extremely rapid nucleation of a fresh vapor layer ("spontaneous nucleation").^{[citation needed]}

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.^{[citation needed]} 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.^{[citation needed]}

There are several types 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 is when a liquid film is formed on the subcooled surface, and usually occurs when the liquid wets the surface.
  • Dropwise condensation is when liquid drops are formed on the subcooled surface, and 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.

Modeling approaches

Complex heat transfer phenomena can be modeled in different ways.

Heat equation

The heat equation is an important partial differential equation that 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 using computational methods. For example, simplified climate models may use Newtonian cooling, instead of a full (and computationally expensive) radiation code, to maintain atmospheric temperatures.^{[citation needed]}

Lumped system analysis

System analysis by the lumped capacitance model is a common approximation in transient conduction that 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, the method assumes that the temperature within the object is completely uniform, although its value may be changing in time.

In this method, the ratio of the conductive heat resistance within the object to the convective heat transfer resistance across the object's boundary, known as the Biot number, is calculated. For small Biot numbers, the approximation of spatially uniform temperature within the object can be used: it can be presumed that heat transferred into the object has time to uniformly distribute itself, due to the lower resistance to doing so, as compared with the resistance to heat entering the object.^{[citation needed]}

Lumped system analysis often reduces the complexity of the equations to one first-order linear differential equation, in which case heating and cooling are described by a simple exponential solution, often referred to as Newton's law of cooling.

Applications and techniques

Heat transfer has broad application to the functioning of numerous devices and systems. Heat-transfer principles may be used to preserve, increase, or decrease temperature in a wide variety of circumstances.^{[citation needed]}

Insulation and radiant barriers

Car exhausts usually require some form of heat barrier, especially high performance exhausts where a ceramic coating is often applied.

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 that 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 a poor insulator.

The effectiveness of an insulator is indicated by its R-value, or resistance value. The R-value of a material is the inverse of the conduction coefficient (k) multiplied by the thickness (d) of the insulator. In most of the world, R-values are measured in SI units: square-meter kelvins per watt (m²·K/W). In the United States, R-values are customarily given in units of British thermal units per hour per square-foot degrees Fahrenheit (Btu/h·ft²·°F).^{[citation needed]}

${R} = {d \over k}$

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

Rigid fiberglass, a common insulation material, has an R-value of four per inch, while poured concrete, a poor insulator, has an R-value of 0.08 per inch.^[15]

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.^{[citation needed]}

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 percent of incoming radiation. Vacuum flasks, or Dewars, are silvered to approach this ideal. In the vacuum of space, satellites use multi-layer insulation, which consists of many layers of aluminized (shiny) Mylar to greatly reduce radiation heat transfer and control satellite temperature.^{[citation needed]}

Critical insulation thickness

Low thermal conductivity (k) materials reduce heat fluxes. The smaller the k value, the larger the corresponding thermal resistance (R) value. Thermal conductivity is measured in watts-per-meter per kelvin (W·m⁻¹·K⁻¹), represented as k. As the thickness of insulating material increases, the thermal resistance—or R-value—also increases.

However, adding layers of insulation has the potential of increasing the surface area, and hence the thermal convection area.

For example, as thicker insulation is added to a cylindrical pipe, the outer radius of the pipe-and-insulation system increases, and therefore surface area increases. The point where the added resistance of increasing insulation thickness becomes overshadowed by the effect of increased surface area is called the critical insulation thickness. In simple cylindrical pipes, this is calculated as a radius:^[16]

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

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 in direct contact. Heat exchangers are widely used in refrigeration, air conditioning, space heating, power generation, and chemical processing. One common example of a heat exchanger is a car's radiator, in which the hot coolant fluid is cooled by the flow of air over the radiator's surface.^{[citation needed]}

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. Common constructions for heat exchanger include shell and tube, double pipe, extruded finned pipe, spiral fin pipe, u-tube, and stacked plate.^{[further explanation needed]}

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.^{[citation needed]}

Heat dissipation

A heat sink is 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 in a car (which is also a heat exchanger). 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.

Buildings

In cold climates, houses with their heating systems form dissipative systems. In spite of efforts to insulate houses to reduce heat losses via 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 air currents, 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.^{[citation needed]}

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 meter 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.^{[citation needed]}

Thermal energy storage

Thermal energy storage refers to technologies that store energy in a thermal reservoir for later use. They can be employed to balance energy demand between daytime and nighttime. 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.^{[citation needed]}

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.^{[citation needed]}

Radiative cooling

Radiative cooling is the process by which a body loses heat by radiation. It 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 (infrared) 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 redistribute it in the atmosphere, making it available for radiative transport at higher altitudes.^{[citation needed]}

Laser cooling

Laser cooling refers to 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 the laser 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 cannot be laser cooled directly.^{[citation needed]}

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. Over time, individual atoms will become much more energetic than the others due to random collisions, 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.^{[citation needed]}

Heat Transfer in the Human Body

The principles of heat transfer in engineering systems can be applied to the human body in order to determine how the body transfers heat. Heat is produced in the body by the continuous metabolism of nutrients which provides energy for the systems of the body.^[17] The human body must maintain a consistent internal temperature in order to maintain healthy bodily functions. Therefore, excess heat must be dissipated from the body to keep it from overheating. When a person engages in elevated levels of physical activity, the body requires additional fuel which increases the metabolic rate and the rate of heat production. The body must then use additional methods to remove the additional heat produced in order to keep the internal temperature at a healthy level.

Heat transfer by convection is driven by the movement of fluids over the surface of the body. This convective fluid can be either a liquid or a gas. For heat transfer from the outer surface of the body, the convection mechanism is dependent on the surface area of the body, the velocity of the air, and the temperature gradient between the surface of the skin and the ambient air.^[18] The normal temperature of the body is approximately 37°C. Heat transfer occurs more readily when the temperature of the surroundings is significantly less than the normal body temperature. This concept explains why a person feels “cold” when not enough covering is worn when exposed to a cold environment. Clothing can be considered an insulator which provides thermal resistance to heat flow over the covered portion of the body.^[19] This thermal resistance causes the temperature on the surface of the clothing to be less than the temperature on the surface of the skin. This smaller temperature gradient between the surface temperature and the ambient temperature will cause a lower rate of heat transfer than if the skin were not covered.

In order to ensure that one portion of the body is not significantly hotter than another portion, heat must be distributed evenly through the bodily tissues. Blood flowing through blood vessels acts as a convective fluid and helps to prevent any buildup of excess heat inside the tissues of the body. This flow of blood through the vessels can be modeled as pipe flow in an engineering system. The heat carried by the blood is determined by the temperature of the surrounding tissue, the diameter of the blood vessel, the thickness of the fluid, velocity of the flow, and the heat transfer coefficient of the blood. The velocity, blood vessel diameter, and the fluid thickness can all be related with the Reynolds Number, a dimensionless number used in fluid mechanics to characterize the flow of fluids.

Latent heat loss, also known as evaporative heat loss, accounts for a large fraction of heat loss from the body. When the core temperature of the body increases, the body triggers sweat glands in the skin to bring additional moisture to the surface of the skin. The liquid is then transformed into vapor which removes heat from the surface of the body.^[20] The rate of evaporation heat loss is directly related to the vapor pressure at the skin surface and the amount of moisture present on the skin.^[18] Therefore, the maximum of heat transfer will occur when the skin is completely wet. The body continuously loses water by evaporation but the most significant amount of heat loss occurs during periods of increased physical activity.

Other

A heat pipe is a passive device 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 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 infrared thermometers, such as those used to measure body temperature via the ear.^{[citation needed]}

A thermal diode or thermal rectifier is a device that preferentially passes heat in one direction: a "one-way valve" for heat.^{[citation needed]}

See also

• Stefan–Boltzmann law
• Thermal contact conductance
• Thermal physics
• Thermal resistance in electronics
• Thermal science
• Boiling

References

1. ^ ^{a b} Geankoplis, Christie John (2003). Transport processes and separation process principles : (includes unit operations) (4th ed. ed.). Upper Saddle River, NJ: Prentice Hall Professional Technical Reference. ISBN 013101367X. 
2. ^ Lienhard, John H., IV; Lienhard, John H., V (2008). A Heat Transfer Textbook (3rd ed.). Cambridge, Massachusetts: Phlogiston Press. ISBN 9780971383531. OCLC 230956959. 
3. ^ ^{a b} New Jersey Institute of Technology, Chemical Engineering Dept. "B.S. Chemical Engineering". NJIT. http://catalog.njit.edu/undergraduate/programs/chemicalengineering.php. Retrieved 9 April 2011. 
4. ^ Welty, James R.; Wicks, Charles E.; Wilson, Robert Elliott (1976). Fundamentals of momentum, heat, and mass transfer (2 ed.). New York: Wiley. ISBN 9780471933540. OCLC 2213384. http://books.google.be/books?cd=3&hl=en&id=hZxRAAAAMAAJ. 
5. ^ ^{a b} Faghri, Amir; Zhang, Yuwen; Howell, John (2010). Advanced Heat and Mass Transfer. Columbia, MO: Global Digital Press. ISBN 978-0984276004. 
6. ^ ^{a b c} Abbott, J.M. Smith, H.C. Van Ness, M.M. (2005). Introduction to chemical engineering thermodynamics (7th ed. ed.). Boston ; Montreal: McGraw-Hill. ISBN 0073104450. 
7. ^ "Thermal-FluidsPedia | Heat conduction".
8. ^ Çengel, Yunus A. (2003). Heat Transfer: a practical approach. McGraw-Hill series in mechanical engineering (2nd ed.). Boston: McGraw-Hill. ISBN 9780072458930. OCLC 300472921. http://books.google.be/books?id=nrbfpSZTwskC&dq=9780072458930&hl=en&ei=1q7YTNKMJ8OqlAe25_CSCQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCkQ6AEwAA. Retrieved 2009-04-20. 
9. ^ "Thermal-FluidsPedia | Convective heat transfer"
10. ^ "Convection — Heat Transfer". Engineers Edge. Engineers Edge. http://www.engineersedge.com/heat_transfer/convection.htm. Retrieved 2009-04-20. 
11. ^ "Thermal-FluidsPedia | Radiation"
12. ^ "Thermal-FluidsPedia | Mass transfer"
13. ^ "Thermal-FluidsPedia | Multiphase systems"
14. ^ Kay, John Menzies; Nedderman, R. M. (1985). Fluid Mechanics and Transfer Processes (2nd ed.). CUP Archive. p. 529. ISBN 9780521316248. 
15. ^ Martin, Randy L. (2008-07-29). "R-Value Table". ColoradoENERGY.org. Windsor, Colorado: R. L. Martin & Associates, Inc.. http://coloradoenergy.org/procorner/stuff/r-values.htm. Retrieved 2010-11-08. 
16. ^ Balku, Şaziye (2007-05-22). "Steady Heat Transfer and Thermal Resistance Networks" PPT Course notes: Mece 310: Thermodynamics and Heat Transfer. p. 20. Ankara, Turkey: Atılım University. Retrieved 2010-11-08.
17. ^ Hartman,Carl and Bibb, Lewis. "The Human body and its enemies: a textbook of physiology hygiene and sanitation", World Book Co., 1913, p.232.
18. ^ ^{a b} Cengel, Yunus A. and Ghajar, Afshin J. "Heat and Mass Transfer: Fundamentals and Applications." , McGraw-Hill, 4th Edition, 2010.
19. ^ Tao, Xiaoming. "Smart fibres, fabrics, and clothing" , Woodhead Publishing, 2001
20. ^ Wilmore, Jack H., Costill, David L., Kenney, Larry, "Physiology of sport and exercise", Human Kinetics, 2008, p.256.

Further reading

• Frontiers in Heat and Mass Transfer
• Heat Transfer Engineering
• Experimental Heat Transfer
• International Journal of Heat and Mass Transfer
• ASME Journal of Heat Transfer
• Numerical Heat Transfer Part A
• Numerical Heat Transfer Part B
• Nanoscale and Microscale Thermophysical Engineering
• Journal of Enhanced Heat Transfer

External links

• Advanced Heat and Mass Transfer - A textbook for free online reading.
• Thermal-FluidsPedia - An online thermal fluids encyclopedia.
• COMSOL Heat Transfer Module - CAD software that models and simulates heat transfer problems.
• Heat Transfer Tutorial Modes of heat transfer (conduction, convection, radiation) within or between media are explained, together with calculations and other issues such as heat transfer barriers - Spirax Sarco
• Heat Transfer Podcast - Arun Majumdar - Department of Mechanical Engineering - University of California, Berkeley
• Heat Transfer Basics - Overview
• A Heat Transfer Textbook - Downloadable textbook (free)
• Thermal Resistance Circuits - Overview
• Hyperphysics Article on Heat Transfer - Overview
• Interseasonal Heat Transfer - a practical example of how heat transfer is used to heat buildings without burning fossil fuels.
• Heat transfer fundamentals
• Aspects of Heat Transfer, Cambridge University
• Thermal-Fluids Central