# Heat transfer

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Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

## Overview

In thermal physics, heat transfer is the passage of thermal energy from a hot to a colder body. When a physical body, e.g. an object or fluid, is at a different temperature than its surroundings or another body, transfer of thermal energy, also known as heat transfer, or heat exchange, occurs in such a way that the body and the surroundings reach thermal equilibrium. Heat transfer always occurs from a hot body to a cold one, a result of the second law of thermodynamics. Where there is a temperature difference between objects in proximity, heat transfer between them can never be stopped; it can only be slowed down.

## Overview

Classical transfer of thermal energy occurs only through conduction, convection, radiation or any combination of these. Heat transfer associated with carriage of the heat of phase change by a substance (such as steam which carries the heat of boiling) can be fundamentally treated as a variation of convection heat transfer. In each case, the driving force for heat transfer is a difference of temperature.There are 3 types of heat transfer known as convection, conduction and radiation.

Heat transfer is of particular interest to engineers, who attempt to understand and control the flow of heat through the use of thermal insulation, heat exchangers, and other devices. Heat transfer is typically taught as undergraduate and graduate subjects in chemical, electrical and mechanical engineering curricula.

• Heat — a transfer of thermal energy, (i.e., of energy and entropy) from hotter material to cooler material. Heat transfer may change the internal energy of materials.
• Internal energy — the internal vibrational energy that the molecules or electrons composing all materials contain (except at absolute zero)
• Conduction — transfer of heat by electron diffusion or phonon vibrations (see below)
• Convection — transfer of heat by conduction in a moving medium, such as a fluid (see below)
• Radiation — transfer of heat by electromagnetic radiation or, equivalently, by photons (see below).
• Phase change — transfer of heat by the potential energy associated with the heat of phase change, such as boiling, condensation, or freezing.
• 1-D Application Using Thermal Circuits — application of heat transfer analysis using the concept of thermal circuits.

## Conduction

Conduction is the transfer of thermal energy from a region of higher temperature to a region of lower temperature through direct molecular communication within a medium or between mediums in direct physical contact without a flow of the material medium. The transfer of energy could be primarily by elastic impact as in fluids or by free electron diffusion as predominant in metals or phonon vibration as predominant in insulators. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from atom to atom. Conduction is greater in solids, where atoms are in constant contact. In liquids (except liquid metals) and gases, the molecules are usually further apart, giving a lower chance of molecules colliding and passing on thermal energy.

Heat conduction is directly analogous to diffusion of particles into a fluid, in the situation where there are no fluid currents. This type of heat diffusion differs from mass diffusion in behaviour, only in as much as it can occur in solids, whereas mass diffusion is limited to fluids.

Metals (eg. copper) are usually the best conductors of thermal energy. This is due to the way that metals are chemically bonded: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons and form a crystalline structure, greatly aiding in the transfer of thermal energy.

As density decreases so does conduction. Therefore, fluids (and especially gases) are less conductive. This is due to the large distance between atoms in a gas: fewer collisions between atoms means less conduction. Conductivity of gases increases with temperature but only slightly with pressure near and above atmospheric. Conduction does not occur at all in a perfect vacuum.

To quantify the ease with which a particular medium conducts, engineers employ the thermal conductivity, also known as the conductivity constant or conduction coefficient, k. The main article on thermal conductivity defines k as "the quantity of heat, Q, transmitted in time (t) through a thickness (L), in a direction normal to a surface of area (A), due to a temperature difference (ΔT) [...]." Thermal conductivity is a material property that is primarily dependent on the medium's phase, temperature, density, and molecular bonding.

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.Note that conduction always takes place from higher to lower temprature.

## Convection

Convection is a combination of conduction and the transfer of thermal energy by fluid circulation or movement of the hot particles in bulk to cooler areas in a material medium. Unlike the case of pure conduction, now currents in fluids are additionally involved in convection. This movement occurs into a fluid or within a fluid, and cannot happen in solids. In solids, molecules keep their relative position to such an extent that bulk movement or flow is prohibited, and therefore convection does not occur.

Convection occurs in two forms: natural and forced convection.

In natural convection, fluid surrounding a heat source receives heat, becomes less dense and rises. The surrounding, cooler fluid then moves to replace it. This cooler fluid is then heated and the process continues, forming a convection current. The driving force for natural convection is buoyancy, a result of differences in fluid density when gravity or any type of acceleration is present in the system.

Forced convection, by contrast, occurs when pumps, fans or other means are used to propel the fluid and create an artificially induced convection current. Forced heat convection is sometimes referred to as heat advection, or sometimes simply advection for short. But advection is a more general process, and in heat advection, the substance being "advected" in the fluid field is simply heat (rather than mass, which is the other natural component in such situations, as mass transfer and heat transfer share generally the same equations).

In some heat transfer systems, both natural and forced convection contribute significantly to the rate of heat transfer.

To calculate the rate of convection between an object and the surrounding fluid, engineers employ the heat transfer coefficient, h. Unlike the thermal conductivity, the heat transfer coefficient is not a material property. The heat transfer coefficient depends upon the geometry, fluid, temperature, velocity, and other characteristics of the system in which convection occurs. Therefore, the heat transfer coefficient must be derived or found experimentally for every system analyzed. Formulae and correlations are available in many references to calculate heat transfer coefficients for typical configurations and fluids.

## Radiation

Radiation is the transfer of heat through electromagnetic radiation. Hot or cold, all objects radiate energy at a rate equal to their emissivity times the rate at which energy would radiate from them if they were a black body. No medium is necessary for radiation to occur; radiation works even in and through a perfect vacuum. The energy from the Sun travels through the vacuum of space before warming the earth. Also, the only way that energy can leave earth is by being radiated to space.

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 while 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 -5C, 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 "colors" of electromagnetic radiation.

## 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, or environment. The law is

${\displaystyle {\frac {dQ}{dt}}=h\cdot A(T_{0}-T_{env})}$
${\displaystyle Q=}$ Thermal energy transfer in joules
${\displaystyle h=}$ Heat transfer coefficient
${\displaystyle A=}$ Surface area of the heat being transferred
${\displaystyle T_{0}=}$ Temperature of the object's surface
${\displaystyle T_{env}=}$ Temperature of the environment

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. The following simplification 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 same uniform temperature as it is cooled from the outside, by the environment. If this is the case, then it is easy to derive from these conditions the behavior of exponential decay 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, and the temperature of the body. If T(t) is the temperature of such a body at time t, and Tenv is the temperature of the environment around the body, then

${\displaystyle {\frac {dT(t)}{dt}}=-r(T-T_{\mathrm {env} })}$

where

r 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 time constant: r = 1/t0.

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

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

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

If:

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

then the Newtonian solution is written as:

${\displaystyle \Delta T(t)=\Delta T(0)\ e^{-rt}.\quad }$

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

## 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:

In cases where there is heat transfer through different media (for example through a composite), the equivalent resistance is the sum of the resistance 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 hi and exposed to air with convective coefficient ho.

Image courtesy of Dr. Rong- Yaw Chen, NJIT.

Using the thermal resistance concept heat flow through the composite is as follows:

## Insulation and radiant barriers

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)

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

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

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.[1]

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.

## Heat exchangers

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 production, 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. More information on heat exchanger flows and arrangements can be found in the heat exchanger article.

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.

## Boiling heat transfer

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, p529).

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 surfase, 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 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 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.

## 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:

## References

1. Two websites: E-star and Coloradoenergy

## Additional Resources

• Class notes of Dr. Rong-Yaw Chen, Department of Mechanical Engineering, NJIT[2]

## Related journals

• Heat Transfer Engineering[3]
• Experimental Heat Transfer[4]
• International Journal of Heat and Mass Transfer[5]
• ASME Journal of Heat Transfer[6]
• Numerical Heat Transfer Part A[7]
• Numerical Heat Transfer Part B[8]
• Nanoscale and Microscale Thermophysical Engineering[9]
• Journal of Enhanced Heat Transfer[10]