# Heat transfer: Wikis

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# Encyclopedia

Heat transfer is the transition of thermal energy from a hotter mass to a cooler mass. When an object is at a different temperature than its surroundings or another object, transfer of thermal energy, also known as heat flow, or heat exchange, occurs in such a way that the body and the surroundings reach thermal equilibrium; this means that they are at the same temperature. Heat transfer always occurs from a higher-temperature object to a cooler-temperature one as described by the second law of thermodynamics or the Clausius statement. Where there is a temperature difference between objects in proximity, heat transfer between them can never be stopped; it can only be slowed.

## Conduction

Conduction is the transfer of heat by direct contact of particles of matter. 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 one atom to another. Conduction is greater in solids, where a network of relatively fixed spacial relationships between atoms helps to transfer energy between them by vibration.

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 behavior, only in as much as it can occur in solids, whereas mass diffusion is mostly limited to fluids.

Metals (e.g. copper, platinum, gold, iron, etc.) 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 which are able to transfer thermal energy rapidly through the metal.

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. Conductivity increases with increasing pressure from vacuum up to a critical point that the density of the gas is such that molecules of the gas may be expected to collide with each other before they transfer heat from one surface to another. After this point in density, conductivity increases only slightly with increasing pressure and density.

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. In thermal conductivity k is defined 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.

• Steady state conduction is the 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 (temperature field) in the conducting object does not change any further. For example, a bar may be cold at one end and hot at the other, but the gradient of temperatures along the bar do not change with time. The temperature at any given section of the rod remains constant, and this temperature varies linearly along the direction of heat transfer.

In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out. In steady state conduction, all the laws of direct current electrical conduction can be applied to "heat currents". In such cases, it is possible to take "thermal resistances" as the analog to electrical resistances. Temperature plays the role of voltage and heat transferred is the analog of electrical current.

• Transient conduction There also exists non-steady-state situations, in which the temperature drop or increase occurs more drastically, such as when a hot copper ball is dropped into oil at a low temperature. Here the temperature field within the object changes as a function of time, and the interest lies in analysing this spatial change of temperature within the object over time. This mode of heat conduction can be referred to as transient conduction. Analysis of these systems is more complex and (except for simple shapes) calls for the application of approximation theories, and/or numerical analysis by computer.
Lumped system analysis

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, is lumped system analysis. This is a method of approximation that suitably 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 resistance to heat transfer across the object's boundary with a uniform bath of different temperature, to the conductive heat resistance within the object. When the thermal resistance to heat transferred into the object is less than the resistance to heat being diffused completely within the object, the Biot number less than 1. This case, and the approximation of spatially uniform temperature within the object can 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. As this is a mode of approximation, the Biot number must be less than 0.1 for accurate approximation and heat transfer analysis. The mathematical solution to the lumped system approximation gives Newton's law of cooling, discussed below.

This mode of analysis has been applied to forensic sciences to analyize the time of death of humans. Also it can be applied to HVAC (heating, ventilating and air-conditioning, or building climate control), to ensure more nearly instantaneous effects of a change in comfort level setting.[1]

## Convection

Convection is the transfer of thermal energy by the movement of molecules from one part of material to another. As fluid motion increases, so does the convective heat transfer. The presence of bulk motion of fluid enhances the heat transfer between the solid surface and the fluid.[2]

There are two types of convective heat transfer:

• Natural convection: when the fluid motion is caused by buoyancy forces that result from the density variations due to variations of temperature in the fluid. For example, in the absence of an external source, when the mass of the fluid is in contact with a hot surface its molecules separate and scatter causing the mass of fluid to become less dense. When this happens, the fluid is displaced vertically or horizontally while the cooler fluid gets denser and the fluid sinks. Thus the hotter volume transfers heat towards the cooler volume of that fluid.[3]
• Forced convection: when the fluid is forced to flow over the surface by external source such as fans and pumps, creating an artificially induced convection current.[4]

Internal and external flow can also classify convection. Internal flow occurs when the fluid is enclosed by a solid boundary such as a flow through a pipe. An external flow occurs when the fluid extends indefinitely without encountering a solid surface. Both these convections, either natural or forced, can be internal or external as they are independent of each other.[citation needed]

The rate of convective heat transfer is given by:[5]

q = hA(TsTb)

A is the surface area of heat transfer. Ts is the surface temperature and Tb is the temperature of the fluid at bulk temperature. However Tb varies with each situation and is the temperature of the fluid “far” away from the surface. The h is the constant heat transfer coefficient which depends upon physical properties of the fluid such as temperature and the physical situation in which convection occurs. Therefore, the heat transfer coefficient must be derived or found experimentally for every system analyzed. Formulas and correlations are available in many references to calculate heat transfer coefficients for typical configurations and fluids. For laminar flows the heat transfer coefficient is rather low compared to the turbulent flows, this is due to turbulent flows having a thinner stagnant fluid film layer on heat transfer surface.[6]

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

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

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

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

### Clothing and building surfaces, and radiative transfer

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

## Physical Transfer

Finally it is possible to move heat by physical transfer of a hot or cold object from one place to another. This can be as simple as placing hot water in a bottle and heating your bed or the movement of an iceberg and changing ocean currents.

## Newton's law of cooling

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

$\frac{d Q}{d t} = h \cdot A( T_{\text{env}}- T(t)) = - h \cdot A \Delta T(t)\quad$
Q = Thermal energy in joules
h = Heat transfer coefficient
A = Surface area of the heat being transferred
T = Temperature of the object's surface and interior (since these are the same in this approximation)
Tenv = Temperature of the environment
ΔT(t) = T(t) − Tenv is the time-dependent thermal gradient between environment and object

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

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

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

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

where

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

Thus the above equation may also be usefully written:

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

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

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

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

If:

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

then the Newtonian solution is written as:

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

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

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

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

"hi and h0 should be ki and k0 in Thermal_Circuits3.jpg"

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

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

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

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

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

The effectiveness of a radiant barrier is indicated by its reflectivity, which is the fraction of radiation reflected. A material with a high reflectivity (at a given wavelength) has a low emissivity (at that same wavelength), and vice versa (at any specific wavelength, reflectivity = 1 - emissivity). An ideal radiant barrier would have a reflectivity of 1 and would therefore reflect 100% of incoming radiation. Vacuum bottles (Dewars) are 'silvered' to approach this. In space vacuum, satellites use multi-layer insulation which consists of many layers of aluminized (shiny) mylar to greatly reduce radiation heat transfer and control satellite temperature.

## Critical insulation thickness

To reduce the rate of heat transfer, one would add insulating materials i.e with low thermal conductivity (k). The smaller the k value, the larger the corresponding thermal resistance (R) value.
The units of thermal conductivity(k) are W·m-1·K-1 (watts per meter per kelvin), therefore increasing width of insulation (x meters) decreases the k term and as discussed increases resistance.

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

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

An obvious example is a cylindrical pipe:

• As insulation gets thicker, outer radius increases and therefore surface area increases.
• The point where the added resistance of increasing insulation width becomes overshadowed by the effects of surface area is called the critical insulation thickness. In simple cylindrical pipes:[8]
${R_{critical}} = {k \over h}$

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

## 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 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.

## 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, p. 529).

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

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

## Condensation heat transfer

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

There are several modes of condensation:

• Homogeneous condensation (as during a formation of fog).
• Condensation in direct contact with subcooled liquid.
• Condensation on direct contact with a cooling wall of a heat exchanger-this is the most common mode used in industry:
• 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. ^ Heat Transfer - A Practical Approach by Yugnus A Cengel
2. ^ Yugnus A Cengel (2003), “Heat transfer-A Practical Approach” 2nd ed. Publisher McGraw Hill Professional, p26 by ISBN 0072458933, 9780072458930, Google Book Search. Accessed 20-04.-09
3. ^ http://biocab.org/Heat_Transfer.html Biology Cabinet organization, April 2006, “Heat Transfer”, Accessed 20/04/09
4. ^ http://www.engineersedge.com/heat_transfer/convection.htm Engineers Edge, 2009, “Convection Heat Transfer”,Accessed 20/04/09
5. ^ Louis C. Burmeister, (1993) “Convective Heat Transfer”, 2nd ed. Publisher Wiley-Interscience, p 107 ISBN 047157709X, 9780471577096, Google Book Search. Accessed 20-03-09
6. ^ http://www.engineersedge.com/heat_transfer/convection.htm Engineers Edge, 2009, “Convection Heat Transfer”,Accessed 20/03/09
7. ^ Two websites: E-star and Coloradoenergy
8. ^ http://mechatronics.atilim.edu.tr/courses/mece310/ch9mechatronics.ppt. Dr. Şaziye Balku: Notes including Critical Insulation Thickness as at 26/03/09

# Study guide

Up to date as of January 14, 2010

# Types of heat transfer

There are four primary mechanisms by which heat is transferred from a hotter material to a cooler material:

## Conduction

This occurs when two solid objects are touching, within fluids, or between touching fluids and solids. The heat in the warmer material, in the form of molecular vibrations, excites molecular vibrations in the cooler material, while the hotter material's molecular vibrations are dampened by contact with the cooler material. Some materials conduct heat much better than others. For example, metals generally conduct heat better than wood. Good thermal conductors, at room temperature, often feel cool to the touch, as they conduct body heat away from the hand of the warmer person. Conduction is a very slow process, often taking hours for heat to move even a few inches.

### Example

A brick house absorbs heat from solar radiation during the day, on the surface of the bricks. This heat slowly conducts through the bricks and heats the house only after it reaches the inside edge. This may take several hours. Thus, houses can actually be hottest after the Sun has set.

## Convection

This type of heat transfer requires a fluid, which may be either a gas or liquid, and a force acting on the fluid, such as gravity. Convection occurs due to density changes in fluids when the temperature of those fluids change. In general, fluids become less dense when heated, but there are exceptions. In the case of a fluid which does become less dense when heated, the hotter portion of the fluid rises and the cooler portion sinks. Just the reverse would happen if the fluid became more dense when heated. If the fluid does not change density when heated, then no convection will occur, although much slower conduction within the fluid will still occur.

### Example

Within the mantle of the Earth, hot magma rises to the crust, releases it's heat by conduction or by volcanism, then sinks back down to the hotter core and repeats the process. This sets up convection cells, where this process repeats in a stable flow pattern for millions or even billion of years. One result is that the location where hot magma rises produces a "hot spot" which creates a series of volcanoes as it punctures the crust as the continental and oceanic plates drift across. The Hawaiian Islands were created by just such a hot spot.

## Chemical phase changes

Heat may cause solids to melt to become liquids, or liquids to boil to become gases. Some heat is absorbed by the phase change itself, and some may then be carried away by the fluid via convection. The combination of phase changes and convection cools an object quicker than convection alone.

### Example

Blacksmiths often drop red-hot or white-hot metals into water in order to "quench" them. This causes the water to boil and carry the heat away as steam.

Radiation occurs from all objects above absolute zero to every other object in its line of sight. This occurs when molecular vibrations cause particles to be emitted from the surface of an object. Many different particles may be emitted, depending on the temperature of the object. Different frequencies are thus emitted; including infrared, visible light, ultraviolet, radio waves, microwaves, X-rays, gamma rays, etc. Radiation is unique in that it is the only type of heat transfer which can occur across a vacuum. Radiation is an extremely quick mechanism for transferring heat (it occurs at the speed of light), provided the hotter object is very hot (thousands of degrees). Cooler objects don't radiate much energy. The radiation received by an object will be inversely proportional to the square of the distance from the radiating object.

### Example

Radiation from stars, such as our Sun, is the method by which light and heat is given off to the planets.

# Reaching equilibrium

Heat transfer within a material or between two materials occurs in both directions, but more heat is transferred from the hotter material to the cooler than from the cooler to the hotter. This process continues until the temperatures approach the same value within the material or between the two materials. At this point an equal amount of heat transfer will occur in both directions, and the system will remain at thermal equilibrium until some change is made to the system.