4Heat Transfer

Heat energy always tends to transfer from high temperature regions to low temperature regions. There are three ways that heat may be transferred between substances at different temperatures. They are:

Conduction;

Convection;

Radiation.

4.1Conduction

Conduction is the transfer of heat energy through solids or stationary fluids. Heat is transferred by lattice vibrations and particle collisions.

In solids atoms are bound together by bonds which behave like springs. Atoms that are hot will vibrate more vigorously with these vibrations, and therefore energy, being transferred to neighbouring atoms until equilibrium is reached (i.e. until all the atoms have the same energy/temperature).

FIGURE 4.1 – CONDUCTION BY LATTICE VIBRATIONS

(taken from Gourmet Engineering @ Tuffs School of Engineering)

Energy is also transferred by particle collisions. Hotter molecules move faster than cooler ones, and energy is transferred to the lower energy molecules when they collide. These random collisions continue until equilibrium is reached, when the molecules are moving with the same average velocity. This behaviour is seen in stationary fluids and with the free electrons in metals.

FIGURE 4.2 – CONDUCTION BY PARTICLE COLLISION

(taken from Gourmet Engineering @ Tuffs School of Engineering

The rate of heat transfer due to conduction is given by;

Where;

Qis the heat transfer, in W;

is the thermal conductivity of the material, in W/mK;

Ais the cross sectional area, in m2;

T1-T2is the temperature difference between the two environments, in K;

Tis the thickness between the two cross sections, in m.

FIGURE 4.3 – RATE OF HEAT TRANSFER DUE TO CONDUCTION

The thermal resistance of conduction is given by;

Where;

is the thermal resistance of conduction, in m2K/W.

Therefore;

It is clear from the above equationsthat there will be lower heat flow (higher resistance) if the thermal conductivity is lower, the heat path is longer, or the area is lower.

4.1.1Relevance of Conduction to Cladding.

Table 4.1lists some thermal conductivities of commonly used materials in cladding. The first thing to note is that aluminium has a very high thermal conductivity. It is used extensively for window and curtain wall frames, panels etc because it is relatively inexpensive, easily extruded/shaped, and corrosion resistant amongst other things. However, thermally it performs very badly, and so you have to introduce things like thermal breaks in order to be able to use it properly.

Material

/ Thermal Conductivity
(W/mK)
Aluminium / 160
Steel / 50
Stainless Steel / 17
Titanium alloy (Ti-6Al-4V) / 7.2
Glass (soda lime) / 1
Reinforced Polyamide / 0.35

TABLE 4.1 – THERMAL CONDUCTIVITIES OF COMMONLY USED MATERIALS

4.2Convection

Convection is the transfer of heat energy through a material by the bodily movement of particles and will occur in fluids (liquids and gases).

Convection arises when a fluid is warmed, and thus expanded. The expanded fluid is less dense and therefore rises and is replaced by cooler fluid which then undergoes the same process. This is called a convection current.

Convection can be natural or forced. Natural convection is when the fluid movement is caused by the fluid itself, whilst forced convection uses external means (such as a fan) to drive the fluid movement.

FIGURE 4.4 – A NATURAL CONVECTION CURRENT

The rate of heat transfer due to convection is given by;

Where;

hcis the convective heat transfer coefficient, in W/m2K;

Ais the surface area, in m2;

TSis the surface temperature, in K;

TAis the fluid temperature, in K.

FIGURE 4.5 – RATE OF HEAT TRANSFER DUE TO CONVECTION

hC will depend upon;

the relative velocity of the fluid;

the temperature difference between the surface and the environment;

the direction of heat flow;

the surface size and orientation;

the fluid properties (density, viscosity, heat capacity etc);

surface roughness.

The resistance of convective heat transfer is given by;

Where;

is the thermal resistance of convection, in m2K/W.

Therefore;

To lower the heat flow due to convective heat transfer you can reduce the area in contact with the fluid, or decrease the convective heat transfer coefficient.

4.2.1Relevance of Convection to Cladding.

Convective losses can be significant. If you consider a window frame for example there are usually lots of cavities within it in which convection will occur due to the temperature difference across it. The larger the cavity the greater the heat loss by convection since there will be comparatively less drag due to surfaces restricting the convection currents. This is one of the reasons why cavities in frames are split up into smaller sizes.

Convective heat flows are also very significant in double glazed units. The width of the air cavity is very important – if it is too small then conduction and radiation losses are high, and if it is too large then convection tends to dominate. The optimum width will depend on the gas that is used to fill the cavity. For air it is approximately 16 mm whereas for krypton it is around 10 mm.

4.3Radiation

Radiation is the transfer of heat energy by electromagnetic waves and therefore does not require a medium to travel through. Radiative heat transfer occurs when the emitted radiation strikes another body and is absorbed. All bodies above 0 Kelvin emit radiation, the wavelength of which will depend upon the actual temperature of the object. Wein’s Law states that;

maxT = 2.898x10-5

Where;

maxis the maximum wavelength of emitted radiation, in m;

Tis the absolute temperature, in K.

The rate of heat transfer due to radiation is given by;

Where;

hris the radiative heat transfer coefficient, in W/m2K;

is the Steffan-Boltzmann constant (5.67x10-8 W/m2K4);

is the emissivity of the surface;

Ais the area of the surface, in m2;

TSis the surface temperature, in K;

TEis the environment temperature, in K;

Tmis the mean temperature, in K.

FIGURE 4.6 – RATE OF HEAT TRANSFER DUE TO RADIATION

The emissivity has a value between 0 and 1 and is a measure of how efficiently a surface emits and absorbs radiation. It is the ratio of the radiation emitted by a surface to the amount of radiation emitted by a perfect emitter at the same temperature.

The resistance of radiation heat transfer is given by;

Where;

is the thermal resistance of radiation, in m2K/W.

Therefore;

The same rules apply as with convection - to lower the heat transfer due to radiative heat transfer you can reduce the area of the body, or decrease the radiative heat transfer coefficient.

4.3.1Relevance of Radiation to Cladding

Radiation accounts for a large proportion of the heat transfer in cavities, and as such represents significant heat loss in cladding products. Some relevant emissivities are listed below.

Material / Emissivity
Black body / 1
Painted surfaces / 0.74 – 0.96
Shiny metal surfaces / 0.02 – 0.21
Glass / 0.845
Glass (low emissivity coating) / 0.04

TABLE 4.2 – TYPICAL EMISSIVITY VALUES

The most common application of using the emissivity to lower heat transfer is with the use of low-e coated glazing units. For example an air filled 6-16-6 double glazed unit has a centre pane U-value of 2.66 W/m2K with uncoated glass, which is reduced to 1.39 W/m2K by using a soft low-e coating.