Solar Hot Water Systems and Materials of Construction

The materials used in solar hot water systems must be carefully chosen to ensure that the unit will be efficient but also affordable. The efficiency of the conversion of sunlight energy to heat energy of the water depends on the materials of construction and the efficiency of heat transfer of the materials. Solar hot water systems use the processes of conduction to transfer the heat absorbed from the sun to the water and convection to move water through their structure. This assignment discusses the materials used in construction of solar hot water systems and their heat transfer properties.

2.0 Conduction

Conduction is the process of transferring energy through a material from one point to another. Conductivity (k) is the rate at which the energy is transferred and its units are Watts per metre Kelvin or (W/mK). The higher the rate of conductivity the faster energy is transferred through the material. Conduction can occur in two different ways in solids; the first is by crystal vibration waves (phonons) where particles of high kinetic energy vibrate rapidly and bump into other particles to transfer energy from one point to another. The second way is by delocalised electrons or free moving electrons which transfer energy throughout materials much better than atoms do, as their energy to mass ratio is much higher than that of atoms. This allows the electrons to travel much faster throughout a substance and transfer energy faster. For a material to be a good conductor of kinetic or electrical energy it requires both methods of conduction, which is found in metals and some other materials (i.e. graphite). The conductivity of a solar hot water system's materials are important ie. adequate insulation is required to prevent energy being lost to the unit's surroundings. Materials for the pipes should not resist the transfer of thermal and kinetic energy being passed through the pipes to the water in the collector panel (shown in Fig 1.).

The conductivity (k) of a material can be described by the following equation. The contribution of ke increases with free electron concentration.

Copper is an abundant, cheap metal with great thermal and electrical conductivity. It is strong, malleable and ductile making it an ideal material for water pipes. Copper has a thermal conductivity (k) value of 398 W/mK, which is below silver's thermal conductivity of 428 W/mK however still much larger than other metals such as Aluminium (247 W/mK) or steel (60 W/mK). This makes copper useful in transferring kinetic energy as it means that is will not use energy whilst transferring water i.e. it is an efficient transfer medium.

Resistivity is the inverse of conductivity and is a measure of how much energy is lost in transfer over a particular length. If a material has a high conductivity it will have a low resistivity like silver and copper.

Why does copper have such a high value of conductivity?

Copper is a heavy metal with a density of 8.69 g/cm3. This high density indicates that the atoms of copper are very closely packed in their crystalline structure allowing thermal energy to be conducted at a faster rate and more efficiently. Copper's crystal packing is called face centred cubic, which is one of the two densest ways of packing atoms in all of the possible packing schemes. Some other metals with the face centred cubic packing include Ag, Al, Au, Ca, Co, Ni, Pb and Pt.

Fig 2. shows how atoms are structured in a unit cell of face centred cubic (fcc) structure. There are a total of 4 atoms in fcc unit cell. A unit cell is defined as the smallest unit of a crystal lattice which can be multiplied to produce an entire lattice. There is half an atom at each face of a cube and an eighth of an atom at each of the eight corners. In total there are 4 atoms per unit cell.

There is only one other packing scheme which allows atoms to be packed at the same ratio as it does in fcc and that is hexagonal close packed (hcp). Fig 3. shows how atoms are structures in a unit cell of hcp. Fcc has a stacking pattern of A, B, C, A, B, C. The atoms in every fourth layer are in line whereas the hcp stacking pattern is A, B, A, B and atoms in every third layer are in line. Although the stacking patterns for fcc and hcp are slightly different the coordination numbers are both 12. Fig 4. and Fig 5. show how the orientation of layers for face centred cubic is slightly different to that of the hexagonal closest packed structure. A coordination number is based on the number of other spheres a single sphere contacts anywhere in the lattice or joins with strong bonds. In fcc each sphere is in contact with six spheres in the same plane, three in the plane above and three in the plane of atoms below. In hcp each sphere is in contact with the same number of spheres in each different plane as fcc is. Some elements, which are hexagonal close packed are Zinc, Magnesium and Titanium.

Body Centred Cubic (bcc) is the most common packed structure adopted by metals. Group 1, group 2 and some early transition metals are structured like body centred cubic (see Fig 6.). The coordination number of bcc is 8. The atoms aren't as closely packed in bcc so the metals aren't as dense as fcc and hcp metals. Bcc metals don't conduct as well as others so they would not be suited for use in piping of solar hot water systems.

The coordination number plays a very important role in conductivity. As you increase the number of contact points between the atoms you increase the number of pathways for energy to be transferred along to other atoms. Thus the rate of conductivity increases with number of contact points and the coordination number.

Fig 7. Comparing the Conductivity of face centred cubic packed

structures to body centred cubic.

Metal (fcc) Conductivity W/mK Metal (bcc) Conductivity W/mK

Silver 428 Iron 80

Copper 398 Tungsten 155

Aluminium 247 Molybdenum 142

Gold 315 Tantalum 54.4

As can be identified in Fig 7. metals which are face centred cubic have on average a higher conductivity than metals which are body centred cubic.

The atomic packing factor is a measurement of the amount of space utilised by atoms in a unit cell (see Fig 8.). The more atoms which are in a unit cell will indicate a larger atomic packing factor.

Fig 8. Calculation