Figure 16.2 Classic early study predicting the benefit of a national renewable energy strategy, from Ryle's 1977 paper in Nature. (a) Seasonal changes in total demand for energy for all purposes in Great Britain. All quantities are gigawatt of primary energy. The two vertical column-bars for each season correspond to total demand (1) on the coldest day of the season and (2) during sleeping hours. Hatched areas represent demand for space heat and potable hot water in public buildings, housing and industry; the remaining column for electricity. The heavy line shows what the demand would be if 7-day storage of heat were available to smooth out the diurnal pattern and weather fluctuations. Note that the hatched areas are for when heat is wanted, i.e. predominantly in daytime, and so even existing ~ 12 h storage in hot water tanks and building fabric substantially reduces the day/night demand fluctuations. (b) Firm power that could potentially be obtained in Great Britain from solar heat (*) and wind and waves (VA) for total (o), allowing for 7-day storage of heat. Note that the total power available from just these three renewable sources (o) exceeds the smoothed total demand (heavy line from (a)). For further details of assumptions, see Problem 16.4.

where mc is its heat capacity, and R is the thermal resistance between the store and the surroundings. The solution of (16.5) is

Ts(0) - T rV mcR, from which it follows that iloSS = 1.3mcR (16.7)

If the store is a sphere of radius a, the thermal resistance is R = r/4wa2, where r is the thermal resistivity of unit area, and m = 4wa3p/3, so for a sphere, iloSS = 0.43pcra (16.8)

Example 16.1 Size and insulation of a domestic heat store A small well-insulated passive solar house requires an average internal heat supply of 1.0 kW. Together with the free gains of lighting, etc., this will maintain an internal temperature of 20 °C. It is decided to build a hot water store in a rectangular tank whose top forms the floor of the house, and of area 200 m2. The heating must be adequate for 100 days as all the heat loss from the tank passes by conduction through the floor, and as the water cools from an initial 60°C to a final 40°C.

1 Calculate the volume of the tank.

2 Calculate the thermal resistivity of the heat path from the tank to the floor.

3 Suggest how the tank should be enclosed thermally.

4 What is the energy density of storage?

Solution 1

Heat required = (1kW)(100day)(24hday-1)(3.6MJkWh-1)

Volume of water =

=8640MJ

2 Assume the heat only leaves through the top of the tank. From (16.7),

(1.3)(103 m3)(1000kgm )(4200Jkg K-1) From (3.6) the thermal resistivity r = A•(area)

3 Insulating material (e.g. dry expanded polystyrene) has a thermal conductivity k ~ 0.04Wm-1K-1. A satisfactory layer on top of the tank, protected against excess pressure, would have a depth d = (3.1 m2 KW-1)(0.04 Wm-1 K-1) = 12cm

To avoid unwanted heat loss, the base and sides should be insulated by the equivalent of 50 cm of dry expanded polystyrene.

4 Energy density of the used storage above 40 cC = (8640MJ)/(103m3) = 84 MJm-3

Energy density above ambient house temperature at 20cC = 168 MJm-3

Note: An active method of extracting the heat by forced convection through a heat exchanger would enable better control, a smaller initial temperature and/or a smaller tank.

Example 16.1 shows that 3-month heat storage is realistic if this forms part of the initial design criteria, and if other aspects of the construction are considered. These include the best standards of thermal insulation with damp-proof barriers, controlled ventilation (best with recycling of heat), and the inclusion of free gains from lighting, cooking and metabolism. Examples exist of such high technology houses, and the best also have imaginative architectural features so that they are pleasant to live in, see Section 6.3. Many such buildings utilise rock bed storage, rather than the water system of the example. It follows from Example 16.1 that short-term heat storage of about 4 days is easily possible, with the fabric of the building used as the store. Similarly thermal capacity and cold storage can have important implications for building design in hot weather conditions.

Materials that change phase offer a much larger heat capacity, over a limited temperature range, than systems using sensible heat. For example, Glauber's salt (Na2SO4 • 10H2O) has been used as a store for room heating. It decomposes at 32°C to a saturated solution of Na2SO4 and an anhydrous residue of Na2SO4. This reactionis reversible and evolves 250kJkg 1 or ~650MJm-3. Since much of the cost of a store for house heating is associated with the construction, such stores may be cheaper overall than simple water tanks of less energy density per unit volume. Nevertheless, this seemingly simple method requires practical difficulties to be overcome. In particular, the solid and liquid phases often separate spatially, so recombination is prevented; consequently, without mixing, the system becomes inefficient after many cycles.

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