Water | Everything about solar energy

As shown in Table 12.1, water has the largest heat capacity both per unit volume and per unit weight. And it is free. Therefore, it is logical to use water as the material for sensible heat storage. A typical case is the hot-water tank used in most homes. The tank is typically insulated by foam polyurethane, which has a thermal conductivity к = 0.02 W/mK and density p = 30 kg/m3.

Table 12.1: Thermal Properties of Some Commonly Used Materials

Materials	Density p 103kg/m3	Heat capacity cp 103J/kg-K	Product pcp 106 J/m3-K	Temperature range AT ◦C
Water	1.00	4.19	4.19	0 to 100
Ethonal	0.78	2.46	1.92	-117 to 79
Glycerine	1.26	2.42	3.05	17 to 290
Canola Oil	0.91	1.80	1.64	-10 to 204
Synthetic Oil	0.91	1.80	1.64	-10 to 400

Source: American Institute of Physics Handbook, 3rd Ed., American Institute of Physics, New York, 1972.

V = 1 nD2 L 4	(12.3)
and the heat capacity is Cp — pcp V.	(12.4)
The total surface area of the tank is
A = – nD2 + nD L.	(12.5)
The rate of heat loss is dQ kA ~QQ — — (Tw – Ta) , dt t	(12.6)
where Tw — Ta is the difference of water temperature Tw The rate of temperature loss is	and ambient temperature Ta.
dT = 2k(D + 2L) (T T ) dt TpepDL ( w a)	. (12.7)

If the entire tank is filled with water, the volume is

The rate of temperature drop through the tank skin is proportional to the total surface area and inversely proportional to the volume. If the tank is too thin or too flat, then the heat loss is high. Therefore, for a tank of fixed volume, there should be an optimal ratio L/D to minimize the heat loss. Intuitively, the condition should be L к D. In Problem 12.1, one can show that the intuition is correct: The optimum condition is L = D, and Eq. 12.7 becomes

It verifies another qualitative argument: The larger the dimension, the better the tank could preserve temperature.

Figure 12.1 Water in an insulating tank.

Calculation of energy storage behavior of an insulated water tank. The energy loss is proportional to the total surface area, and the energy content is proportional to the volume. The rate of temperature drop is minimized when the diameter D equals the length L. With a tank of linear dimension about 1 m with a 5-cm-thick foam polyurethane insulation, it take 8 h for the water temperature to drop by 1°C.