Chen C.J. Physics of Solar Energy

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254  Energy Storage

ﬁnal temperature T

Q = M



dT, (12.1)

where M is the mass, c

is the isobaric speciﬁc heat. In most applications, the density

and speciﬁc heat can be treated as a constant. Equation 12.1 can be simpliﬁed to

Q = Mc

− T

) . (12.2)

The quantity of material required for the storage tank and the heat losses are

approximately proportional to the surface area of the tank. The storage capacity is

proportional to the volume of the tank. Larger tanks have a smaller surface area–

volume ratio and therefore are less expensive and have less heat losses per unit energy

stored.

An important issue in thermal energy storage is thermal conduction, or temper-

ature equalization in the medium. In liquids, heat conduction has two major paths:

conduction and convection. Temperature in a liquid medium can become equalized

much faster than in a solid. Therefore, liquid is preferred whenever applicable. Ta-

ble 12.1 shows some thermal properties of commonly used liquids for sensible heat

thermal energy storage.

12.1.1 Water

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 κ

= 0.02 W/mK and density ρ = 30 kg/m

Table 12.1: Thermal Properties of Some Commonly Used Materials

Materials Density Heat Product Temperature

ρ capacity c

ρc

range ΔT

kg/m

J/kg·K10

J/m

·K

◦

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,3rdEd.,

American Institute of Physics, New York, 1972.

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12.1 Sensible Heat Energy Storage  255

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

V =

πD

L (12.3)

and the heat capacity is

= ρc

V. (12.4)

The total surface area of the tank is

A =

πD

+ πD L. (12.5)

The rate of heat loss is

κA

− T

) , (12.6)

where T

−T

is the diﬀerence of water temperature T

and ambient temperature T

The rate of temperature loss is

2κ(D +2L)

τρc

− T

) . (12.7)

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 ≈ D. In Problem 12.1, one can show that the intuition is correct: The optimum

condition is L = D, and Eq. 12.7 becomes

6κ

τρc

− T

) . (12.8)

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 in-

sulated water tank. The energy loss is propor-

tional to the total surface area, and the energy

content is proportional to the volume. The rate

of temperature drop is minimized when the diam-

eter D equals the length L. With a tank of lin-

ear dimension about 1 m with a 5-cm-thick foam

polyurethane insulation, it take 8 h for the water

temperature to drop by 1

◦

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256  Energy Storage

Here is a numerical example. If D = L =1m,τ = 5 cm = 0.05 m, T

=80

◦

C, and

=20

◦

C, the rate of temperature drop is

6 × 0.02

0.05 × 4.19 × 10

× 1

× 60 = 3.4 ×10

−5 ◦

C/s=0.124

◦

C/h. (12.9)

The temperature takes 8 h to drop by 1

◦

C. Such an energy storage unit is extensively

used in hot-water systems.

12.1.2 Solid Sensible Heat Storage Materials

In contrast to water and other liquids, solid materials can provide a larger temperature

range and can be installed without a container. However, thermal conductivity be-

comes a signiﬁcant parameter. Table 12.2 shows the thermal properties of typical solid

materials. For many items, such as soil and rock, the values are only approximate or

an average, because those materials vary widely. For example, the thermal parameters

of soil could vary by one order of magnitude depending on the water content.

As shown in Table 12.2, materials with high thermal conductivities usually have

low heat capacity. To use solid materials with high heat capacities, a long temperature

equalizing time is expected.

Table 12.2: Thermal Properties of Solid Materials

Material Density Heat Product Thermal

ρ Capacity c

ρc

Conductivity k

(10

kg/m

)(10

J/kg·K) (10

J/m

·K) (W/m·K)

Aluminum 2.7 0.89 2.42 204

Cast iIron 7.90 0.837 3.54 29.3

Copper 8.95 0.38 3.45 385

Earth (wet) 1.7 2.1 3.57 2.5

Earth (dry) 1.26 0.795 1.00 0.25

Limestone 2.5 0.91 2.27 1.3

Marble 2.6 0.80 2.08 2.07 - 2.94

Granite 3.0 0.79 2.37 3.5

Bricks 1.7 0.84 1.47 0.69

Concrete 2.24 1.13 1.41 0.9 - 1.3

Wood (oak) 0.48 2.0 0.96 0.16

Source: American Institute of Physics Handbook ,3rdEd.,

American Institute of Physics, New York, 1972; and Ref. [31].

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12.2 Phase Transition Thermal Storage  257

Figure 12.2 Rock-bed thermal energy storage system. Using a mixture of synthetic oil

and pebbles, a thermal energy storage system at high temperature (e.g. 400

◦

C) can be built with

reasonable cost. The heat conduction is mainly through convection of oil, and the pebbles provide

heat capacity.

12.1.3 Synthetic Oil in Packed Beds

Because the temperature range of water is limited, in order to store sensible heat

at higher temperature, for example, in solar power generation systems, synthetic oil

should be used. However, synthetic oil is expensive. A compromised solution is to use a

mixture of synthesized oil and inexpensive solid materials, such as pebbles. Figure 12.2

shows such a thermal energy storage system schematically. A thermal energy storage

system at high temperature (e.g. 400

◦

C) can be built with limited cost. The heat

conduction is mainly through convection of oil, and the pebbles provide heat capacity.

12.2 Phase Transition Thermal Storage

In sensible heat thermal energy storage systems, the process of charging or discharging

of energy is related to a change of temperature, and the temperature is related to the

amount of heat energy content. The storage density is limited by the heat capacity

of the material. Using phase-change materials (PCMs), a considerably higher thermal

energy storage density can be achieved that is able to absorb or release large quantities

of energy (“latent heat”) at a constant temperature by undergoing a change of phase.

Theoretically, three types of phase changes can be applied: solid–gas, liquid–gas and

solid–liquid. The ﬁrst two phase changes are generally not employed for energy storage

in spite of their high latent heats, since gases occupy large volumes. Large changes in

volume make the system large, complex, and impractical. Solid–liquid transformations

involve only a small change in volume (often only a few percent) and are therefore

appropriate for phase-change energy storage.

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258  Energy Storage

Table 12.3: Commonly Used Phase-Change Materials.

Materials Transition Density Latent

Temperature ρ Heat h

◦

C10

kg/m

J/m

Water-ice 0 1.00 335

Paraﬃn wax 58 – 60 0.90 180 – 200

Animal fat 20 – 50 0.90 120 – 210

CaCl

(6→2)H

O 29 1.71 190.8

(10→0)H

O 32.4 1.46 251

Ba(OH)

(8→0)H

O 72 2.18 301

MgCl

(6→4)H

O 117 1.57 172

Source: Refs. [28] and [31].

In general, the heat absorbed or released during the phase transition is

ΔQ = H

− H

, (12.10)

where H is the enthalpy before and after the transition. The latent heat h, or speciﬁc

enthalpy, is deﬁned by

H = hV, (12.11)

where V is the volume of the material.

Table 12.3 shows the thermal properties of several commonly used PCMs. A good

PCM should provide energy storage at the desired temperature, have a large latent

heat and a small volume change, and be non-ﬂammable, noncorrosive, nontoxic, and

inexpensive.

In general, PCMs are more expensive than sensible heat systems. They undergo

solidiﬁcation and therefore cannot generally be used as heat transfer media in a solar

collector or the load. A separate heat transport medium must be employed with a

heat exchanger in between. Many PCMs have poor thermal conductivity and therefore

require large amount of heat exchange liquid. Others are corrosive and require special

containers. These increase the system cost.

12.2.1 Water–Ice Systems

As shown in Table 12.3, the latent heat of the freezing of water or melting of ice is one

of the highest. The water-ice system has already used in industry to save energy in

air-conditioning systems. Figure 12.3 is a photo of a water–ice energy storage system,

named Ice Bear, designed and manufactured by Ice Energy, Inc. The system has a

large insulated tank ﬁlled with water and a lot of copper heat exchange coils. During

the night, the refrigerator uses inexpensive electricity and cool air to make ice from the

water. As we shown in Chapter 6, the lower the ambient temperature, the higher the

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12.2 Phase Transition Thermal Storage  259

Figure 12.3 Ice Bear energy storage system. An insulated tank is ﬁlled with water and many

copper heat exchange coils. During the night, the refrigerator uses inexpensive electricity and cool air

to make ice from the water. As shown in Chapter 6, the lower the ambient temperature, the higher

COP. Therefore, to make a well-deﬁned mass of ice during the night, the electricity cost is much lower

than in the hot daytime. Courtesy of Ice Energy, Inc.

coeﬃcient of performance (COP). Therefore, to make a well-deﬁned mass of ice during

the night, the electricity cost is much lower than in the hot daytime. During the hot

daytime, the system uses the ice to cool the building. With this system, the eﬃciency

of energy storage can be better than 90%. The overall energy savings can be as high

as 30%.

Below is a numerical example of a water–ice system. Using the insulated container

in Fig. 12.1, the total latent heat is

Q =ΔH = H

− H

, (12.12)

Using Eq. 12.3,

ΔH =

πhD

L. (12.13)

For a tank of D = L = 1 m, the total enthalpy of phase transition is

ΔH = 335 × π × 4 ×10

J=2.63 × 10

J. (12.14)

Iftheambienttemperatureis20

◦

C, for such a tank, according to Eq. 12.6, the rate of

heat loss is

3 × π × 0.02

2 × 0.05

× 20 = 1.89 W. (12.15)

If at the beginning the tank is full of ice, then it can keep the temperature at 0

◦

Cfor

2.63 × 10

/1.89 = 1.39 × 10

s, or 4.4 years. Therefore, using a moderate means, the

energy storage is eﬃcient.

The freezing temperature of pure water is 0

◦

C. If the working temperature is other

than 0

◦

C, a mixture of water and other materials can do the job. An example is

solar-operated refrigerator (U.S. Patent 7,543,455). The freezer should work at around

-10

◦

C. Because the refrigerator is used for food and medicine, the additive must be

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260  Energy Storage

Figure 12.4 Freezing point

of water–glycerin system.

By mixing water and glycerin,

the freezing point can be low-

ered from 0 to -40

◦

C depend-

ing on the ratio. By mixing

with a few percent of alcohol,

the freeing point ca be lowered

further.

nontoxic. Glycerin and ethanol are good additives because both are ingredients of food

and medical substances. Figure 12.4 shows the freezing points of a mixture of water

and glycerin. By mixing with alcohol, the freezing temperature can be lowered further.

Glycerin is a byproduct of biodiesel production, and there is a surplus of raw glyc-

erin. The impurities in raw glycerin as byproducts of biodiesel production are water,

salt, fatty acids and alcohol, and there is no need to use high-purity glycerin. Therefore,

Figure 12.5 Solar-powered refrigerator. The design of a solar-powered refrigerator. The com-

position of the water–glycerin–alcohol system determines the working temperature of the freezer. The

temperature of the cooler is controlled by a thermostat to the brine circulation, which can be set by

the user. See U.S. Patent 7,543,455.

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12.2 Phase Transition Thermal Storage  261

economically it is advantageous. Figure 12.5 shows the design of a solar-powered refrig-

erator. The composition of the water–glycerin–alcohol system determines the working

temperature of the freezer. The temperature of the cooler is controlled by a thermostat

to the brine circulation, which can be set by the user.

12.2.2 Paraﬃn Wax and Other Organic Materials

Paraﬃn wax is a byproduct of petroleum reﬁning. The melting point of paraﬃn wax

ranges from 50 to 90

◦

C. Currently, paraﬃn wax only has a few commercially valuable

applications, such are candles and ﬂoor wax. For such applications, only these with

melting temperature between 58 and 60

◦

are usable. But the supply is abundant.

The melting temperature of paraﬃn matches the range needed for space heating and

domestic hot water. It is also nontoxic and noncorrosive. One problem is its low

thermal conductivity. This can be mitigated with encapsulation; see Section 12.2.4.

Other organic materials have similar properties as paraﬃn wax. An example is

animal fat. Lard and chicken fat are considered harmful to human health because they

can increase blood triglyceride and cause obesity. In some sense they are wastes of the

food-processing industry. Animal fat is nontoxic and noncorrosive, thus it can be safely

utilized for energy storage in residential environments.

12.2.3 Salt Hydrates

Many inorganic salts crystallize with a well-deﬁned number of water molecules to be-

come salt hydrates. Heating a salt hydrate can change its hydrate state. For example,

hydrated sodium sulfate (Glauber’s salt) undergoes the transition at 32.4

◦

10H

O+ΔQ −→ Na

+ 10H

O. (12.16)

In general, the transition is

Salt mH

O+ΔQ −→ Salt nH

O+(m −n)H

O. (12.17)

Thus, at the melting point the hydrate crystals break up into anhydrous salt and water

or into a lower hydrate and water. The latent heat could be quite large, thus the

storage density could be very high. If the water released is suﬃcient, a water solution

of the (partially) dehydrated salt is formed.

These salt hydrates can be used in solar-operated space-heating or hot-water sys-

tems to provide uniform temperature over a longer period of time.

12.2.4 Encapsulation of PCM

To mitigate the problem of low thermal conductivity of PCMs, the material is often

encapsulated in various forms. Figure 12.6 shows an example of a PCM encapsulated

in ﬂat or tubular parcels. A heat transfer ﬂuid is required to make it operational.

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262  Energy Storage

Figure 12.6 Encapsulation of PCM. An example of PCM encapsulated in ﬂat or tubular parcels,

to mitigate the low thermal conductivity of PCM.

12.3 Rechargeable Batteries

In the last decades, the technology of rechargeable batteries has observed a phenomenal

expansion. To date, the century-old lead–acid rechargeable battery has been constantly

improved and is still in widespread use. New types of batteries, especially lithium ion

rechargeable batteries, are experiencing an explosive growth, and will soon become the

dominating distributed storage device for electricity.

Table 12.4 gives the speciﬁcations of several types of rechargeable batteries. One of

the basic parameters is nominal voltage. Cells with higher nominal voltage are certainly

advantageous, because fewer cells are needed to construct the desired system. Energy

density and speciﬁc energy are also signiﬁcant parameters. For static applications such

as street lights, a smaller speciﬁc energy is not a serious problem. For automobile

applications, energy density and speciﬁc energy are critical parameters. Lifetime is

also a critical parameter for automobile applications. Not shown here is the unit cost.

Currently, lead–acid batteries are still the least expensive and thus widely used.

Table 12.4: Comparison of Rechargeable Batteries

Type Voltage Energy Density Speciﬁc Energy Lifetime

(V) (Wh/liter) (Wh/kg) (cycles)

Lead–acid 2.1 70 30 300

NiMH 1.4 240 75 800

LiCoO

3.7 400 150 1000

LiMn

4.0 265 120 1000

LiFePO

3.3 220 100 3000

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12.3 Rechargeable Batteries  263

Figure 12.7 Electrochemistry of rechargeable batteries. (a) Discharging process. By con-

necting the cell to an external load, electrons ﬂow from NE, the anode, to PE. The electric circuit is

completed in the electrolyte by the ﬂow of anions and cations to the anode and cathode, respectively.

(b) Charging process. An external DC power supply forces electrons to ﬂow into NE, then the circuit

is completed in the electrolyte by the ﬂow of anions and cations.

12.3.1 Electrochemistry of Rechargeable Batteries

The basic structure and the charging–discharging processes of rechargeable batteries

are shown in Fig. 12.7. For reference, deﬁnitions are provided as below. For more

details, see, for example, Handbook of Batteries [51].

Cell The basic electrochemical unit converting electrochemical energy to electrical

energy.

Battery One or more electrochemical cells connected in series or parallel to provide

electrical power.

Primary cells or batteries One-time source of electricity, cannot be recharged after

usage. Are discarded after usage.

Secondary (rechargeable) cells or batteries Can be recharged electrically after

usage to their original condition.

Oxidation Loss of electron(s).

Reduction Gain of electron(s).

Redox Reduction and oxidation.