Materials For Storage Heaters

• Introduction
• The Model
• The Selection
• Postscript
• Further reading
• Related case studies

Introduction

The demand for electricity is greater during the day than in the small hours of the night, for obvious reasons. It is not economic for electricity companies to reduce output, so they seek instead to smooth demand by charging less for off-peak electricity. Cheap, off-peak electrons can be exploited for home or office heating by using them to heat a large mass of thermal-storage material from which heat is later extracted when the demand — and cost — of power are at their peak.

The way such a storage heater works is shown schematically in Figure 24.1. A heating element heats a thermal mass during off-peak hours. During the expensive peak-demand hours the element is switched off and the thermostatically-controlled fan blows air over the hot mass, extracting heat and passing it to the room as needed.

Figure 24.1 A storage heater. The heat-storage medium is chosen to have the highest heat capacity per unit cost.

What is the best material for the thermal mass? To hold enough heat to be useful, the thermal mass has to be large. It performs no other function, but just sits there, inert and invisible. No-one wants to pay more than they have to for inert, invisible mass. The best material is that which stores the most thermal energy (for a given temperature rise, ΔT) per unit cost. It must also be capable of withstanding indefinitely the temperature of the heater itself — that is, its maximum working temperature must exceed that of the surface temperature of the heating element. The design requirements are summarized in Table 24.1.

Table 24.1 The design requirements

The Model

First, then, maximizing energy per unit cost. The thermal energy E stored in a mass m of solid when heated through a temperature interval ΔT is

(M24.1)

where C_p (kJ/kg.K) is the specific heat capacity of the solid (at constant pressure). The material cost is

(M24.2)

where C_m is the cost per kg of the material. The energy stored per unit cost is therefore

,

(M24.3)

This is the objective function. The energy per unit cost is maximized by maximizing

.

(M24.4)

The constraint is that the maximum working temperature T_max be greater than the surface temperature of the heating element T_h, which we take to be 320°C, approximately 600 K.

.

(M24.5)

The Selection

Figure 24.2 shows the appropriate diagram: C_p/C_m plotted against T_max. The selection results are listed in Table 24.2.

Figure 24.2 A chart showing heat capacity per unit cost plotted against maximum service temperature

Table 24.2 Materials for storage heaters

Postscript

An important consideration is the rate at which heat can be extracted from the heater. This rate depends on the dimensions of the thermal mass and on the thermal diffusivity of the material of which it is made. Roughly speaking, the time-constant t for the cooling of a block of material of minimum dimension x is approximately

(M24.6)

where the thermal diffusivity of the material is

(M24.7)

λ is its thermal conductivity and ρ is its density. A large block cools slowly; small pieces cool more quickly if air can flow between them. So by breaking up the mass into loose gravel-like pieces, or by putting air channels through the brick, the rate of power output can be increased. In practice, the thermal diffusivity of the materials listed above (except for cast iron) all lie near 10^-6 m²/s. If the heat is to be extracted over a 6 hour period, then, according to equation M24.6 the block size should not exceed 0.2 m, otherwise the heat put in at night does not have time to leak out again during the day.

Further Reading

Holman, JP 'Heat Transfer', 5th Edition, (1981), McGraw-Hill, NY, USA.

Related Case Studies

1. Insulation for Isothermal Containers

2. Energy-Efficient Kiln Walls

3. Materials for Sauna Walls

4. Heat Exchanger Tubes