Materials For Sauna Walls

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

Introduction

If you build a sauna these days, you are concerned to minimize the energy it consumes. A sauna (Figure 22.1) like a kiln, has insulated walls to minimize the heat lost by conduction during the heating cycle. But if the heat capacity of the walls is high, a great deal of energy is lost simply in heating it up. So choosing the best material for a sauna wall requires a compromise between thermal conductivity λ and specific heat C_p. And it must also be cheap. Table 22.1 itemizes the design requirements.

Figure 22.1 A Sauna. The material of the wall must insulate, at low heat capacity.

Table 22.1 The design requirements

The Model

Case Study Kiln Walls analyzes the material requirements for thermal insulation chosen to minimize the total energy consumed during a heating cycle. The analysis for the sauna is the same as that for the kiln: we seek materials with high values of

,

(M22.1)

where λ is the thermal conductivity, (W/m.K), C_p the specific heat (J/kg.K), ρ the density (kg/m³) and a the thermal diffusivity (m²/s). The right thickness of a material with a large value of M₁ (Figure 22.2) minimizes the sum of the conduction losses and the energy used to heat the sauna walls themselves (which is lost when the sauna is switched off). The appropriate thickness, w, is given (Case Study Kiln Walls) by

,

(M22.2)

where t is the time for which the sauna is at its operating temperature (assumed to be long compared with the heat-up time). As with the kiln, we may wish to impose an upper limit on w for reasons of space. This implies an upper limit on diffusivity, a :

.

(M22.3)

There is a second objective: than of minimizing material cost. The cost of the insulation is

(M22.4)

per unit area of sauna wall. Substituting for w from equation (M22.2) gives

(M22.5)

The cost is minimized by maximizing

.

(M22.6)

The Selection

The neatest way to approach this problem, as with the Kiln of Case Study Kiln Walls, is by a two-stage selection, starting with a chart of the thermal diffusivity (a compound-property)

plotted against thermal conductivity, λ, as in Figure 22.2. Contours of M₁ are lines of slope 2. One has been positioned at M₁ = 10^-3 (m²K/W.s^1/2). To this can be added lines of constant wall thickness using equation (M22.2); those shown assume a cycle time of 2 hours. Materials with high values of M₁ which also lie below the appropriate thickness contour minimize the total energy lost during the cycle.

Figure 22.2a A chart of thermal diffusivity, a, plotted against thermal conductivity, λ. The line shows M₁.

Figure 22.2b A chart of thermal diffusivity, a, plotted against thermal conductivity, λ. The line shows the wall thickness, w.

The second chart (Figure 22.3) allows selection to minimize cost, again allowing a constraint on wall thickness to be applied. The selection line for M₂ has slope -2. Materials which satisfy the conditions shown in the two charts are listed in Table 22.2.

Postscript

Traditionally, saunas were made of solid wood, many inches thick, built, often, like a log cabin. A wood-finished interior is part of the sauna culture, but (as the table shows) solid wood is not the best choice; its heat capacity is too high and its thermal conductivity — though low — is not as low as that of polymer foams or fiberglass. An energy-efficient sauna has an interior panelled in wood which is as thin as possible, consistent with sufficient mechanical strength; the real insulation, usually polymer foam or fiberglass, is invisible.

Figure 22.3 A chart of thermal diffusivity, a, plotted against cost per unit volume, C_mρ. The line shows M₂.

Table 22.2 Materials for energy-efficient sauna walls

Further Reading

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

Related Case Studies

1. Insulation for Isothermal Containers

2. Energy-Efficient Kiln Walls

3. Materials for Passive Solar Heating

4. Materials for Storage Heaters