Thermal Calculations
Heat loss from insulated surfaces:
May be calculated either from a knowledge of the thermal conductivity and thickness of each individual insulation layer or from a knowledge of the “equivalent thermal conductivity.”
Heat gain:
When the surface to be insulated is below ambient temperature, heat will be gained rather than lost. This fact will be indicated in the formulae in this section by a negative value being show for “Q”.
Ambient conditions:
Calculations are based on “still air” conditions. It is possible to consider “exposed’ conditions, but this then needs details of wind speed, size, type and orientation of the surface being insulated. However, it is the heat loss from bare or uninsulated surfaces that is most affected by exposed conditions and the increase in heat loss from well insulated surfaces is minimal.
Surface temperature of pipe/vessel:
Calculations are based on the assumption that the surface temperature of the pipe/vessel is the same as that of the contained fluid. This is not quite true, but the difference is very small.
Surface Heat Transfer Coefficient
The surface heat transfer coefficients of the cladding will vary according to the nature of the surface and the temperature. Each surface material has its own unique emissivity. For practical purposes these can be grouped into three categories – Bright, Planished and Normal. Bright surfaces are those with low emissivity, e.g. bright metal surfaces, polished aluminium, etc. Planished surfaces are those with medium emissivity, e.g. galvanised steel, hammered aluminium, aluminium paint, etc. Normal surfaces are those with high emissivity, e.g. composition, canvas, plastic sheeting, unfaced Rockwool, painted metal surfaces, etc.
The surface coefficients are:
• Bright f =5.7 W/m²K ………….. Aluminium f = 5.7 W/m²K
• Planished f = 8.0 W/m²K ………….. Galv. Steel f = 6.3 W/m²K
• Normal f = 10.0 W/m²’K ………….. Mastics f = 10.0 W/m²K
Above approximately 50ºC, the surface coefficients will increase slightly with an increase in temperature. For a given hot face temperature and thickness of insulation, a Bright finish will give a higher surface temperature and lower heat loss than other finishes. A Normal finish will give a lower surface temperature but a higher heat loss. Thus, when designing for specific surface temperatures, the nature of the surface finishes can have a considerable effect on the thickness of insulation required.
Calculation Procedures
Most calculations must start by making an estimate of the outer surface temperature of the insulation and, for multi-layer insulation, estimates of the interface temperatures. The surface coefficients can be established. The k-value can be determined from the relevant nomographs, using the estimated temperatures. Inserting the hot face and ambient temperatures, the insulation thick ness and k-values and, if appropriate, the pipe diameter into the heat loss formula, will result in a heat loss. The surface temperature (and interface temperatures for multi-layer insulation) is then calculated. If the calculated temperatures agree, or are within 1ºC of the estimated temperatures, the calculations can be considered to be correct. Agreement is seldom reached on the first calculation, so the calculation must be repeated, using the calculated.
Heat flow calculations and R-value
Heat flow passing through pipe insulation can be calculated by following the equations set out in either the ASTM C 680 or EN ISO 12241 standards. Heat flow is given by the following equation:
Where:
- Θi is the internal pipe temperature,
- Θa is the external ambient temperature, and
- RT is the sum total thermal resistance of all insulation layers and the internal- and external-surface heat-transfer resistances.
In order to calculate heat flow, it is first necessary to calculate the thermal resistance (“R-Value”) for each layer of insulation.
For pipe insulation, the R-Value varies not only with the insulation thickness and thermal conductivity (“k-value”) but also with the pipe outer diameter and the average material temperature. For this reason, it is more common to use the thermal conductivity value when comparing the effectiveness of pipe insulation, and R-Values of pipe insulation are not covered by the US FTC R-Value rule.
The thermal resistance of each insulation layer is calculated using the following equation:
Where:
- De represents the insulation outer diameter,
- Di represents the insulation inner diameter, and
- λ represents the thermal conductivity (“k-value”) at the average insulation temperature (for accurate results iterative calculations are necessary).
Calculating the heat transfer resistance of the inner- and outer-insulation surfaces is more complex and requires the calculation of the internal- and external-surface coefficients of heat transfer. Equations for calculating this are based on empirical results and vary from standard to standard (both ASTM C 680 and EN ISO 12241 contain equations for estimating surface coefficients of heat transfer).
