**Heat Loss Calculation Principles**

Factors Affecting Heat Transfer and Thermal Performance Factors affecting heat transfer and thermal performance through fibrous materials occur in a combination of the following three mechanisms

- CONDUCTION – through the fibers and across the air spaces
- RADIATION
- CONVECTION

The physical characteristics of the mineral wool fibers (Rockwool or Glasswool) and their orientation in the insulation material will affect the thermal performance. Thus density, fiber diameter, fiber orientation and shot content, all influence the overall conductivity.

In general, the thermal conductivity will increase with temperature, as the component heat transfer mechanisms increase, but the rate of increase and the final value at any temperature will depend on the density and the quality of the fiber in the insulating material.

**Symbols**

Q Heat loss through the insulation – per square meter (W/M²)

Q’ Heat loss through the insulation – per linear meter of pipe run (W/m) th Hot face temperature, i.e. temperature of vessel/pipe (ºC)

tc Cold face temperature, i.e. temperature of outer surface of insulation (ºC) ta Ambient temperature of still air (ºC)

tj Temperature at junction/inter-face of two layers of insulation (ºC)

t1 Temperature of lst interface (between lst and 2nd layer) of insulation (ºC)

t2 Temperature of 2nd interface (between 2nd and 3rd layer) of insulation (ºC)

tn Temperature of nth inter-face (between nth and n+l layer) of insulation (ºC)

x Overall thickness of insulation (m=01001 mm) (m) xl Thickness of lst (inner) layer of insulation (m=0,001 mm) (m)

x2 Thickness of 2nd layer of insulation (m=0,001 mm) (m)

xn Thickness of nth layer of insulation (m=0,001 mm) (m)

k Thermal conductivity of insulation (W/mK)

kl Thermal conductivity of lst (inner) layer of insulation (W/mK)

k2 Thermal conductivity of 2nd layer of insulation (W/mK)

kn Thermal conductivity of nth layer of insulation (W/mK)

R Thermal resistance of insulation (m²/KW)

Rs Thermal resistance of outer surface of insulation (m²/KW)

dp Outer diameter of pipe (m=0,001 mm) (m)

ds Outer diameter of total insulation (m=0,001 mm) (m)

d1 Outer diameter of lst (inner) layer of insulation (m=0,001 mm) (m)

d2 Outer diameter of 2nd layer of insulation (m=0,001 mm) (m)

dn Outer diameter of nth layer of insulation (m=0,001 mm) (m)

f Surface heat transfer coefficient (W/m²K) 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 formulas 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 un-insulated 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. galvanized steel, hammered aluminium, aluminium paint, etc.

Normal surfaces are those with high emissivity, e.g. composition, canvas, plastic sheeting, un-faced 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 thickness 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 temperatures as the new .estimates”, bearing in mind that the relevant k-values will change according to the change in the hot face and cold face/interface temperatures.

Repeat the procedure of using the calculated temperatures as the new estimates until agreement is reached.

**Thermal Conductivity**

The units of thermal conductivity – k-value – are W/mK, where K represents 1 degree Kelvin which is exactly the same as 1 degree Celsius.

The thermal conductivity of the Rockwool products can be determined from the relevant nomographs.

Determine Required Insulation Thickness for Condensation Control

Condensation will occur if the surface temperature falls below the dew point temperature – the temperature at which the ambient air of a certain relative humidity will be become saturated if cooled.

The insulation thickness must be sufficient to ensure that the surface temperature of the vapor barrier is above the dew point temperature for the worst anticipated conditions of temperature and humidity.

Specialized Conditions at the point of Delivery

During the flow through a pipe system, a fluid will lose or gain heat, the effects of which are associated directly with the transmission of heat through the insulation and also with that in local areas of bare surfaces.

**The heat transmission to or from the system remains constant given constant temperature conditions, but the change in temperature depends on:**

- The rate of mass flow
- The specific heat capacity of fluid
- Variation in pressure during passage through the system is an additional consideration if the fluid is a gas or a vapor.