# Radiation‚ Convection‚ and Other Losses

The Boiler Efficiency Calculator takes into account only major energy losses‚ which typically represent 10 to 20% of fuel input. The major energy losses fall into two categories: stack losses‚ and radiation and convection losses.

This section deals with the second type of losses‚ that is the heat lost to the surroundings from the warm surfaces of a boiler or high-temperature water generator. Other losses that are largely applicable to coal firing have been listed below‚ but generally account for no more than 2 or 3 % of heat input.

The external surface of an operating steam boiler or high-temperature water generator is hotter than its surroundings and therefore loses heat by both radiation and convection.

Measurement of the actual loss is complex‚ tedious‚ time-consuming and seldom undertaken‚ but there is a convenient and widely accepted shortcut. The American Boiler Manufacturers Association’s (ABMA) standard radiation loss chart is quite satisfactory for boilers where the furnace and heat exchange surfaces are enclosed in a single housing. This is the case with package boilers and many field-erected units. The exceptions are installations such as cogeneration systems having a separate waste heat boiler and circulating fluidized bed boilers where the furnace‚ hot cyclone and backpass generating surfaces are all separate units.

The radiation and convection loss (LR ) is proportional to the external surface area of a unit‚ whereas the unit’s capacity is proportional to its volume. Thus‚ LR ‚ as a percentage of fuel input‚ is larger for small units than large ones. Furthermore‚ with the fully water-walled boilers that are now in common usage‚ the external surface temperatures remain fairly constant over the load range. This means that the actual loss in Btu/h is also fairly constant over the load range‚ therefore LR ‚ as a percentage of fuel input‚ increases as output is reduced. For example‚ if LR is 1 % at full load it will be 2 % at half load‚ and 4 % at one-quarter load.

From the standpoint of efficiency‚ it is better to have one unit operating at close to full load than to have two units operating at half load. This is particularly true for smaller units. Likewise‚ there are advantages to having boilers of different capacity in the same plant‚ so smaller units can be employed for periods of low demand.

For steam boilers and high-temperature water generators with output ratings up to 200‚000 lb/h of steam or 200 million Btu/h‚ and of conventional configuration‚ such as package boilers‚ LR ‚ as % of fuel input‚ can be estimated using the table that follows. In it‚ LR at 100 % output was selected from the ABMA chart‚ for the range of sizes (maximum output) shown. It was assumed that all units have four water-cooled walls‚ and that for steam boilers‚ 1 lb of steam is equivalent to 1000 Btu. LR at part load was calculated by dividing the loss at full load by the ratio of actual load to full load. It should be noted that the accuracy of results is limited to one decimal place.

Example:

Determine LR for a steam boiler rated at 45‚000 lb/h of steam‚ operating at an output of 25‚000 lb/h

Calculate:

• Maximum rated output in Btu/h.

Maximum output = 45‚000 x 1000 = 45 million Btu/h.

• Ratio of operating output to maximum output.
25‚000 ÷ 45‚000 = 0.56

Determine:

• LR at 100 % output.

Interpolate between 40 million and 50 million Btu/h in the left-hand column of the table.

LR at 100 % capacity = 0.70 % of fuel input.

Calculate:

• LR at 56 % output.

LR at 56 % output = 0.70 ÷ 0.56 = 1.25 % of fuel input

Approximate radiation and convection loss‚ LR% of heat input
Max output‚
millions of Btu
100 % 80 % 60 % 50 % 40 % 20 %
10 1.60 2.00 2.67 3.20 4.00 8.00
20 1.05 1.31 1.75 2.10 2.62 5.25
30 0.84 1.05 1.40 1.68 2.10 4.20
40 0.73 0.91 1.22 1.46 1.82 3.65
50 0.66 0.82 1.10 1.32 1.65 3.30
60 0.62 0.78 1.03 1.24 1.55 3.10
70 0.59 0.74 0.98 1.18 1.48 2.95
80 0.56 0.70 0.93 1.12 1.40 2.80
90 0.54 0.68 0.90 1.08 1.35 2.70
100 0.52 0.65 0.87 1.04 1.30 2.60
120 0.48 0.60 0.80 0.96 1.20 2.40
140 0.45 0.56 0.75 0.90 1.12 2.25
160 0.43 0.54 0.72 0.86 1.08 2.15
180 0.40 0.50 0.67 0.80 1.00 2.00
200 0.38 0.48 0.63 0.76 0.95 1.90

### Other Losses

There are several additional losses that are addressed in the ASME Boiler Test Code. Many of these are applicable only to coal firing‚ and even then are unlikely to account for more than 2 or 3 % of heat input.

They are:

– unburned carbon in refuse
– moisture in fuel
– moisture in air
– heat in atomizing steam
– unburned carbon monoxide‚ hydrogen and hydrocarbons