Heat Release Rate of a Burning PoolMass flux × heat of combustion × area
What this calculates
This sheet uses the mass burning rate (or flux) of a fuel item in combination with its heat of combustion and surface area to compute a heat release rate. This allows us to figure out a heat release rate for a fuel package when we don’t have the luxury of burning it under an oxygen consumption calorimeter.
How to use it
This spreadsheet gives a quick way of determining the heat release rate from a preset list of fuel items. If the item is in the list, you can quickly get a fire size based on the area of burning; if it is not on the list, you’d need to look up the effective heat of combustion and mass burning flux and multiply as shown in the equation below.
Calculate the area of the burning surface (see “discussion” below”) and enter that into the yellow cell in the top block. The heat release rate will be calculated and shown below it. For convenience, I’ve also provided a simple calculation for determining the area of a circle.
Variables
- Q
- Heat release rate [kW]
- m″
- Mass burning flux [g/m²·s]
- A
- Burning surface area [m²]
- ΔH_c
- Effective heat of combustion [kJ/g]
Equations
Discussion
This sheet provides a quick way to figure out a maximum likely heat release rate for a pile/pool of burning fuel without taking into account any limiting factors such as ventilation.
For the area of the fuel, you should use the surface area of a pool fire. Or if the fuel is more three-dimensional (a stack of wood) you should use the burning surface area, which might involve the top of the pile as well as the sides.
Remember that there is a slight difference between total heat of combustion and effective heat of combustion. Total heat of combustion is an almost perfect amount of energy squeezed out of a material in a laboratory test. Effective heat of combustion is more realistic for real world fires where there is some unburned stuff left over. This spreadsheet uses effective heat of combustion. If all you can find for a material is total heat of combustion that is ok too, just keep in mind that you may be overestimating the heat release rate by a bit in that case.
Worked example
Example 1
Calculate the heat release rate for a circular pool of gasoline that has a radius of 2 meters.
First, figure out the surface area of the pool. The area of a circle is πr2, with a radius of 2 meters that would give an area of 12.6 m2.
Enter 12.6 into the top yellow cell and choose “gasoline” from the dropdown menu. The answer should be 30,284 kW, or just over 30 MW.
Example 2
A wood pile is 5 meters long, 1 meter wide and 2 meters tall. A witness reports seeing the woodpile engulfed in flames on all sides, from about the mid-height of the pile. Calculate the heat release rate for this fire.
The burning surface area of the wood, as reported by the witness, would be the top of the pile and half the height of each end of the pile and each side:
Top = 5 x 1 = 5m2
Ends of pile = 1 x 2/2 = 1m2 x two ends = 2m2
Sides of pile = 5 x 2/2 = 5m2 x two sides = 10m2
Total burning surface area = 5 + 2 + 10 = 17m2
Enter 17 into the top yellow cell and choose “wood” from the dropdown menu. The answer should be 2,618 kW (2.6 MW).
References
- Quintiere, J. G., Principles of Fire Behavior, Chapter 6, eq. 6-2.
- Effective heat of combustion — Quintiere, Table 6-3.
- Maximum burning flux — Quintiere, Table 6-2.