Heat Release Rate Formula

HRR is a crucial measure that indicates the fire’s intensity in terms of heat energy release. This is necessary for predicting fire cascade effects (transmission effects) in the environment in general and in particular to nearby cells in a battery. Other fire characterization factors, such as mass loss or gas development, are, to a first approximation, directly connected to the HRR.

Meaning of HRR

The single most essential parameter in fire accidents is heat release rate. A bench-scale calorimeter may be used to measure the rate of heat emission at various heat fluxes. The most typical devices for this purpose are based on the oxygen demand theory, which states that a roughly constant quantity of heat is emitted per unit weight of oxygen used over a wide variety of materials undergoing full combustion. The average amount of energy spent per gram of oxygen absorbed is 13.1 kJ/g. The removal efficiency from room fires and burning things such as furniture and different commodities may be measured using large-scale oxygen consumption calorimeters.

The drop in heat provided by the burner is precisely matched by the energy generated by the burning sample. The reduction in the gas flow is used to calculate the sample’s rate of heat emission. The system’s constant temperature eliminates inertia and allows for a fast adjustment in thermal efficiency.

Measurement of HRR

HRR can be expressed as energy or as total area normalized HRR (e.g., kW m²). The HRR is calculated according to ISO 5660-1, which specifies that the forced irradiance (heat flux) on the cell be given in kW m². Normally, HRR measurements are expressed as the mean HRR, which is calculated by dividing the total heat energy emitted by the length of time the fire has been burning.

Formula

ΔQ_c = ΔW + ΔQh + ΔU

where, 

• ΔW denotes the work output
• ΔQh denotes the heat transfer
• ΔU denotes the contents’ internal energy

Sample Problems

Question 1. Calculate the HRR given that the internal energy is 342 KJ/kg, heat transfer and work output being 123 KJ/kg and 33 KJ/kg.

Solution:

Given: ΔW = 33 KJ/kg, ΔQh = 123 KJ/kg, ΔU = 342 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 33 + 123 + 342

ΔQ_c = 498 KJ/kg

Question 2. Calculate the HRR given that the internal energy is 144 KJ/kg, heat transfer and work output being 69 KJ/kg and 177 KJ/kg.

Solution:

Given: ΔW = 177 KJ/kg, ΔQh = 69 KJ/kg, ΔU = 144 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 177 + 69 + 144

ΔQ_c = 390 KJ/kg

Question 3. Calculate the HRR given that the internal energy is 333 KJ/kg, heat transfer and work output being 222 KJ/kg and 111 KJ/kg.

Solution:

Given: ΔW = 111 KJ/kg, ΔQh = 222 KJ/kg, ΔU = 333 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 111 + 222 + 333

ΔQ_c = 666 KJ/kg

Question 4. Calculate the HRR given that the internal energy is 75 KJ/kg, heat transfer and work output being 64 KJ/kg and 11 KJ/kg.

Solution:

Given: ΔW = 11 KJ/kg, ΔQh = 64 KJ/kg, ΔU = 75 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 11 + 64 + 75

ΔQ_c = 150 KJ/kg

Question 5. Calculate the HRR given that the internal energy is 592 KJ/kg, heat transfer and work output being 466 KJ/kg and 197 KJ/kg.

Solution:

Given: ΔW = 466 KJ/kg, ΔQh = 197 KJ/kg, ΔU = 592 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 466 + 197 + 592

ΔQ_c = 1255 KJ/kg

Question 6. Calculate the HRR given that the internal energy is 333 KJ/kg, heat transfer and work output being 200 KJ/kg and 81 KJ/kg.

Solution:

Given: ΔW = 81 KJ/kg, ΔQh = 200 KJ/kg, ΔU = 333 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 81 + 200 + 333

ΔQ_c = 614 KJ/kg

Question 7. Calculate the HRR given that the internal energy is 543 KJ/kg, heat transfer and work output being 991 KJ/kg and 1000 KJ/kg.

Solution:

Given: ΔW = 991 KJ/kg, ΔQh = 1000 KJ/kg, ΔU = 543 KJ/kg

Since, ΔQc = ΔW + ΔQh + ΔU

= 991 + 1000 + 543

ΔQ_c = 2534 KJ/kg