Detailed Derivations of Formulas for Heat Release Rate Calculations Revisited: A Pedagogical and Systematic Approach

Area of Science:

• Combustion science
• Chemical engineering
• Thermodynamics

Background:

• Oxygen consumption calorimetry is a key method for determining heat release rates.
• Existing formulas for heat release rate calculations often rely on numerous assumptions.
• A more generalized and systematic approach is needed for accurate calculations.

Purpose of the Study:

• To revisit and derive generalized formulas for heat release rate calculations.
• To simplify the derivation process using a structured and pedagogical approach.
• To reduce the number of assumptions required in heat release rate calculations.

Main Methods:

• Revisiting derivations based on the oxygen consumption principle.
• Treating oxygen consumption calorimetry as a chemical flow process.
• Formulating the problem in matrix notation and solving material balances using a tie component concept.

Main Results:

• Generalized formulas for heat release rate calculations were derived with fewer assumptions.
• The derivation procedure is intuitive, systematic, and easy to follow.
• The developed framework facilitates the inclusion of other chemical species in calculations.

Conclusions:

• The generalized framework provides a more robust method for heat release rate calculations.
• This approach simplifies complex calculations in combustion science and chemical engineering.
• The method enhances the flexibility and accuracy of oxygen consumption calorimetry.