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# How to distribute the heat of reaction in a multiphase system?

## How to distribute the heat of reaction in a multiphase system?

(OP)
I am trying to model the combustion of aluminum particles in air. The first step is to vaporize the particles according to the equation Δc=(3Φsρs/τ)(1+0.276∗sqrt(Re)), which describes the inter-phase mass transfer rate. Something that I am trying to understand is, whether the heat of formation of aluminum vapor should be added to added to/subtracted from the gas phase total energy, and why? Also, what about the total energy/internal energy for the particle phase? Does it not change? I am only talking about the effect of the heat of formation. I understand the changes in energy due to change in kinetic energy and Pseudo Thermal Energy.

The other question is that if I have aluminum vapor burning in oxygen that produces aluminum oxide condensate, I know the heat of reaction, but how do I distribute the energy produced due to the reaction between the gas and solid phases? What happens to the energies of the gas and solid phases? Do they reduce/increase, and how much?

In order to make the problem description more clear, I am modeling the burning of Al in air inside a closed domain. So the vaporization occurs only due to either the burning of Al or some shock passing through the domain, etc., i.e., there is no external heating.

I would really appreciate it if someone can provide me with some insight on this.

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