A system of differential equations is derived from basic laws of mass conservation dynamics and thermodynamics for a gas-particle reacting system. The concept of two superimposed continua occupying the same control volume is used throughout. A number of terms appearing in the basic equations, physically identified with the presence of particles, are defined as source terms for the gas motion. With the introduction of phenomenological relations for these terms and the thermodynamic variables, a complete set of differential equations is obtained. The equations governing the one-dimensional flow in an arbitrarily shaped duct are presented as a special case.

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