Abstract
The analysis of nonisothermal transport phenomena in multiphase systems is almost always accompanied by the use of some type of volume-averaged or spatially-smoothed temperature. In such systems one always encounters parameters, such as a reaction rate coefficient or a viscosity, that are temperature dependent. Given the point relation for some generic parameter in the β-phase, i.e., ψβ = ψβ(T β), one can wonder how the volume-averaged form of this parameter depends on the volume-averaged temperature. In this paper we show that the local volume-averaged form of ψβ is given by $ in which A represents a second order tensor that depends on the system parameters. A somewhat more complex form is encountered for area-averaged functions of the temperature. These functions are especially prevalent in reactor design calculations, which are considered both in terms of early intuitive developments and from the perspective of the method of volume averaging.
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