Microwave-assisted
process intensification is a promising technique
hindered by the unavailability of design rules for optimization and
scale-up. High-throughput computational models allowing the exploration
of a vast design space are imperative for the rapid development and
deployment of intensified microwave reactors. Recently, structured
reactors, especially monoliths, are emerging as a canonical multiphase
reactor setup in the microwave-heating community. The vast separation
of scales in these reactors leads to a large number of mesh elements,
making the simulations time-consuming and challenging to converge.
To this end, we employ volume and asymptotic averaging to represent
monoliths, a multiphase system consisting of a fluid and a solid phase,
as a continuum or effective medium. We rigorously verify the adequacy
of the averaging techniques to predict the spatiotemporal distribution
of the electric field, electromagnetic power dissipation, and temperature
against fully resolved monolith simulations. The developed continuum
model can replicate the three-dimensional transient behavior obtained
from the multiphase simulations with an order of magnitude lower computational
expense. Moreover, the continuum model allows easier mesh generation
and convergence of numerical solution than the multiphase model. The
developed multiscale framework can be used to simulate microwave-heated
monoliths and other multiphase reactors, such as packed beds and open-cell
foams.