A detailed two-dimensional mathematical model is studied for the unsteady heat-and mass-transfer equations coupled with a quasi-steady formulation of the electromagnetic field for the microwave-induced pyrolysis of a wood block. The aspects examined include the description of the flow field based on either the assumption of constant pressure and one-dimensional flow velocity directed along the wood fibers or the linked two-dimensional variation of pressure and velocity in accordance with the Darcy law and deviations from the assumptions of local thermal equilibrium between the solid and gas/ vapor phase. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 610-624, 2012