The development of Eulerian computational schemes for transported pdf methods in turbulent reacting flows is of great practical interest. This is because a large number of commercially available CFD codes use the Eulerian formulation in the solution of fluid flow problems. Particle based Monte Carlo schemes have been widely used to simulate turbulent reacting flows. The Lagrangian approach is used in these methods and hence requires the tracking of a large number of particles which may be computationally expensive for the simulation of practical combustion or fire scenarios. In this study we use the direct quadrature method of moments (DQMOM) for the simulation of an idealized furnace. We consider two inlet streams of fuel and oxidant fed into a reaction vessel and an outlet that removes combustion products. The reactor is characterised by perfect macromixing (i.e. no spatial gradients of the scalars) but imperfect micromixing (i.e. finite scalar dissipation rate) and finite rate chemistry. To represent a turbulent combustion problem, we also allow a fluctuating temperature field to influence the reaction dynamics. The means and variances of mixture fraction and reaction progress variable computed using DQMOM are compared with Monte Carlo simulations of the transported pdf equations.