A numerical formulation capable of simulating fluid flow and non-equilibrium heat and mass transfer in three-dimensional conjugate fluid/solid/porous domains is presented. The governing transport equations are presented for the fluid, solid, and porous regions, with special consideration given towards the manner in which moisture is accounted for in the air-water vapour mixture. Mathematical conditions are also presented to ensure that heat and mass transfer occurs smoothly across fluid-porous, fluid-solid and porous-solid interfaces. The developed formulation is validated by simulating direct and indirect evaporative cooling problems. The results demonstrate that the formulation is capable of simulating evaporative cooling in conjugate three-dimensional domains, with and without the addition of sensible heat. Moreover, different simulated cases show that the results are accurate compared to available experimental results, and are physically realistic throughout the domain and at interfaces between conjugate regions. The unsteady problem of drying of an initially saturated porous material is also simulated to demonstrate the non-equilibrium mass transfer feature of the developed formulation. The results show the correct trends in drying time with respect to the flow Reynolds number and the relative humidity of the inlet air-water vapour mixture. (C) 2014 Elsevier Ltd. All rights reserved.