We assess the performances of incremental unknown method when used in solving a time dependent 2D coupled linear and nonlinear heat and mass transfer in a homogenous porous slab of thickness L and width W. The formulation of this coupled heat and mass transfer phenomena is based on the simplified model of De Vries where it is assumed that the heat transfer due to the mass transfer is negligible and that the time variation of the condensed water is also negligible. The system of equations is numerically solved when the sides of the slab are subjected to ambient and initial conditions in terms of temperature and moisture content and the results are compared to those obtained using finite difference schemes and finite element method. Validation tests are performed in 2D situation the system is solved in linear and nonlinear cases using the Incremental Unknowns, classical finite differences and finite element method and results obtained from different schemes are compared among them. Time marching solution is achieved in all cases using ADI method. The numerical results show clearly the perfect agreement between the numerical scheme and finite element method also the transient evolution is greatly affected when non linear effects are taken into account.

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