The evaporative drying or a two-dimensional rectangular brick is studied numerically as a conjugate problem. The conservation equations for the solid are obtained using the continuum approach. The Navier-Stokes equations have been employed for obtaining the flow field and the corresponding flow solutions are used for predicting the drying behavior of the brick. The predictions of temperature and moisture content show that the leading edge dries faster compared to other sides of the solid. The full two-dimensional solutions differ considerably from the solutions based on heat and mass transfer through the boundary layers over the top surface. Average heat and mass transfer coefficients appropriate to the conjugate problem have been defined, based on constant temperature and moisture differentials between the solid and the ambient. The corresponding Nusselt and Sherwood number values indicate that analogy does not exist between heat and mass transfer, until the entire brick reaches wet bulb conditions. Free convection effects on drying are also studied for some initial period for low Reynolds number. Due to the influence of buoyant forces imparted by gravity, the overall drying rate has improved.