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This work is intended to study the problem of heat and mass transfer with single-phase flow in a porous cavity. The model of this problem consists of the conservation laws of energy, momentum, and mass. The cavity boundaries are described by mixed Dirichlet-Neumann boundary conditions. The momentum equation which is represented by Darcy’s law has been solved with the continuity equation to give the pressure implicitly, then the velocity of the field has been calculated explicitly. Therefore, both energy equation and concentration equations are solved implicitly. The multiscale time-splitting implicit method has been used to treat the temporal discretization of the system of governing equations. The Courant-Friedrichs-Lewy condition has been used to achieve the time step-size adaptation. Some results are represented in graphs such as temperature, concentration, pressure, velocity, local Nusselt number and local Sherwood number. Two numerical cases are considered for different boundary conditions.

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