Cellular convection caused by Rayleigh and Marangoni instability can greatly enhance the mass and heat transfer rate across the interface between fluids. Expressions for the liquid-phase mass and heat transfer rate enhanced by cellular convection were established, employing the theory of second order and first order non-equilibrium phase transitions for roll convection and hexagonal convection, respectively. These expressions can be used for cases where initially unperturbed concentration or temperature profiles can be described by a film model. The validity of the expressions was tested using heat transfer data measured by previous authors.