A criterion beyond conservation equations for complex transport process modeling - A case of Rayleigh-Bénard convection

Heat or mass transfer becomes usually complicated if coupled with fluid flow. To model the process, the mass, heat, and momentum conservation equations have been well established, which are shown in our work not the only governing laws. We analyzed heat transfer entropy generation rate and viscous dissipation of coupled heat and momentum transport phenomena in Rayleigh-Bénard convection, and proposed a hypothesis that the velocity and temperature distributions can be governed by the balance between the maximization of entropy generation and the minimization of viscous dissipation. Such a criterion, combined with a multi-scale model, was used to formulate a variational problem, which was then solved to reconstruct the velocity, temperature, and Nusselt number distributions in the Rayleigh-Bénard convection. As a result, three parameters obtained can be used to correct the error caused by the computations with low resolution of meshes. We show that the proposed method consumes significantly less computational effort than a traditional DNS, and can hopefully mitigate the limit by computational burden of the traditional conservation equation based simulations.