In this study, the relationship among the concepts of entropy generation rate, entransy theory, and generalized thermal resistance to the optimal design of thermal systems is discussed. The equations of entropy and entransy rates are compared and their implications for optimization of conductive heat transfer are analyzed. The theoretical analyses show that based on entropy generation minimizat...

We consider solving a generalized Allen-Cahn equation coupled with passive convection for given incompressible velocity field. The numerical scheme consists of the first order accurate stabilized implicit explicit time discretization and fourth finite difference scheme, which is obtained from formulation $Q^2$ spectral element method. prove that discrete maximum principle holds under suitable m...

The generalized free energy inequality known from statistical mechanics is stated in the finite dimension setting and the maximizing matrix is restored. Our approach uses the maximum-entropy inference principle and numerical range methods.

A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown...

We study the dynamical equations of nonlinear inductor-capacitor circuits. We present a novel Lagrangian description of the dynamics and provide a variational interpretation, which is based on the maximum principle of optimal control theory. This gives rise to an alternative method for deriving the dynamic equations. We show how this generalized Lagrangian description is related to generalized ...