Linear irreversible thermodynamic principles are used to demonstrate, by counterexample, the existence of a fundamental incompleteness in the basic pre-constitutive mass, momentum, and energy equations governing fluid mechanics and transport phenomena in continua. The demonstration is effected...

The principles of linear irreversible thermodynamics are used to show that near-equilibrium linear constitutive equations governing the diffuse fluxes through fluids of momentum, energy, and other extensive properties, and valid for the case of general unsteady flows, can be derived by...

A heat conduction problem is studied using extended hydrodynamic equations obtained from Enskog's equation for a simple case of two planar systems in contact through a porous wall. One of the systems is in equilibrium and the other one in a steady conductive state. The example is used to put to...

In the present work, the entransy and entransy dissipation are defined from the thermodynamic point of view. It is shown that the entransy is a state variable and can be employed to describe the second law of thermodynamics. For heat conduction, a principle of minimum entransy dissipation is...

A flexible solution method for the initial-boundary value problem of the temperature field in a one-dimensional domain of a solid with significantly nonlinear material parameters and radiation boundary conditions is proposed. A transformation of the temperature values allows the isolation of the...

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of...

Classical equations for transport processes predict infinite speed of the perturbations propagation. From molecular point of view, this feature is rather doubtful, because, for instance in gas or plasma, any perturbation propagates as a result of molecules or charged particles (ions, electrons)...

In this paper, by taking into account effects of the user and object correlations on a heat conduction (HC) algorithm, a weighted heat conduction (WHC) algorithm is presented. We argue that the edge weight of the user–object bipartite network should be embedded into the HC algorithm to measure...

Pucci and Saccomandi [J. Phys. A 26 (1993) 681] have obtained invariant solutions for the Fokker–Planck (FP) equation via potential symmetries. Herein, we analyze the generalized one-dimensional FP equation for various cases corresponding to the physically interesting situations through the...

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved...