# Up-and-coming scientists

There will be one session at the JETC 11 where up-and-coming scientists, i.e. Ph.D. students and postdocs (at most 5 years after finishing their PhD thesis), will get the chance to present their work to the participants.

Possible speakers need to apply by 1 April 2011.

The following documents should be submitted as pdf-files per e-mail or as CD:

- a letter of application with the applicant's name, address, phone number and e-mail
- an extended abstract of the work that shall be presented at JETC 11 (max. 2 pages)
- a curriculum vitae of the applicant

The candidates will be chosen by an international selection committee.

The application should be sent to:

jetc11@physik.tu-chemnitz.de

Prof. Dr. Karl Heinz Hoffmann

TU Chemnitz

Institut für Physik

09107 Chemnitz

The selected scientists were:

*Vita Triani*

Department of Mathematics and Computer Science, University of Basilicata, Campus Macchia Romana, 85100, Potenza, Italy

vita.triani@gmail.com

**Second Law of Thermodynamics in the presence of non-regular processes**

In physics, it is very frequent the occurrence of non-regular processes, i.e., the presence of domains across which the fundamental fields and/or some of their derivatives are discontinuous. These discontinuous solutions have considerable physical significance, since they may be interpreted in terms of important physical phenomena such as, for example, phase transitions or shock wave propagation. In this talk, I will examine, first from a mathematical point of view, and then with a worked example, what is the role of Second Law of Thermodynamics for classical [1, 2], and generalized [3–5], exploitation procedures, when dealing with nonregular processes. More in detail, it will be shown that the proof proposed by Muschik and Ehrentraut in their celebrated paper [6], according to which the dissipation inequality is necessarily a constraint on the constitutive equations and not on the thermodynamic processes, conserves its validity on both sides of the discontinuity domain, allowing so the exploitation of Second Law separately in these regions.

As an example, I will consider the case of a plane material interface separating a Korteweg fluid by a perfect one. The entropy flux J will be taken in the classical form J = q/theta, with q is the heat flux and theta is the absolute temperature.

It is worth noticing that the balance equations on the material interface contain jump quantities [7] whose form, owing to our result above, may be assigned in accordance with Second Law.

Both in the bulk phases and on the interface, the exploitation of the Entropy Principle by a generalized Coleman-Noll procedure [4], leads to the conclusion that, in contrast to the classical case, the entropy density can depend on the gradients of the unknown fields, too. Further thermodynamic restrictions, which generalize the standard relations theta = ds/d epsilon and T = −p(rho, epsilon)I, with s as the specific entropy, epsilon as the specific internal energy, rho as the mass density, p as the pressure and T as the stress tensor, will be derived, too.

Finally, some open problems as, for instance, the physical interpretation of the jump term into the balances equations on the interface when applying the generalized procedures, will be focused as possible further developments of the theory.

[1] Coleman, B. D., Noll, W., The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167-178.

[2] Liu, I-Shih, Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Rational Mech. Anal., 46 (1972), 131-148.

[3] Cimmelli V. A., Oliveri F., Triani, V., Exploitation of the entropy principle: proof of Liu Theorem if the gradients of the governing equations are considered as constraints, J. Math. Phys., 52 (2011), 023511 (15 pages).

[4] Cimmelli, V. A., Sellitto A., Triani V., A new perspective on the form of the first and second laws in rational thermodynamics: Korteweg fluids as an example, J. Non-Equilib. Thermodyn., 35 (2010), 251–265.

[5] Cimmelli, V. A., Sellitto A., Triani V., A new thermodynamic framework for secondgrade Korteweg-type viscous fluids, J. Math. Phys., 50 (2009), 053101 (16 pages).

[6] Muschik W, Ehrentraut H., An Amendment to the Second Law, J. Non-Equilib. Thermodyn. 21 (1996), 175-192.

[7] Moeckel, G. P., Thermodynamics of an Interface, Arch. Rational Mech. Anal., 57 (1975), 255-280.

*Lucjan Nastalek*

Institute of Fluid Flow Machinery Polish Academy of Sciences, Gdansk, POLAND

lucjan.nastalek@imp.gda.pl

**Thermodynamics of Enhanced flow**

Fuel cells are profitable modern devices being the best examples of a useful machinery where complex conversion of energy at nano-scale takes place. Expecially, we observe such conversion at high temperatre solid oxide fuel cell (SOFC) that is built from ceramic nanomaterials. Anode supported fuel cell consists mainly of two nanoporous electrodes (cermets, lanthanum strontium manganite) separated by a thin, very dense solid electrolyte (yttria-stabilized zirconia or perovskite-type material). Finding of a mathematical model of an acting SOFC at temperatures as high as 1000 degrees C is a serious challenge as well for nanomecahnics as for nano-thermo-chemistry[1][2][3].

In the paper we present a further development of the authors’ model of thermochemical flow of fuel, air, species, ionic and electron currents within nano channels of the porous electrodes. Different transport enhancement models are taken into account – among them the most important are: the velocity slip connected with complex external friction, Darcy mobility and Reynolds transpiration. Increasing gas path to the triple-phase-boundary (TPB) enhances mass and electricity fluxes due to the concentration jump and electron resistivity jump. Enhancement of heat transport due to the von Smoluchowski jump is considered within the frame of generalized model of Navier-Stokes slip boundary condition.

Particular elements of the model have been tested and calibrated on the literature benchmark experiments concerning nanoflows. Integrated geometrical characteristics on nano-electrode materials such as: porosity, toutuosity and mean radii are finally involved into a macroscopic continuum model, and implemented into the standard CFD code [3]. As a result of analysis the power-current density characteristics have been examined and compared with the benchmark data.

[1] M.Karcz, M. Lemanski, J. Badur, Nowe kierunki w mechanice nanomaterialow, VIII konf. PTMTiS „Nowe kierunki rozwoju mechaniki”, 2009, Suchedniow, POLAND

[2] M. Karcz, From 0D to 1D modeling of tubular solid oxide fuel cel, Energy Conv. Man. 50 (2009) 2307-2315

[3] M. Karcz, S. Kowalczyk, J. Badur, “On the influence of geometric microstructural properties of porous materials on the modeling of a tubular fuel cell”, Chem. Proc. Eng. 31 (2010) 489-503

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Vita_Triani.pdf | 356.08 KB |

Lucjan_Nastalek.pdf | 508.48 KB |