148 research outputs found

    Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations

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    We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.Comment: 22 pages, 2 figure

    Non-isothermal transport of multi-phase fluids in porous media. The entropy production

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    We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.Comment: 25 pages, 7 figures, Talk at Interpore, New Orleans, 201

    Elevsamarbeid En sammenliknende casestudie av fire læreres bruk av elevsamarbeid på ungdomstrinnet

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    Masteroppgave pedagogikk- Universitetet i Agder, 2015Forskning på samarbeid mellom elever studerer i stor grad selve elevsamarbeidet, og ønsker å gi beskrivelser av hva som må til for å få et godt samarbeid mellom elevene eller vilkår for gode læringsresultater. Problemstillingen i denne undersøkelsen legger didaktisk teori til grunn, og tar for seg hvordan elevsamarbeidet kan forstås didaktisk. Oppgaven tar utgangspunkt i danningsdidaktisk tenkning, som vektlegger at innholdet må velges slik at det kan skape betydning for elevene, i tillegg til teori fra lærings- og undervisningsteoretisk didaktikk. Undersøkelsen tar form som en casestudie, der direkte observasjon og intervju av lærere på ungdomstrinnet har blitt gjort med sikte på å finne ut hvordan lærere bruker, begrunner og vurderer elevsamarbeid i fellesundervisning, og hvordan konteksten påvirker deres valg. Analysen tar utgangspunkt i Heimann/Schulz-modellen, som vektlegger undervisningens kompleksitet gjennom seks elementer som læreren må forholde seg til ved analyse og planlegging. Resultatene viser at elevsamarbeid kan oppleves problematisk for lærere på ungdomstrinnet. Lærerens vurdering av elevenes forutsetninger for å mestre samarbeidsformen spiller inn som en viktig faktor. Større prosjekter velges bort til fordel for mindre gruppearbeid der læreren i større grad styrer prosessen. Rammet inn av fellesundervisningen kan elevsamarbeidet blir brukt for å skape en god følgbarhet i undervisningen, og i forlengelsen av klasseromskommunikasjonen kan elevsamarbeidet gi elevene flere muligheter til å oppleve mening i innholdet

    Theory and simulation of shock waves: Entropyproduction and energy conversion

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    We have considered a shock wave as a surface of discontinuity and computed the entropy production using non-equilibrium thermodynamics for surfaces. The results from this method, which we call the "Gibbs excess method" (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock front region, but with different assumptions about local equilibrium. Non-equilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number M2M \approx 2 and a strong shock with M6M \approx 6 and with a Prandtl number of the gas Pr1.4Pr \approx 1.4 in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97 \% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.Comment: 27 pages, 16 figures, Supporting material, Symbol list

    Violations of local equilibrium and linear response in classical lattice theories

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    We study the dynamics of ϕ4\phi^4 theory and the FPU β\beta model under thermal gradients, from first principles. We analyze quantitatively how local equilibrium and linear response are violated, paying special care to how we find observables that unambiguously display these violations. Relations between these quantities to equations of state are also examined. Further, we discuss how we can approach similar dynamical problems in continuum quantum field theory. We analyze how close we are to obtaining the continuum results.Comment: 7pp, 4figs, talk given by KA at "Thermal field theory and applications" workshop 200
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