Nonlocal electron heat flux revisited

A known nonlocal model of electron heat flux, applying for (scale length/thermal ion-electron mean-free path) of order Z)1/2(e*/T)312, ionization number Z, large, and e*~ 6.5 T (the energy of electrons carrying most of the flux), is reconsidered. The large e*/T ratio simplifies the complete formalism. A simple flux formula, exact for both smooth and steep profiles, is given. Thermoelectric effects and other models are discussed.

Self-consistent, nonlocal electron heat flux at arbitrary ion charge number

A single, nonlocal expression for the electron heat flux, which closely reproduces known results at high and low ion charge number 2, and “exact” results for the local limit at all 2, is derived by solving the kinetic equation in a narrow, tail-energy range. The solution involves asymptotic expansions of Bessel functions of large argument, and (Z-dependent)order above or below it, corresponding to the possible parabolic or hyperbolic character of the kinetic equation; velocity space diffusion in self-scattering is treated similarly to isotropic thermalization of tail energies in large Z analyses. The scale length H characterizing nonlocal effects varies with Z, suggesting an equal dependence of any ad hoc flux limiter. The model is valid for all H above the mean-free path for thermal electrons.

Self-similar expansion of laser plasmas with nonlocal heat flux

A previous hydrodynamic model of the expansion of a laser-produced plasma, using classical (Spitzer) heat flux, is reconsidered with a nonlocal heat flux model. The nonlocal law is shown to be valid beyond the range of validity of the classical law, breaking down ultimately, however, in agreement with recent predictions.

Nonlocal electron heat-flux

Electron thermal conduction in a not quite collisional unmagnetlzed plasma is analysed. The failure of classical results for temperature scale-length up to 100 times larger than thermal mean-free-path for electron scattering, and large ion-charge number Z , is discussed. Recent results from a nonlocal model of conduction at large Z are reviewed. Closed form expressions for Braginskii's coefficients a ,/3 , y for Z =0(1) are derived. An extension of the nonlocal model for Z =0(1) is discussed.

Analog network to convert surface temperature to heat flux.

Mode of access: Internet.

Mechanisms for increasing the peak heat flux in boiling saturated water at atmospheric pressure; a report for National Science Foundation, Grant GP 788.

Mode of access: Internet.

Pre-development study of a heat flux measurement device suitable for use on flight vehicles,

"Project no. AA-1577-Y. Subcontract no. 112705."

Nonlinear analog network to convert surface temperature to heat flux.

Mode of access: Internet.

Radiation fluxes, soil heat flux, air temperature, soil temperature, soil moisture and vegetation at dwarf shrubs and wet sedges in Kytalyk, NE Siberia

Vegetation changes, such as shrub encroachment and wetland expansion, have been observed in many Arctic tundra regions. These changes feed back to permafrost and climate. Permafrost can be protected by soil shading through vegetation as it reduces the amount of solar energy available for thawing. Regional climate can be affected by a reduction in surface albedo as more energy is available for atmospheric and soil heating. Here, we compared the shortwave radiation budget of two common Arctic tundra vegetation types dominated by dwarf shrubs (Betula nana) and wet sedges (Eriophorum angustifolium) in North-East Siberia. We measured time series of the shortwave and longwave radiation budget above the canopy and transmitted radiation below the canopy. Additionally, we quantified soil temperature and heat flux as well as active layer thickness. The mean growing season albedo of dwarf shrubs was 0.15 ± 0.01, for sedges it was higher (0.17 ± 0.02). Dwarf shrub transmittance was 0.36 ± 0.07 on average, and sedge transmittance was 0.28 ± 0.08. The standing dead leaves contributed strongly to the soil shading of wet sedges. Despite a lower albedo and less soil shading, the soil below dwarf shrubs conducted less heat resulting in a 17 cm shallower active layer as compared to sedges. This result was supported by additional, spatially distributed measurements of both vegetation types. Clouds were a major influencing factor for albedo and transmittance, particularly in sedge vegetation. Cloud cover reduced the albedo by 0.01 in dwarf shrubs and by 0.03 in sedges, while transmittance was increased by 0.08 and 0.10 in dwarf shrubs and sedges, respectively. Our results suggest that the observed deeper active layer below wet sedges is not primarily a result of the summer canopy radiation budget. Soil properties, such as soil albedo, moisture, and thermal conductivity, may be more influential, at least in our comparison between dwarf shrub vegetation on relatively dry patches and sedge vegetation with higher soil moisture.

Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Automatization of feeding the heat flux data to water circulation simulations of recovery boilers

Tässä työssä perehdytään soodakattiloiden vesikiertomallin rakentamiseen. Työn päätavoitteena on kehittää simulointimallia varten taulukkolaskentapohja, jonka avulla soodakattilan lämpövuotietoja on yksinkertaista ja nopeaa käsitellä ja siirtää Apros 6 -simulointiohjelmaan. Lisäksi tarkoituksena on pyrkiä automatisoimaan työvaiheet mahdollisimman pitkälle, jolloin vesikiertolaskennan tekeminen yksinkertaistuisi, yhtenäistyisi ja tarkentuisi. Tämä on mahdollista Excel- makrojen ja Apros 6:n uusien toimintojen avulla. Apros 6:ssa on nyt mahdollista hyödyntää SCL- komentotiedostoja, joiden avulla sujuva tiedonsiirto Aproksen ja Excelin välillä vodaan toteuttaa. Vesikiertolaskentaan käytettävän datan käsittely on aikaisemmin ollut työlästä ja sen tarkkuus on pitkälti riippunut mallintajasta. Tässä diplomityössä päästään hyödyntämään uusimpia ja realistisempia soodakattiloiden CFD- malleja, joiden avulla pystytään luomaan aikaisempaa tarkemmat lämpövuojakaumat soodakattilan lämpöpinnoille. Tämä muutos parantaa vesikiertolaskennan tarkkuutta. Työn kokeellisessa osassa uutta Excel laskentatyökalua ja uusia lämpövuoarvoja testataan käytännössä. Eräs vanha Apros- vesikiertomalli päivitetään uusilla lämpövuoarvoilla ja sen rakenteeseen tehdään muutoksia tarkkuuden parantamiseksi. Uuden mallin toimivuutta testataan myös 115 %:n kapasiteetilla ja tutkitaan kuinka kyseinen vesikiertopiiri reagoi suurempaan lämpötehoon. Näitä kolmea eri tilannetta vertaillaan toisiinsa ja tarkastellaan eroavaisuuksia niiden vesi-höyrypiireissä.

Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.