Physical-Statistical Model of Thermal Conductivity of Nanofluids

A physical-statistical model for predicting the effective thermal conductivity of nanofluids is proposed. The volumetric unit of nanofluids in the model consists of solid, liquid, and gas particles and is treated as a system made up of regular geometric figures, spheres, filling the volumetric unit by layers. The model assumes that connections between layers of the spheres and between neighbouring spheres in the layer are represented by serial and parallel connections of thermal resistors, respectively. This model is expressed in terms of thermal resistance of nanoparticles and fluids and the multinomial distribution of particles in the nanofluids. The results for predicted and measured effective thermal conductivity of several nanofluids (Al2O3/ethylene glycol-based and Al2O3/water-based; CuO/ethylene glycol-based and CuO/water-based; and TiO2/ethylene glycol-based) are presented. The physical-statistical model shows a reasonably good agreement with the experimental results and gives more accurate predictions for the effective thermal conductivity of nanofluids compared to existing classical models

Effects of tractor traffic on spatial variability of soil strength and water content in grass covered and cultivated sloping vineyard.

Abstract Frequent machinery traffic on sloping vineyard influences spatial distribution of soil physical properties. Our objective was to assess the effects of crawler tractor traffic across the slope (20%) on spatial distribution of soil strength and water content of silt loam soil under controlled grass cover and conventionally cultivated vineyard. The experiment was situated on hillside vineyard (NW, Italy) arranged with rows crosswise the slope. The grass covered treatment included periodical mowing and chopping of herbs and the cultivated treatment-autumn ploughing (18 cm) and spring and summer rotary-hoeing in the vineyard inter-rows (2.7 m). A crawler tractor (2.82 Mg) was used at the same locations across the slope for all tillage and chemical operations. The measurements of soil bulk density, penetration resistance and volumetric water content were done in autumn (after vintage) within the sloping inter-row. The results were analyzed using classic statistics and geostatistics with and without trend. The highest variability was obtained for penetration resistance (CV 56.6%) and the lowest for bulk density (9.6%). In most cases, the semivariograms of the soil parameters were well described by spherical models. The semivariance parameters of all properties measured were influenced by trend. Three-dimensional (3D) maps well identified areas with the highest soil strength in lower crawler ruts being positioned in the upper side of vine row and successively lower strength in upper ruts situated on other side of the same row and inter-rut area. Higher strength in lower than upper ruts was induced by tractor's tilt and resulting higher ground contact pressure. Soil water content in both treatments was the lowest below the upper rut and increased in inter-rut and lower rut areas. The differences in the soil properties between the places within the inter-row were more pronounced in grass covered than in cultivated soil.

Statistical-physical models of mass and energy transfer in porous medium

he exchange of mass and energy taking place in a porous medium is the main goal of studies of many scientific branches and agrophysics belongs to them. This process is measured and calculated as the quantity of mass and energy transferred from one thermodynamic system to another and is to be determined on the basis of its transport properties. A new statistical model of the mass and energy transfer has been formulated in this paper on the bases of the most fundamental conceptions and ideas of mechanics, thermodynamics and electrodynamics. This new model makes possible the description of connection between the properties of the porous medium and the directly measured physical values. The model enabled for consideration of the following porous medium properties:electrical properties of the porous medium from the viewpoint of determination of its salinity on the basis of the measured bulk electrical conductivity and determination of its moisture content from the measurement of the porous medium dielectric constant, hydraulic, pneumatic and diffusive properties of porous medium resulting in determination of its gas and water conductivity as well as in determination of its diffusivity from the water retention curves, thermal properties of the porous medium leading to determination of its thermal conductivity from the basic properties of solid, liquid and gas phases forming this medium. The calculations based on this new statistical model and comparison of the calculated results with the data measured as well as statistical analysis can be a basis to the statement, that this model predicts the mass and energy transfer with the satisfactory accuracy. This procedure confirms correctness of the assumptions introduced and simplifications used during its construction as well as permits for the statement that the parameters were fitted properly

Cieplne wlasciwosci wybranych podlozy ogrodniczych

Opracowanie oparto na wynikach pomiarów podstawowych wielkości fizycznych organicznych podłoży oraz o wartości cieplnych właściwości wyznaczone metodami obliczeniowymi. Dane pomiarowe tj. wilgotność, gęstość podłoża, gęstość fazy stałej i skład granulometryczny pochodziły z literatury. Obliczenia cieplnych właściwości dokonano zgodnie z algorytmem odwzorowującym statystyczno-fizyczny model przewodnictwa cieplnego i matematyczną formulę na pojemność i dyfuzyjność cieplną ośrodka porowatego. Stwierdzono, że przewodnictwo cieplne podłoży organicznych nie przekracza wartości przewodnictwa cieplnego wody. Przewodnictwo cieplne podłoży ogrodniczych z dodatkami pochodzenia mineralnego wzrastało ponad przewodnictwo cieplne wody i było tym większe im większa była zawartość minerałów - głównie kwarcu. Najmniejszą i największą pojemność cieplną obserwowano dla podłoży organicznych przy niskich gęstościach w stanie suchym i pełnego nasycenia wodą. Wzrost gęstości podłoża powodował równoległe przesunięcie charakterystyki pojemności cieplnej w stronę wyższych wartości, jednocześnie zmniejszała się maksymalna pojemność cieplna podłoża. Dyfuzyjność cieplna podłoży wykazywała charakterystyczne ekstrema, a jej wartości przy tym samym uwilgotnieniu były większe dla wyższych zagęszczeń podłoża, natomiast minimum lub maksimum dyfuzyjności wykazywało tendencję przesuwania się w stronę niższych wilgotności dla wyższych zagęszczeń.This paper is based on measurement data of principal physical magnitudes of organic substrates and on thennal properties detennined with numerical methods. The measurement data, i.e. moisture, substrate density, solid phase density, and granulometric composition were taken from literature. Thermal properties were calculated according to an algorithm which describes a statistical physical model of thennal conductivity and according to mathematical fonnula of heat capacity and diffusivity of a porous medium. It was found that thermal conductivity of horticultural substrates do not exceed the value of water thermal conductivity. The thermal conductivity of horticultural substrates with mineral additives increased over the water thennal conductivity. The higher the content of minerals (mainly quartz), the higher thermal conductivity was. The lowest and the highest heat capacity values were observed in substrates at low densities in the dry state and at full water saturation state. The increase in substrate density caused parallel shift of heat capacity characteristics towards higher values. At the same time, maximal heat capacity of the substrate decreased. The thennal diffusivity of substrates showed characteristic extremes and its value, at the same moisture level, was higher at higher substrate density. The diffusivity minimum or maximum showed the shifting tendency towards lower moisture at higher densities

Application of geostatistical analysis and fractal theory for the investigation of moisture dynamics in soil profile of cultivated field

W pracy dokonano oceny czasowo-przestrzennej zmienności wilgotności gleby na polu z roślinami i bez przy zastosowaniu analizy geostatystycznej oraz obliczone wymiary fraktalne. Wykazano, że rozkład wilgotności gleby w okresie wiosenno-letnim w profilu glebowym był zdeterminowany przez opady atmosferyczne i rośliny. Stwierdzono występowanie czasowej zależności wilgotności gleby w profilu glebowym, przy czym promień autokorelacji czasowej zwiększał się wraz z głębokością. Na poletkach z roślinami wymiary fraktalne wykazywały wyraźny spadek wartości wraz z głębokością, natomiast na poletku bez roślin niewiele się zmieniały w obrębie badanego profilu. Tym samym wskazywały, że czasowy rozkład wilgotności gleby w profilu glebowym na poletku bez roślin był bardziej losowy niż na poletkach z roślinami.The estimation of the spatial-time variability of soil moisture in field under plant cover as compared to the moisture variability of bare soil has been performed using a geostatistical analysis and fractal dimensions. It was shown, that the moisture distribution during spring-summer period in soil profile is determined by rainfall and plant cover. The dependence of the soil moisture on time was established and the increase of the autocorrelation radius with increasing depth was found. The fractal dimension apparently decreased with depth in fields under plant cover whereas in soil without plants its value did not undergo considerable changes. It can be concluded then, that the time distribution of soil moisture in the soil profile without plants is morę random than that with plants

Izmeritel' gustoty potoka tepla poristykh materialov

The present work presents a measuring device for the density of the heat flux on the soil surface and thermal properties of the surface layers of the soil with or without plants.Przedmiotem artykułu jest przyrząd do pomiaru gęstości strumienia ciepła na powierzchni gleby oraz cieplnych właściwości powierzchniowej warstwy gleby z roślinami lub bez.В статье даётся описание прибора для измерения густоты потока тепла на поверхности почв, а также тепловых качеств поверхностного слоя почвы с растениями или без них