Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1

Aerodynamic noise from wave-turbulence interaction

Abstract. In order to estimate the acoustic energy scattered when a unit volume of free turbulence, such as in free jets, interacts with a plane steady sound wave, theoretical expressions are derived for two simple models of turbulence: eddy model and isotropic model. The effect of convection by mean motion of the energy-bearing eddies on the incident sound wave and on the sound generated from wave-turbulence interaction is taken into account. Finally, by means of a representative calculation,the directionality pattern and Mach number dependence of the noise so generated is discussed.

Compressible Boundary-Layer Swirling Flow in a Nozzle and a Diffuser With Highly Cooled Wall

The steady laminar compressible boundary-layer swirling flow with variable gas properties and mass transfer through a conical nozzle, and a diffuser with a highly cooled wall has been studied. The partial differential equations governing the nonsimilar flow have been transformed to a system of coordinates using modified Lees transformation. The resulting equations are transformed into coordinates having finite ranges by means of a transformation which maps an infinite region into a finite region. The ensuing equations are then solved numerically using an implicit finite-difference scheme. The results indicate that the variation of the density-viscosity product across the boundary layer and mass transfer have strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying suction. The results are found to be in good agreement with those of the local nonsimilarity method but they differ appreciably from those of the local similarity method.

Carbon dioxide and methane exchange between a boreal pristine lake and the atmosphere

Lakes serve as sites for terrestrially fixed carbon to be remineralized and transferred back to the atmosphere. Their role in regional carbon cycling is especially important in the Boreal Zone, where lakes can cover up to 20% of the land area. Boreal lakes are often characterized by the presence of a brown water colour, which implies high levels of dissolved organic carbon from the surrounding terrestrial ecosystem, but the load of inorganic carbon from the catchment is largely unknown. Organic carbon is transformed to methane (CH4) and carbon dioxide (CO2) in biological processes that result in lake water gas concentrations that increase above atmospheric equilibrium, thus making boreal lakes as sources of these important greenhouse gases. However, flux estimates are often based on sporadic sampling and modelling and actual flux measurements are scarce. Thus, the detailed temporal flux dynamics of greenhouse gases are still largely unknown. ----- One aim here was to reveal the natural dynamics of CH4 and CO2 concentrations and fluxes in a small boreal lake. The other aim was to test the applicability of a measuring technique for CO2 flux, i.e. the eddy covariance (EC) technique, and a computational method for estimation of primary production and community respiration, both commonly used in terrestrial research, in this lake. Continuous surface water CO2 concentration measurements, also needed in free-water applications to estimate primary production and community respiration, were used over two open water periods in a study of CO2 concentration dynamics. Traditional methods were also used to measure gas concentration and fluxes. The study lake, Valkea-Kotinen, is a small, humic, headwater lake within an old-growth forest catchment with no local anthropogenic disturbance and thus possible changes in gas dynamics reflect the natural variability in lake ecosystems. CH4 accumulated under the ice and in the hypolimnion during summer stratification. The surface water CH4 concentration was always above atmospheric equilibrium and thus the lake was a continuous source of CH4 to the atmosphere. However, the annual CH4 fluxes were small, i.e. 0.11 mol m-2 yr-1, and the timing of fluxes differed from that of other published estimates. The highest fluxes are usually measured in spring after ice melt but in Lake Valkea-Kotinen CH4 was effectively oxidised in spring and highest effluxes occurred in autumn after summer stratification period. CO2 also accumulated under the ice and the hypolimnetic CO2 concentration increased steadily during stratification period. The surface water CO2 concentration was highest in spring and in autumn, whereas during the stable stratification it was sometimes under atmospheric equilibrium. It showed diel, daily and seasonal variation; the diel cycle was clearly driven by light and thus reflected the metabolism of the lacustrine ecosystem. However, the diel cycle was sometimes blurred by injection of hypolimnetic water rich in CO2 and the surface water CO2 concentration was thus controlled by stratification dynamics. The highest CO2 fluxes were measured in spring, autumn and during those hypolimnetic injections causing bursts of CO2 comparable with the spring and autumn fluxes. The annual fluxes averaged 77 (±11 SD) g C m-2 yr-1. In estimating the importance of the lake in recycling terrestrial carbon, the flux was normalized to the catchment area and this normalized flux was compared with net ecosystem production estimates of -50 to 200 g C m-2 yr-1 from unmanaged forests in corresponding temperature and precipitation regimes in the literature. Within this range the flux of Lake Valkea-Kotinen yielded from the increase in source of the surrounding forest by 20% to decrease in sink by 5%. The free water approach gave primary production and community respiration estimates of 5- and 16-fold, respectively, compared with traditional bottle incubations during a 5-day testing period in autumn. The results are in parallel with findings in the literature. Both methods adopted from the terrestrial community also proved useful in lake studies. A large percentage of the EC data was rejected, due to the unfulfilled prerequisites of the method. However, the amount of data accepted remained large compared with what would be feasible with traditional methods. Use of the EC method revealed underestimation of the widely used gas exchange model and suggests simultaneous measurements of actual turbulence at the water surface with comparison of the different gas flux methods to revise the parameterization of the gas transfer velocity used in the models.

Flow and heat transfer in steady laminar compressible boundary layer swirling flow in a nozzle

The axisymmetric steady laminar compressible boundary layer swirling flow of a gas with variable properties in a nozzle has been investigated. The partial differential equations governing the non-similar flow have been transformed into new co-ordinates having finite ranges by means of a transformation which maps an infinite range into a finite one. The resulting equations have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for compressible swirling flow through a convergent conical nozzle. The results indicate that the swirl exerts a strong influence on the longitudinal skin friction, but its effect on the tangential skin friction and heat transfer is comparatively small. The effect of the variation of the density-viscosity product across the boundary layer is appreciable only at low-wall temperature. The results are in good agreement with those of the local-similarity method for small values of the longitudinal distance.

Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

The effect of surface mass transfer velocities having normal, principal and transverse direction components (�vectored� suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.

Interaction of metal ions with nucleic acids and related compounds. II. Studies on Au(III)-nucleic acid system

The nature of interaction of Au(III) with nucleic acids was studied by using methods such as uv and ir spectrophotometry, viscometry, pH titrations, and melting-temperature measurements. Au(III) is found to interact slowly with nucleic acids over a period of several hours. The uv spectra of native calf-thymus DNA 9pH 5.6 acetate buffer containing (0.01M NaCIO4) showed a shift in λ max to high wavelengths and an increase in optical density at 260 nm. There was a fourfold decrease in viscosity (expressed as ηsp/c). The reaction was faster at pH 4.0 and also with denatured DNA (pH 5.6) and whole yeast RNA (pH 5.6). The order of preference of Au(III) (as deduced from the time of completion of reaction) for the nucleic acids in RNA > denatured DNA > DNA. The reaction was found to be completely reversible with respect KCN. Infrared spectra of DNA-Au(III) complexes showed binding to both the phosphate and bases of DNA. The same conclusions were also arrived at by melting-temperature studies of Au(III)-DNA system. pH titrations showed liberation of two hydroxylions at r = 0.12 [r = moles of HAuCl4 added per mole of DNA-(P)] and one hydrogen ion at r = 0.5. The probable binding sites could be N(1)/N(7) of adenine, N(7) and/or C(6)O of guanine, N(3) of cytosine and N(3) of thymine. DNAs differing in their (G = C)-contents [Clostridium perfingens DNA(G = C, 29%), salmon sperm DNA (G + C, 42%) and Micrococcus lysodeikticus DNA(G + C, 29%), salmon sperm DNA (G = C, 72%)] behaved differently toward Au(III). The hyperchromicity observed for DNAs differing in (G + C)-content and cyanide reversal titrations indicate selectivity toward ( A + T)-rich DNA at lw values of r. Chemical analysis and job's continuous variation studies indicated the existence of possible complexes above and below r = 1. The results indicate that Au(III) ions probably bind to hte phosphate group in the initial stages of the reaction, particularly at low values of r, and participation of the base interaction also increases. Cross-linking of the two strands by Au(III) may take place, but a complete collapse of the doulbe helix is not envisaged. It is probable that tilting of the bases or rotaiton of the bases around the glucosidic bond, resulting in a significant distrotion of the double helix, might take place due to binding of Au(III) to DNA.

Unsteady laminar compressible boundary-layer flow at a three-dimensional stagnation point

Unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point for both cold and hot walls has been studied for the case when the velocity of the incident stream varies arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. The results indicate that the variation of the density-viscosity product across the boundary layer, the wall temperature and the nature of stagnation point significantly affect the skin friction and heat transfer.

Aitosuklaa jäätelöpuikon kuorrutteena

Tutkimuksen kirjallisuuskatsauksessa keskityttiin jäätelöpuikkoihin, erilaisiin suklaakuorrutteisiin ja elintarvikkeiden kuorruttamiseen suklaalla. Lisäksi kirjallisuuskatsauksessa perehdyttiin suklaan koostumukseen, nestemäisen suklaan virtausominaisuuksiin ja koostumuksen ja virtausominaisuuksien välisiin vuorovaikutuksiin. Kokeellisessa osassa tavoitteena oli selvittää, miten maitosuklaakuorrutteen rasvapitoisuuden, emulgointiainepitoisuuden ja kuorrutteen lämpötilanvaihtelut vaikuttavat kuorrutteen viskositeettiin, myötöjännitykseen, jähmettymisaikaan ja jäätelöpuikon päälle jäävän kuorrutteen määrään. Erityisesti pyrittiin selvittämään, miten jäätelöpuikon päälle jäävän kuorrutteen määrää saadaan säädeltyä kuorrutteen rasvapitoisuutta, emulgointiainepitoisuutta ja lämpötilaa muuttamalla. Tutkimuksen koeasetelma tehtiin Box-Behnken-mallilla. Selittäviksi muuttujiksi tutkimukseen valittiin kuorrutteen rasvan määrä, emulgointiaineen määrä ja kuorrutteen lämpötila jäätelöpuikkoja kuorrutettaessa. Vastemuuttujina oli kuorrutteen jähmettymisaika, viskositeetti, myötöjännitys ja jäätelöpuikon päälle jäävän kuorrutteen määrä. Tulokset käsiteltiin regressioanalyysin avulla. Muuttujien välisiä vuorovaikutuksia tutkittiin vastepintamallilla. Vastemuuttujien välisiä korrelaatioita tutkittaessa käytettiin Pearsonin korrelaatiokerrointa. Kuorrutteen rasvan määrän lisääntyminen vähensi tilastollisesti merkitsevästi jäätelöpuikon päälle jäävän kuorrutteen määrää, kuorrutteen jähmettymisaikaa, viskositeettia ja myötöjännitystä. Emulgointiaineen määrän lisääminen kuorrutteessa pienensi kuorrutteen määrää jäätelöpuikon päällä, kuorrutteen jähmettymisaikaa ja kuorrutteen myötöjännitystä. Kuorrutteen lämpötilan lisääminen jäätelöpuikkoja kuorrutettaessa pienensi kuorrutteen määrää ja viskositeettia. Kuorrutteen jähmettymisaika sen sijaan piteni lämpötilaa lisättäessä. Tutkimuksen perusteella voidaan sanoa, että jäätelöpuikkoja kastettaessa suklaakuorrutteen lämpötila, rasvan määrä ja lesitiinin määrä vaikuttivat jäätelöpuikon päälle jäävän kuorrutteen määrään. Vastepintamallinnuksen käyttö soveltui hyvin suklaakuorrutteen määrän tutkimiseen. Sen avulla saatiin selvitettyä, miten jäätelöpuikon päälle jäävän kuorrutteen määrää saadaan säädeltyä muuttamalla kuorrutteen emulgointiainepitoisuutta, rasvapitoisuutta ja lämpötilaa.

Non-enzymatic Degradation of (1→3)(1→4)-β-D-glucan in Aqueous Processing of Oats

Cereal water-soluble β-glucan [(1→3)(1→4)-β-D-glucan] has well-evidenced health benefits and it contributes to the texture properties of foods. These functions are characteristically dependent on the excellent viscosity forming ability of this cell wall polysaccharide. The viscosity is affected by the molar mass, solubility and conformation of β-glucan molecule, which are further known to be altered during food processing. This study focused on demonstrating the degradation of β-glucan in water solutions following the addition of ascorbic acid, during heat treatments or high pressure homogenisation. Furthermore, the motivation of this study was in the non-enzymatic degradation mechanisms, particularly in oxidative cleavage via hydroxyl radicals. The addition of ascorbic acid at food-related concentrations (2-50 mM), autoclaving (120°C) treatments, and high pressure homogenisation (300-1000 bar) considerably cleaved the β-glucan chains, determined as a steep decrease in the viscosity of β-glucan solutions and decrease in the molar mass of β-glucan. The cleavage was more intense in a solution of native β-glucan with co-extracted compounds than in a solution of highly purified β-glucan. Despite the clear and immediate process-related degradation, β-glucan was less sensitive to these treatments compared to other water-soluble polysaccharides previously reported in the literature. In particular, the highly purified β-glucan was relatively resistant to the autoclaving treatments without the addition of ferrous ions. The formation of highly oxidative free radicals was detected at the elevated temperatures, and the formation was considerably accelerated by added ferrous ions. Also ascorbic acid pronounced the formation of these oxidative radicals, and oxygen was simultaneously consumed by ascorbic acid addition and by heating the β-glucan solutions. These results demonstrated the occurrence of oxidative reactions, most likely the metal catalysed Fenton-like reactions, in the β-glucan solutions during these processes. Furthermore, oxidized functional groups (carbonyls) were formed along the β-glucan chain by the treatments, including high pressure homogenisation, evidencing the oxidation of β-glucan by these treatments. The degradative forces acting on the particles in the high pressure homogenisation are generally considered to be the mechanical shear, but as shown here, carbohydrates are also easily degraded during the process, and oxidation may have a role in the modification of polysaccharides by this technique. In the present study, oat β-glucan was demonstrated to be susceptible to degradation during aqueous processing by non-enzymatic degradation mechanisms. Oxidation was for the first time shown to be a highly relevant degradation mechanism of β-glucan in food processing.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Effect of favorable pressure gradient on transitional spot formation rate

The calculation of the transitional boundary layer requires estimates of the extent of the transition zone, which in turn depends on the rate at which turbulent spots are formed. This rate has been found to scale with local boundary layer thickness and viscosity, and the resulting nondimensional group (called crumble) is a function of the pressure gradient, among other parameters. Available experimental data are analyzed to show that the crumble increases slowly with increasing favorable pressure gradients, being about four times as large as in constant-pressure flow when the Thwaites pressure gradient parameter at the effective origin of the resulting turbulent boundary layer is 0.1 and when transition is driven by free-stream turbulence.

Mixed Convection Induced in a Gas Flowing Past a Hot Horizontal Flat Plate

A boundary layer analysis of mixed convective motion over a hot horizontal flat plate is performed under the conditions of steady flow and low speed. Use of the Howarth-Dorodnytsyn transformation makes it possible to dispense with the usual Boussinesq approximation, and variable gas properties are accounted for via the assumption that dynamic viscosity and thermal conductivity are proportional to the absolute temperature. The formulation presented enables the entire mixed convection regime to be described by a single set of equations. Finite difference solutions when the Prandtl number is 0.72 are obtained over the entire range of the mixed convection parameter ξ from 0 (free convection) to 1 (forced convection) and heating parameter ▵ values from 2 to 12. The effects of both ξ and ▵on the velocity profiles, the temperature profiles, and the variation of skin friction and heat transfer functions are clearly illustrated in tables and graphs.

Synthesis and characterization of thiocarbonohydrazone-based epoxy resins

Novel epoxy resins of various thiocarbonohydrazones have been synthesized by reacting the aldehyde or ketone derivatives of thiocarbohydrazide with excess of epichlorohydrin. The resins have been characterized by elemental analyses, epoxy equivalents, 1H-NMR and IR spectra, thermal analyses, and viscosity measurements. Curing of the resins has been carried out by mixing with thiocarbohydrazide or ethylenediamine and heating at 80°C for 48 h. A comparison of the thermal stability of the cured resin samples has been made.

Ruismallasuute vähägluteenisessa kauraleivonnassa

Tutkielman kirjallisuuskatsauksessa tarkasteltiin kauran leivontateknologisia ominaisuuksia, entsyymiaktiivista leivontaa ja ruismaltaan hyödyntämistä vähägluteenisessa leivonnassa. Kokeellisessa osiossa tutkittiin ruismallashapantaikinasta valmistetun uutteen vaikutusta kaurataikinan viskositeettiin ja kauraleivän ominaisuuksiin. Työn tarkoituksena oli kehittää maultaan ja rakenteeltaan onnistunut rukiinmakuinen kauraleipä. Ruismaltaan entsyymien annettiin pilkkoa keliaakikolle haitallisia rukiin prolamiineja hapantaikinaprosessissa. Hapantaikinasta erotettiin uute sentrifugoimalla. Leivontakokeisiin käytettiin entsyymiaktiivista ja kuumentamalla inaktivoitua uutetta. Uutteella korvattiin taikinavettä 15, 25 ja 30 % (taikinan painosta). Leivonta toteutettiin miniatyyrikoossa, vuokaleivontana 20 g:n taikinapaloja käyttäen. Taikinoiden viskositeetti mitattiin tarkoituksena seurata beetaglukaanin hydrolyysiä. Rukiin makua mitattiin koulutetun raadin avulla. Happaman uutteen lisäys laski taikinan pH-arvoa noin 5,8:sta noin 4,4:ään. Entsyymiaktiivisen uutteen lisäys laski taikinan viskositeettia ja inaktivoitu uute puolestaan kasvatti sitä. Leipien sisus tiivistyi, jolloin mitatut sisuksen kovuudet kasvoivat uutteen lisäyksen myötä. Uutelisäys paransi leipien makua ja aromia. Uutteen vaikutuksesta leipien huokoset olivat pienempiä ja ne jakaantuivat tasaisemmin leipämatriisiin. Jos uutetta käytettiin inaktivoituna, leipien murenevuus kasvoi. Tutkimuksessa kehitetyn teknologian avulla oli mahdollista valmistaa hyvänlaatuinen, rukiinmakuinen kauraleipä myös ilman että uutteen entsyymit inaktivoitiin keittämällä. Tähän vaikutti ilmeisesti taikinan alhainen pH, joka inhiboi alfa-amylaasia, ja kauratärkkelyksen korkea liisteröitymislämpötila, jolloin entsyymien inaktivoituminen paiston aikana tapahtui ennen kuin tärkkelys tuli alttiiksi liialliselle pilkkoutumiselle. Tämä mahdollistaa uutteen käytön osana leivontaprosessia ilman inaktivointia. Hapantaikinafermentaatio osana gluteenitonta leivontaa havaittiin toimivaksi yhdistelmäksi, sillä se paransi leivän väriä, makua ja rakennetta. Myös leivän homeeton aika parani jo vähäisenkin uutelisäyksen vaikutuksesta. Näyttää siltä, että tämän teknologian avulla on mahdollista tuoda esille pitkään kaivattua rukiin makua vähägluteenisten kauraleipien valikoimassa. Laskennallisesti ja aiempiin tuloksiin tukeutuen, voitiin päätellä, että leivän prolamiinipitoisuudessa on mahdollista päästä tasolle 63,5 mg/kg, mutta jatkokehityksen avulla päästäisiin luultavasti vielä parempiin tuloksiin.