Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Free convection heat transfer in vertical annuli

Free convection heat transfer in vertical concentric, cylindrical annuli is investigated analytically and experimentally. The approximate double boundary layer model used by Emery and Chu for the case of vertical parallel plates is extended to the present case in obtaining heat transfer correlations in laminar free convection. Different correlations for the inner cylinder depending on the radius to the length ratio of the inner cylinder and the Rayleigh number, were used in the derivation of correlations for the annuli. The results for the case of short cylinders inside tubes are in agreement (within about 10 per cent) with the existing correlations. For other cases, namely long cylinders in annuli and wires in annuli, experiments conducted show the agreement of the analysis with experiments.

Steady laminar flow with suction or injection and heat transfer through porous pipe

Following the method due to Bhatnagar (P. L.) [Jour. Ind. Inst. Sic., 1968, 1, 50, 1], we have discussed in this paper the problem of suction and injection and that of heat transfer for a viscous, incompressible fluid through a porous pipe of uniform circular cross-section, the wall of the pipe being maintained at constant temperature. The method utilises some important properties of differential equations and some transformations that enable the solution of the two-point boundary value and eigenvalue problems without using trial and error method. In fact, each integration provides us with a solution for a suction parameter and a Reynolds number without imposing the conditions of smallness on them. Investigations on non-Newtonian fluids and on other bounding geometries will be published elsewhere.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

Disjunct eddy covariance measurements of volatile organic compound fluxes using proton transfer reaction mass spectrometry

Volatile organic compounds (VOCs) are emitted into the atmosphere from natural and anthropogenic sources, vegetation being the dominant source on a global scale. Some of these reactive compounds are deemed major contributors or inhibitors to aerosol particle formation and growth, thus making VOC measurements essential for current climate change research. This thesis discusses ecosystem scale VOC fluxes measured above a boreal Scots pine dominated forest in southern Finland. The flux measurements were performed using the micrometeorological disjunct eddy covariance (DEC) method combined with proton transfer reaction mass spectrometry (PTR-MS), which is an online technique for measuring VOC concentrations. The measurement, calibration, and calculation procedures developed in this work proved to be well suited to long-term VOC concentration and flux measurements with PTR-MS. A new averaging approach based on running averaged covariance functions improved the determination of the lag time between wind and concentration measurements, which is a common challenge in DEC when measuring fluxes near the detection limit. The ecosystem scale emissions of methanol, acetaldehyde, and acetone were substantial. These three oxygenated VOCs made up about half of the total emissions, with the rest comprised of monoterpenes. Contrary to the traditional assumption that monoterpene emissions from Scots pine originate mainly as evaporation from specialized storage pools, the DEC measurements indicated a significant contribution from de novo biosynthesis to the ecosystem scale monoterpene emissions. This thesis offers practical guidelines for long-term DEC measurements with PTR-MS. In particular, the new averaging approach to the lag time determination seems useful in the automation of DEC flux calculations. Seasonal variation in the monoterpene biosynthesis and the detailed structure of a revised hybrid algorithm, describing both de novo and pool emissions, should be determined in further studies to improve biological realism in the modelling of monoterpene emissions from Scots pine forests. The increasing number of DEC measurements of oxygenated VOCs will probably enable better estimates of the role of these compounds in plant physiology and tropospheric chemistry. Keywords: disjunct eddy covariance, lag time determination, long-term flux measurements, proton transfer reaction mass spectrometry, Scots pine forests, volatile organic compounds

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Effect of vibration on heat transfer from a horizontal cylinder to a normal air stream

The effect of vibration on heat transfer from a horizontal copper cylinder, 0.344 in. in diameter and 6 in. long, was investigated. The cylinder was placed normal to an air stream and was sinusoidally vibrated in a direction perpendicular to the direction of the air stream. The flow velocity varied from 19 ft/s to 92 ft/s; the double amplitude of vibration from 0.75 cm to 3.2 cm, and the frequency of vibration from 200 to 2800 cycles/min. A transient technique was used to determine the heat transfer coefficients. The experimental data in the absence of vibration is expressed by NNu = 0.226 NRe0.6 in the range 2500 < NRe < 15 000. By imposing vibrational velocities as high as 20 per cent of the flow velocity, no appreciable change in the heat transfer coefficient was observed. An analysis using the resultant of the vibration and the flow velocity explains the observed phenomenon.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.

European Union and the developing nations' external debt : EU-15's debt policy, 1960–2008

This Master's Thesis defines the debt policy of the current European Union Member States towards the developing nations. Since no official policy for debt exists in the EU, it is defined to include debt practices (loans and debt relief in development cooperation) and debt within the EU development policy framework. This study (1) describes how the issue of external debt appears in the development policy framework, (2) compares EU Member States' given loans and debt relief to grants for the developing nations (1960s to the 2000s), and (3) measures the current orientation in ODA of each EU Member State between grant aid and loan aid using the Grant-Loan Index (GLI). Theoretical aspects include reasons for selecting between loans (Bouchet 1987) and grants (Odedokun 2004, O'Brien and Williams 2007), policy context of the EU (Van Reisen 2007) and the meaning of external debt in the set-up between the North and the South. In terms of history, the events and impact of the colonial period (where loans have originated) are overviewed and compared in light of today's policies. Development assistance statistics are derived from the OECD DAC statistics portal and EU development policy framework documents from the EU portal. Methodologically, the structure of this study is from policy analysis (Barrien 1999, Hill 2008, Berndtson 2008), but it has been modified to fit the needs of studying a non-official policy. EU Member States are divided into three groups by Carbone (2007a), the Big-3, Northern and Southern donors, based on common development assistance characteristics. The Grant-Loan Index is used to compare Carbone's model, which measures quality of aid, to the GLI measuring the structure of aid. Results indicate that EU- 15 countries (active in debt practices) differ in terms of timing, stability and equality of debt practices in the long-term (1960s to the 2000s). In terms of current practices, (2000-2008), it is noted that there lies a disparity between the actual practices and the way in which external debt is represented in the development policy framework, although debt practices form a relevant portion of total ODA practices for many EU-15 Member States, the issue itself plays a minor role in development policy documents. Carbone’s group division applies well to the Grant – Loan Index’s results, indicating that countries with similar development policy behaviour have similarities in debt policy behaviour, with one exception: Greece. On the basis of this study, it is concluded that EU development policy framework content in terms of external debt and debt practices are not congruent. The understanding of this disparity between the policy outline and differences in long-term practices is relevant in both, reaching the UN’s Millennium Development Goals, and in the actual process of developing development aid.

Thionucleotides in the transfer ribonucleic acid of Image Image

tRNA isolated from Image Image , grown in the presence of radioactive sulfur was analyzed for the occurrence of thionucleotides. The analysis revealed the presence of at least five thionucleotides, of which three were identified as 4-thiouridylic acid, 5-methylaminomethyl-2-thiouridylic acid and 2-thiocytidylic acid. Iodine-oxidation affected the acceptor ability of several amino acid specific tRNAs, those for lysine and serine being affected most. The tRNA of Image Image differs from that of Image . Image both in the number and the relative proportion of thionucleotides.

The Art of Adaptation : A study on the Europeanization of Finland's foreign and security policy

This study examines how Finnish foreign and security policy has been influenced by the European Union and its Common Foreign and Security Policy. It points to a growing interplay and misfit between the external expectations originating from the European level and the domestic expectations and traditional ways-of-doing-things. It is concluded that the deepening European integration in the sphere of foreign, security and defence policy has played a significant role in a number of transformations in the Finnish policies since 1995. New, more European, meanings have been attached to the key concepts of Finnish foreign and security policy. Neutrality and traditional peacekeeping have been replaced by a minimalist reading of military non-alignment and participation in crisis management operations and EU battle groups. Traditional small state identity has been recast more and more as small member stateness . At the same time Finland has entered an era of post-consensus in national foreign and security policy. A key theoretical argument in the background of the study is that collective understandings attached to European policies, when not resonating well with domestic understandings, cause adaptation pressures on domestic-level processes and may lead to changes in the way interests and identities are constructed. This means that Europeanization is principally seen as identity reconstruction. Consequently, the theoretical framework of the study builds on the Europeanization research literature and constructivist IR theory on state identity. Foreign and security policy is defined as the practice in which state identity is reproduced, and the key foreign and security policy concepts are seen as the vehicles of identity production. It is concluded that for Finland, participation in the EU s foreign, security and defence policies represents not only a tool for responding to the changes in the international security environment but also a new means of self-identification. Concerning the Finnish attempts of projecting national interests on the European security policy agenda, it is concluded that they mainly relate to the compatibility of the potential development of EU s defence dimension with the Finnish military non-alignment. Although neutrality was cast aside in the official security policy when Finland joined the EU, the analysis shows that its impact has continued in the domestic political debate and in the mind-set of the decision-makers. The primary research material includes official Finnish foreign and security policy documentation and the related parliamentary debates from 1994 to 2007. This study serves also as a comprehensive empirical overview on Finland s reactions and contributions to the EU Common Foreign and Security Policy.

Mass Transfer Coefficients in Mixer-Settlers

Mass transfer coefficients have been determined for transfer into a highly viscous phase in a stirred tank involving high Schmidt numbers. The results have been used to compute mass transfer coefficients in the extraction of free fatty acids from oils using alcohol and show good agreement with experimental results