Pressure drop coefficients for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers

The objective of the present work is the experimental determination of pressure drop coefficients (loss coefficients) for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers. The experiments permitted to correlate the dimensionless loss coefficient with the flow Reynolds number in the rectangular channel formed by the plate fins. The experimental technique consisted of the measurement of the longitudinal pressure distribution along the flow channel, for several values of air mass flow rate. The total number of data runs, each one characterized by the flow Reynolds number, was 216. The present geometry is used in compact heat exchangers for air conditioning systems, heaters, radiators, and others. Also, it is verified the influence of the utilization of elliptic tubes, instead of circular ones, in the pressure drop. The measurements were performed for Reynolds numbers ranging from 200 to 1900.

Towards a Unified Theory of Health-Disease: I. Health as a complex model-object

Theory building is one of the most crucial challenges faced by basic, clinical and population research, which form the scientific foundations of health practices in contemporary societies. The objective of the study is to propose a Unified Theory of Health-Disease as a conceptual tool for modeling health-disease-care in the light of complexity approaches. With this aim, the epistemological basis of theoretical work in the health field and concepts related to complexity theory as concerned to health problems are discussed. Secondly, the concepts of model-object, multi-planes of occurrence, modes of health and disease-illness-sickness complex are introduced and integrated into a unified theoretical framework. Finally, in the light of recent epistemological developments, the concept of Health-Disease-Care Integrals is updated as a complex reference object fit for modeling health-related processes and phenomena.

Regional myocardial function in healthy adults: assessment through tissue Doppler echocardiography

OBJECTIVE: To characterize left ventricular regional myocardial function through tissue Doppler echocardiography in healthy adults and to assess the influence of aging in this function. METHODS: In 45 healthy volunteers divided in two groups (< 45 and > 45 years old) we assessed longitudinal and radial regional function (velocities, times intervals and velocity-time integrals). Data were compared in each group and between groups. RESULTS: Systolic function: a) longitudinal: higher velocities and integrals in lateral and inferior walls and in basal segments, with a trend to reduction of these parameters with aging; b) radial: higher basal velocities, no significant change with aging. Diastolic function: a) longitudinal: higher velocities in lateral and inferior walls and in basal segments. With aging e and e/a velocities and integrals decreased, a increased and older individuals showed lower percentage of segments with e/a >1; b) radial: aging was associated with lower e and higher a velocities. CONCLUSION: 1) Tissue Doppler echocardiography detects physiological differences between regional myocardial function of different ventricular segments, in velocities, times intervals and integrals, with physiological heterogeneity and asynchrony; 2) Many of these data are age dependent; 3) Our data contribute to define normal values, and may become useful when compared with data from populations with heart diseases.

Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

Um caso especial de integrais binômias

The present paper shows that the sum of two binomial integrals, such as A ∫ x p (a + bx q)r dx + B ∫ x p (a + bx q)r dx, where A and B are real constants and p, q, r are rational numbers, can, in special cases, lead to elementary integrals, even if each by itself is not elementary. An example of the case considered is given by the integral ∫ x _____-___ 3 dx = 1/2 ∫ x-½ (x - 1)-⅓ dx - 6 √ x ³√(x - 1)4 = 1/3 ∫ x-½ (x - 1)-¾ dx On the rigth hand side of the last equality both integral are not elementary. But the use of integration by parts of one of them leads to the solution: ∫ x _____-___ 3 dx = x½ (x - 1)-⅓ + C. 6 √ x ³√(x - 1)4

Caracterização da pureza de fosfatidilcolina da soja através de RMN de ¹H e de 31P

A strategy is proposed to evaluate the purity of phosphatidylcholine from soybean lecithin, obtained by extraction or column chromatography, using the integrals ratio of ¹H NMR spectra. Integrals of methylene signals, around 1.3 and 1.6 ppm, are added and divided by the integral of the choline methyl groups, around 3.3 ppm. Before purification, a ratio of 19.68±1.37 was determined. Using extraction, a ratio of 10.70±0.61 was found, while from column chromatography, a value of 2.99±0.25 was detected. 31P NMR of standard phosphatidylcholine showed signals at -0.2 and -0.9 ppm, whereas the purified one showed a single signal at -0.9 ppm.

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.

An experimental investigation of the effects of nozzle ellipticity on the flow structure of co-flow jet diffusion flames

The flow structure of cold and ignited jets issuing into a co-flowing air stream was experimentally studied using a laser Doppler velocimeter. Methane was employed as the jet fluid discharging from circular and elliptic nozzles with aspect ratios varying from 1.29 to 1.60. The diameter of the circular nozzle was 4.6 mm and the elliptic nozzles had approximately the same exit area as that of the circular nozzle. These non-circular nozzles were employed in order to increase the stability of attached jet diffusion flames. The time-averaged velocity and r.m.s. value of the velocity fluctuation in the streamwise and transverse directions were measured over the range of co-flowing stream velocities corresponding to different modes of flame blowout that are identified as either lifted or attached flames. On the basis of these measurements, attempts were made to explain the existence of an apparent optimum aspect ratio for the blowout of attached flames observed at higher values of co-flowing stream velocities. The insensitivity of the blowout limits of lifted flames to nozzle geometry observed in our previous work at low co-flowing stream velocities was also explained. Measurements of the fuel concentration at the jet centerline indicated that the mixing process was enhanced with the 1.38 aspect ratio jet compared with the 1.60 aspect ratio jet. On the basis of the obtained experimental data, it was suggested that the higher blowout limits of attached flames for an elliptic jet of 1.38 aspect ratio was due to higher entrainment rates.

Lagrangian multipliers for coast-arcs of optimum space trajectories

Some properties of generalized canonical systems - special dynamical systems described by a Hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. A complete closed-form solution for Lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. Classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. For circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Panel Method Formulation for Oscillating Airfoils in Sonic Flow

The mathematical model for two-dimensional unsteady sonic flow, based on the classical diffusion equation with imaginary coefficient, is presented and discussed. The main purpose is to develop a rigorous formulation in order to bring into light the correspondence between the sonic, supersonic and subsonic panel method theory. Source and doublet integrals are obtained and Laplace transformation demonstrates that, in fact, the source integral is the solution of the doublet integral equation. It is shown that the doublet-only formulation reduces to a Volterra integral equation of the first kind and a numerical method is proposed in order to solve it. To the authors' knowledge this is the first reported solution to the unsteady sonic thin airfoil problem through the use of doublet singularities. Comparisons with the source-only formulation are shown for the problem of a flat plate in combined harmonic heaving and pitching motion.

Wind tunnel simulation of atmospheric boundary layer flows

The present work shows how thick boundary layers can be produced in a short wind tunnel with a view to simulate atmospheric flows. Several types of thickening devices are analysed. The experimental assessment of the devices was conducted by considering integral properties of the flow and the spectra: skin-friction, mean velocity profiles in inner and outer co-ordinates and longitudinal turbulence. Designs based on screens, elliptic wedge generators, and cylindrical rod generators are analysed. The paper describes in detail the experimental arrangement, including the features of the wind tunnel and of the instrumentation. The results are compared with experimental data published by other authors and with naturally developed flows.