Heat Transfer From an Annular Fin of Constant Thickness

1959 ◽  
Vol 81 (2) ◽  
pp. 151-156 ◽  
Author(s):  
H. H. Keller ◽  
E. V. Somers
Keyword(s):  
Graphical Form ◽  
Constant Thickness ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Small Height ◽  
Annular Fin ◽  
Inner Radius ◽  
The One ◽  
Group B ◽  
Annular Fins

The two-dimensional solution for annular fins, given in graphical form with the efficiency plotted versus the design-parameter group, (b − a)[(2h)/(kw)]1/2, supplies needed design information for fins of small height-to-thickness ratio and large height-to-inner radius ratio. The one-dimensional solutions previously given for annular fins are accurate for height-to-width ratios of the order of 10 or more, while the two-dimensional results for rectangular fins are useful as approximations to annular fins when curvature is not large. With height-to-width ratios less than 10 and for annular fins with large curvature, design of fins can be computed with the results presented in this paper.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

scholarly journals Currents induced by long waves propagating towards a beach over a wavy bed

2000 ◽  
Vol 413 ◽  
pp. 317-343 ◽  
Author(s):  
H. KYOTOH ◽  
S. FUJII ◽  
D. V. TO
Keyword(s):  
Mass Flux ◽  
Wave Motion ◽  
Shallow Water Equation ◽  
Swash Zone ◽  
Two Dimensional ◽  
Maclaurin Series ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Bed Slope ◽  
The One

For the understanding of longshore currents along a natural beach, the effects of bottom unevenness are considered to be important, especially for the flow in the swash zone. Currents in the swash zone are strongly influenced by the bed slope because the effect of gravity overwhelms the effect of the depth change. In the present paper, we investigate these effects and focus on waves propagating from offshore over a flat ocean basin of constant depth to a beach with a sloping wavy bottom. The waves are incident at a small angle to the beach normal, and the bed slope in the alongshore direction is varied slowly. To simplify the problem, only cnoidal waves and solitary waves are considered and the bed level is varied sinusoidally in the longshore direction.A perturbation method is applied to the two-dimensional nonlinear shallow water equation (two-dimensional NLSWE) for the wave motion in order to generate a more simplified model of wave dynamics consisting of a one-dimensional NLSWE for the direction normal to the beach and an equation for the alongshore direction. The first equation, the one-dimensional NLSWE, is solved by Carrier & Greenspan's transformation. The solution of the second one is found by extending Brocchini & Peregrine's solution for a flat beach. Two methods for the solution of the one- dimensional NLSWE are introduced in order to get a solution applicable to large-amplitude swash motions, where the amplitude is comparable to the beach length. One is the Maclaurin expansion of the solution around the moving shoreline, and the other is Riemann's representation of the solution, which exactly satisfies the one-dimensional NLSWE and the boundary conditions. After doing a consistency check by confirming that Riemann's method, a numerical solution, agrees with the exact solution for an infinitely long, sloping beach, we assumed that the Maclaurin series solution can also describe wave motion in the swash zone properly not only for this model but also for our ‘wavy’, finite beach model.The solution obtained from the Maclaurin series is then plugged into the equation for the alongshore direction to calculate the shore currents induced by wave run-up and back-wash motions, where a ‘weakly two-dimensional solution’ is derived from geometrical considerations. The results show that since the water depth near the shoreline is comparable to the bed level fluctuations, the flow is strongly affected by the bed unevenness, leading to recognizable changes in shoreline movement and the time-averaged velocity and the mass flux of the flow in the swash zone. More specifically, the inhomogeneity of the alongshore mass flux generates offshore currents because of the continuity condition for the fluid mass.

Nonlinear Ion Acoustic Waves in a Magnetized Dusty Plasma in the Presence of Nonthermal Electrons

2009 ◽  
Vol 64 (5-6) ◽  
pp. 370-376 ◽  
Author(s):  
Taraknath Saha ◽  
Prasanta Chatterjee ◽  
Mohamed Ruhul Amin
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Two Dimensional ◽  
Ion Acoustic Waves ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Nonthermal Electrons ◽  
Magnetized Dusty Plasma ◽  
Ion Acoustic ◽  
The One

The Kadomtsev-Petviashili (KP) equation is derived for weakly nonlinear ion acoustic waves in a magnetized dusty plasma in the presence of nonthermal electrons. Soliton solutions are obtained in both the one-dimensional and two-dimensional framework. For the one-dimensional soliton solution the ‘tanh’ method is considered while the two-dimensional solution is obtained by a method introduced by S.V. Manacov et al., Phys. Lett. A 63, 205 (1977). It is found that in case of the onedimensional solution, both compressive and rarefactive solitary waves exist which could be obtained depending on the ratio of the electron and ion density. It is also seen that the nonthermal distribution of electrons has some significant effect in the shape of both the one-dimensional and two-dimensional solitary wave.

The generation of waves in an infinite elastic solid by variable body forces

1956 ◽  
Vol 248 (955) ◽  
pp. 575-607 ◽  
Keyword(s):  
General Solution ◽  
Fourier Transforms ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Physical Nature ◽  
Graphical Form ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Numerical Work ◽  
Body Forces

This paper is concerned with the determination of the distribution of stress in an infinite elastic solid when time-dependent body forces act upon certain regions of the solid. It is assumed throughout that the strains are small. In §2 a general solution of the equations of motion for any distribution of body forces is derived by the use of four-dimensional Fourier transforms, and from that is derived the general solution for an isotropic solid (§ 3). From the latter solution are deduced the general solution of the statical problem (§4) and the two-dimensional problem (§5). The solution of the equations of motion in the case in which the distribution of body forces is symmetrical about an axis is derived in §6. The remainder of the paper consists in deducing the solution of special problems from these general solutions. In §§7 to 13 some typical two-dimensional problems are considered and exact analytical expressions found for the components of the stress tensor. In §§14 to 16 examples are given of the use of the general non-symmetrical three-dimensional solution derived in § 3, and in §§17 to 19 examples are given to illustrate the use of the general solution of the axially symmetrical problem. A certain amount of numerical work (presented in graphical form) is quoted to give some idea of the physical nature of the solutions.

Temperature Depression Under Heat Sources With Cylindrical Contact Thermocouples

2015 ◽  
Author(s):  
Kayvan Abbasi ◽  
Sukhvinder Kang
Keyword(s):  
Heat Sink ◽  
Numerical Solutions ◽  
Heat Sources ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Dimensionless Groups ◽  
Dimensional Approximation ◽  
The One ◽  
Temperature Depression

The thermal performance of heat sinks is commonly measured using heat sources with spring loaded thermocouples contained within plastic poppets that press against the heat sink to measure its surface temperature where the heat is applied. However, when the thickness of the heat sink base is small or the effective heat transfer coefficient on the fin side is large, the temperature at the thermocouple contact point is less than the nearby temperature where the heat source contacts the heat sink. This temperature depression under the contact thermocouples has been studied. The heat conduction equation is solved analytically to determine the temperature distribution around the contact thermocouple using a one-dimensional approximation and also a detailed two-dimensional approach. Two dimensionless groups are identified that characterize the detailed two-dimensional solution. The combination of the two dimensionless groups also appears in the one dimensional solution. The temperature distributions are validated using finite difference numerical solutions. It is shown that the one dimensional solution is the limit of the detailed solution when one of the dimensionless groups tends to infinity. A simple equation is provided to estimate the temperature measurement error on the heat sink surface.

F.VIII R:Ag in Hepatitis

1979 ◽  
Author(s):  
R. Kotitschke ◽  
J. Scharrer
Keyword(s):  
Chronic Hepatitis ◽  
Blood Donors ◽  
Blood Donation ◽  
Normal Population ◽  
Rabbit Antiserum ◽  
Two Dimensional ◽  
Plastic Plate ◽  
Significant Difference ◽  
Acute Hepatitis B ◽  
The One

F.VIII R:Ag was determined by quantitative immunelectrophoresis (I.E.) with a prefabricated system. The prefabricated system consists of a monospecific f.VIII rabbit antiserum in agarose on a plastic plate for the one and two dimensional immunelectrophoresis. The lognormal distribution of the f.VIII R:Ag concentration in the normal population was confirmed (for n=70 the f.VIII R:Ag in % of normal is = 95.4 ± 31.9). Among the normal population there was no significant difference between blood donors (one blood donation in 8 weeks; for n=43 the f.VIII R:Ag in % of normal is = 95.9 ± 34.0) and non blood donors (n=27;f.VIII R:Ag = 94.6 ± 28.4 %). The f.VIII R:Ag concentration in acute hepatitis B ranged from normal to raised values (for n=10, a factor of 1.8 times of normal was found) and was normal again after health recovery (n=10, the factor was 1.0). in chronic hepatitis the f.VIII R:Ag concentration was raised in the majority of the cases (for n=10, the factor was 3.8). Out of 22 carrier sera 20 showed reduced, 2 elevated levels of the f.VIII R:Ag concentration. in 5 sera no f.VIII R:Ag could be demonstrated. The f.VIII R:Ag concentration was normal for n=10, reduced for n=20 and elevated for n=6 in non A-non B hepatitis (n=36). Contrary to results found in the literature no difference in the electrophoretic mobility of the f.VIII R:Ag was found between hepatitis patients sera and normal sera.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Impact Assessment of Urethral Meatus Morphology and Penile Biometry in Transurethral Prostate and Bladder Surgery

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Rodrigo Ribeiro Vieiralves ◽  
Paulo Henrique Pereira Conte ◽  
Eduardo Medina Felici ◽  
Nádia Cristina Pinheiro Rodrigues ◽  
Tomás Accioly de souza ◽  
...  
Keyword(s):  
Average Length ◽  
Intervention Group ◽  
Urethral Meatus ◽  
New Classification ◽  
Average Width ◽  
Front Position ◽  
Determining Factors ◽  
Group A ◽  
The One ◽  
Group B

Objective. To analyze the penile and urethral meatus biometry and its correlation with meatoplasty during endoscopic resections. We also propose a new classification for urethral meatus morphology.Materials and Methods. We prospectively studied 105 patients who underwent prostate and bladder transurethral resections. We performed standardized measurement of penile and urethral meatus biometry followed by penile photo in the front position. The need to perform meatoplasty or dilatation during resectoscope introduction was registered. Data were analyzed comparing the correlation between two groups: without intervention (Group A) and with intervention (Group B).Results. We observed in Group A and Group B, respectively, the average length of urethral meatus of 1.07 cm versus 0.75 cm (p<0.001) and average width of urethral meatus of 0.59 cm versus 0.38 cm (p<0.001). Considering the morphology of the urethral meatus, we propose a new classification, in the following groups: (a) typical; (b) slit; (c) point-like; (d) horseshoe; and (e) megameatus. The point-like meatus was the one that most needed intervention, followed by the slit and the typical meatus (p<0.001).Conclusions. Point-like and slit-shaped urethral meatus, as well as reduced length and width of the urethral meatus, are the determining factors.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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