The Flat Plate Fin of Constant Thickness, Straight Base, and Symmetrical Shape

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Alejandro Rivera-Alvarez ◽  
Juan C. Ordonez
Keyword(s):  
Flat Plate ◽  
Shape Factor ◽  
Temperature Fields ◽  
Constant Thickness ◽  
Two Dimensional ◽  
One Dimensional ◽  
Symmetrical Shape ◽  
Extended Surface ◽  
And Performance ◽  
Biot Numbers

A plate fin is an extended surface made from a plate. Classical longitudinal and radial fins are particular cases of plate fins with very simple shapes and no curvature. In this paper, the problem of a flat plate fin of constant thickness, straight base, and symmetrical shape given by a proposed power law is considered. Particular attention is paid to some basic shapes: rectangular, triangular, convex parabolic, concave parabolic, convergent trapezoidal, and divergent trapezoidal. One- and two-dimensional analyses are conducted for every shape and comparison of results is carried through the usage of a proposed shape factor. Beyond shape, temperature fields and performance for the considered plate fins are shown to be dependent on a set of three Biot numbers characterizing the ratio between conduction resistances through every direction and convection resistance at the fin surface. Effectiveness and shape factor are found to be hierarchically organized by an including-figure rule. For the rectangular, zero-tip, and convergent trapezoidal cases, effectiveness is limited by a maximum possible value of Bit-1/2, and two-dimensional effects are very small. For the divergent trapezoidal case instead, effectiveness can be larger than Bit-1/2, and one-dimensional over-estimation of the actual heat transfer can be substantially large.

Analysis of Conduction-Controlled Rewetting of a Vertical Surface

1975 ◽  
Vol 97 (2) ◽  
pp. 161-165 ◽  
Author(s):  
C. L. Tien ◽  
L. S. Yao
Keyword(s):  
Initial Temperature ◽  
Empirical Relation ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Functional Relationships ◽  
Semi Empirical ◽  
Biot Numbers

The present paper presents a two-dimensional analysis of conduction-controlled rewetting of a vertical surface, whose initial temperature is greater than the rewetting temperature. The physical model consists of an infinitely extended vertical slab with the surface of the dry region adiabatic and the surface of the wet region associated with a constant heat transfer coefficient. The physical problem is characterized by three parameters: the Peclet number or the dimensionless wetting velocity, the Biot number, and a dimensionless temperature. Limiting solutions for large and small Peclet numbers obtained by utilizing the Wiener-Hopf technique and the kernel-substitution method exhibit simple functional relationships among the three dimensionless parameters. A semi- empirical relation has been established for the whole range of Peclet numbers. The solution for large Peclet numbers possesses a functional form different from existing approximate two-dimensional solutions, while the solution for small Peclet numbers reduces to existing one-dimensional solution for small Biot numbers. Discussion of the present findings has been made with respect to previous analyses and experimental observations.

Two-Dimensional Performance Analysis and Design of MHD Channels

1981 ◽  
Vol 103 (2) ◽  
pp. 307-314 ◽  
Author(s):  
E. Doss ◽  
H. Geyer ◽  
R. K. Ahluwalia ◽  
K. Im
Keyword(s):  
Operating Conditions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Channel Geometry ◽  
One Dimensional ◽  
Analysis And Design ◽  
Voltage Drops ◽  
And Performance ◽  
Carry Over ◽  
Mhd Channel

A two-dimensional model for MHD channel design and analysis has been developed for three different modes of operation: velocity, Mach number, and pressure. Given the distribution of any of these three parameters along the channel, the channel aspect ratio, and the channel operating conditions, the MHD channel geometry can be predicted. The developed two-dimensional design model avoids unnecessary assumptions for surface losses and boundary layer voltage drops that are required in one-dimensional calculations and, thus, can yield a better prediction of MHD channel geometry and performance. The subject model includes a simplified treatment for possible arcing near the electrode walls. A one-dimensional model for slag flow along the channel walls is also incorporated. The effects of wall temperature and slag carry-over on channel performance are discussed.

scholarly journals One-, Two-, and Three-Dimensional Supramolecular Assemblies Based on Tubular and Regular Polygonal Structures of Pillar[n]arenes

CCS Chemistry ◽  
2019 ◽  
pp. 50-63 ◽  
Author(s):  
Shixin Fa ◽  
Takahiro Kakuta ◽  
Tada-aki Yamagishi ◽  
Tomoki Ogoshi
Keyword(s):  
Surface Modification ◽  
Supramolecular Chemistry ◽  
Three Dimensional ◽  
Supramolecular Assemblies ◽  
Two Dimensional ◽  
Macrocyclic Compounds ◽  
Tubular Structures ◽  
One Dimensional ◽  
Symmetrical Shape

Pillar[ n]arenes, which were first reported by our group in 2008, are promising macrocyclic compounds in supramolecular chemistry. The simple, tubular, and highly symmetrical shape of pillar[ n]arenes has allowed various supramolecular assemblies with well-defined structures to be constructed. The pillar-shaped structures of pillar[ n]arenes are suitable for surface modification and formation of one-dimensional (1D) channels. The regular polygonal prism shape of organized pillar[ n]arenes contributes to the construction of highly assembled structures such as two-dimensional (2D) sheets and three-dimensional (3D) spheres. In this minireview, we describe supramolecular assemblies with various dimensions. First, we discuss 1D supramolecular assemblies based on tubular structures of pillar[ n]arenes. Second, 2D supramolecular sheet formation based on regular polygonal structures is described. Finally, 3D supramolecular assemblies such as vesicles and 3D frameworks constructed from pillar[ n]arenes are discussed.

Discrete ice lens theory for frost heave beneath pipelines

1992 ◽  
Vol 29 (3) ◽  
pp. 487-497 ◽  
Author(s):  
J. F. (Derick) Nixon
Keyword(s):  
Mass Flow ◽  
Two Dimensions ◽  
Frozen Soil ◽  
Temperature Fields ◽  
Frost Heave ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Buried Pipeline ◽  
Soil Columns ◽  
One Dimensional

The discrete ice lens theory of frost heave in one-dimensional soil columns was developed to provide a better physical basis for engineering predictions of frost heave in soils. The theory has now been extended to the two-dimensional heat- and mass-flow situation beneath a buried chilled pipeline. Although the frozen and unfrozen soil regions beneath a buried cold pipeline are two dimensional, and the temperature and water-flow fields are potentially complex, considerable simplifications can be made by invoking the so-called quasi-static approach for estimating temperature fields around the buried pipeline. It is proposed that the curved, quasi-static temperature profiles available from published relationships are appropriate for frost-heave predictions in the two-dimensional region beneath a pipeline. Using these curved temperature profiles in the same program and solution procedure developed previously for one-dimensional soil columns allows frost-heave predictions for a buried pipeline to be carried out with a minimum of computational effort. Therefore, the lengthy and tedious numerical procedures that have been a feature of previous attempts to model heat and mass flow and the resulting frost heave in two dimensions can be avoided. The procedure has been used to predict the frost depth and heave beneath two well-documented pipeline test sections at Calgary, Alta., and Caen, France, with very good agreement between prediction and observation. Some predictions for a practical field situation indicate the initial ground temperature plays an important role in frost heave, frost penetration, and the time at which the final ice lens forms in the freezing soil. Key words : frost heave, discrete ice lens, pipeline, segregation potential, hydraulic conductivity of frozen soil.

The Heat Balance Integral in Steady-State Conduction

1976 ◽  
Vol 98 (3) ◽  
pp. 466-470 ◽  
Author(s):  
A. A. Sfeir
Keyword(s):  
Heat Balance ◽  
Integral Method ◽  
Two Dimensional ◽  
One Dimensional ◽  
Heat Balance Integral Method ◽  
Extended Surfaces ◽  
Different Shapes ◽  
The One ◽  
Biot Numbers ◽  
The Heat Balance

The Heat Balance Integral Method is applied to solve for the heat flow and temperature distribution in extended surfaces of different shapes and boundary conditions. In most cases the analysis is found to be identical to the exact two-dimensional solutions at Biot numbers for which the one-dimensional analysis is almost 100 percent off. Other possible extensions of the method are briefly described.

scholarly journals Phase-retardation effects at radio frequencies in flat-plate conductors

2004 ◽  
Vol 45 (4) ◽  
pp. 495-510
Author(s):  
D. P. Bulte ◽  
L. K. Forbes ◽  
S. Crozier
Keyword(s):  
Integral Equation ◽  
Radio Frequency ◽  
Flat Plate ◽  
Integral Equations ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Phase Retardation ◽  
One Dimensional ◽  
Singular Equations ◽  
Current Densities

AbstractA system of new integral equations is presented. They are derived from Maxwell's equations and describe radio-frequency (RF) current densities on a two-dimensional flat plate. The equations are generalisations of Pocklington's integral equation showing phase-retardation in two dimensions. These singular equations are solved, numerically, for the case of one-dimensional geometry. The solutions are shown to display effects which correspond to damped resonance when the wavelength of the current matches aspects of the geometry of the conductor.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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