A Comparison of Numerical Solutions of the Unsteady Flow Equations Applied to Reciprocating Compressor Systems

The paper reviews briefly a number of methods which are now available to facilitate solutions to the hyperbolic partial differential equations describing unsteady compressible fluid flow. Various schemes are considered and their merits and disadvantages discussed. Equations describing unsteady one-dimensional flow with heat transfer, area change and friction are presented in conservation-law, normal and characteristic forms. Pulsations in a compressor system are predicted using both the two-step Lax-Wendroff scheme and a scheme based on the characteristic form of the equations. The Lax-Wendroff scheme was simpler to apply, required less computer time, and gave better agreement with experimental results obtained from a single-stage reciprocating air-compressor system.

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Use of a Zener Approximation for Heat Transfer Analyses of Quasi One-Dimensional Welding Problems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.941.2313 ◽

2018 ◽

Vol 941 ◽

pp. 2313-2318

Author(s):

Jerry E. Gould

Keyword(s):

Heat Transfer ◽

Numerical Solutions ◽

One Dimensional ◽

Copper Electrodes ◽

Wide Range ◽

Linear Friction ◽

Diffusion Transfer ◽

Cooling Behavior ◽

Transfer Problems ◽

Analytical Approaches

Most welding methods in use today involve heating and subsequent cooling of the substrates for joining. Not surprisingly, understanding of associated thermal cycles implicit with the various processes has been a key facet of welding research. While the tools are available for sophisticated numerical solutions, much insight can be gained from simplified analytical approaches. A wide range of joining technologies in use today can be addressed by nominal one-dimensional heat transfer analyses. These include, for example, resistance spot, flash-butt, and linear friction welding. In addressing heat transfer problems, the mathematical constructs for heat transfer are analogous to those for mass (diffusion) transfer. Not surprisingly, one dimensional heat transfer problems can be greatly simplified by adapting the Zener approximation from mass transfer. The work described here employs the Zener approximation to address the direct spot welding of aluminum to steel. The Zener approximation is used to understand heat flow progressively from the steel into the aluminum and finally the copper electrodes. The results are used to understand weld morphology and implicit cooling behavior

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Groundwater flow equation, overview, derivation, and solution

E3S Web of Conferences ◽

10.1051/e3sconf/202131404007 ◽

2021 ◽

Vol 314 ◽

pp. 04007

Author(s):

Lhoussaine El Mezouary ◽

Bouabid El Mansouri

Keyword(s):

Heat Transfer ◽

Differential Equation ◽

Groundwater Flow ◽

Numerical Solutions ◽

Flow Equation ◽

Heat Transfer Equation ◽

Flow Equations ◽

Basic Law ◽

Flow Through ◽

Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

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Differential Approximation of Radiative Heat Transfer in a Gray Medium: Axially Symmetric Radiation Field

Journal of Heat Transfer ◽

10.1115/1.3244379 ◽

1980 ◽

Vol 102 (4) ◽

pp. 719-723 ◽

Cited By ~ 11

Author(s):

J. Higenyi ◽

Y. Bayazitogˇlu

Keyword(s):

Heat Transfer ◽

Radiation Field ◽

Radiative Heat ◽

Numerical Solutions ◽

Radiant Energy ◽

Axially Symmetric ◽

Differential Approximation ◽

Emissive Power ◽

One Dimensional ◽

Gray Medium

The differential approximation is used to analyze an axially symmetric radiation field for a gray medium within a finite, cylindrical enclosure. The medium emits, absorbs, and isotropically scatters radiant energy and is subject to a specified heat generation. Numerical solutions are obtained for the radiative heat flux and emissive power distributions. It is found that the accuracy of the differential approximation is of the same order for the axially symmetric and one-dimensional problems.

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The Preliminary Analysis of Axial Turbines by a Simplified Throughflow Procedure

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1982_024_004_02 ◽

1982 ◽

Vol 24 (1) ◽

pp. 5-10

Author(s):

N. A. Mitchell

Keyword(s):

Axisymmetric Flow ◽

Design Procedure ◽

Computer Time ◽

One Dimensional ◽

Flow Equations ◽

Streamline Curvature ◽

Flow Through ◽

Axial Turbines ◽

Turbine Design ◽

Performance Calculation

A new iterative scheme for calculating the axisymmetric flow through a turbine, which converges to a given value of turbine exit pressure, is described. It is intended to be used at a preliminary stage in a turbine design procedure instead of a one-dimensional calculation, since it enables spanwise variations of turbine performance to be calculated with reasonable accuracy and with minimum data preparation in approximately 1/30 of the computer time of a conventional axisymmetric calculation. The method solves the full axisymmetric flow equations on three streamlines through the machine at hub, midspan, and tip, although an approximation is introduced regarding the curvature of the centre streamline. Agreement with a full streamline curvature analysis is shown to be good, and comparisons with a one-dimensional Ainley-Mathieson based performance calculation show how the method is sensitive to root and tip behaviour.

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A Theoretical Model for Peripheral Tissue Heat Transfer Using the Bioheat Equation of Weinbaum and Jiji

Journal of Biomechanical Engineering ◽

10.1115/1.3138646 ◽

1987 ◽

Vol 109 (1) ◽

pp. 72-78 ◽

Cited By ~ 30

Author(s):

Wei Jie Song ◽

Sheldon Weinbaum ◽

Latif M. Jiji

Keyword(s):

Heat Transfer ◽

Numerical Solutions ◽

Quantitative Model ◽

Peripheral Tissue ◽

Whole Body ◽

Bioheat Equation ◽

One Dimensional ◽

Physiological Conditions ◽

Tissue Organization ◽

Body Heat

In this paper the new bioheat equation derived in Weinbaum and Jiji [7] is applied to the three layer conceptual model of microvascular surface tissue organization proposed in [1]. A simplified one-dimensional quantitative model of peripheral tissue energy exchange is then developed for application in limb and whole body heat transfer studies. A representative vasculature is constructed for each layer and the enhancement in the local tensor conductivity of the tissue as a function of vascular geometry and blood flow is examined. Numerical solutions for the boundary value problem coupling the three layers are presented and these results used to study the thermal behavior of peripheral tissue for a wide variety of physiological conditions from supine resting state to maximum exercise.

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