Similarity Solutions: A Group-Theoretic Approach for Students

1997 ◽  
Vol 25 (4) ◽  
pp. 243-262 ◽  
Author(s):  
E. R. Tuttle ◽  
S. W. J. Welch
Keyword(s):  
Heat Transfer ◽  
Group Theory ◽  
Graduate Students ◽  
Fluid Mechanics ◽  
Similarity Solutions ◽  
Theoretic Approach ◽  
Theory Method ◽  
Physically Based ◽  
Group Theory Method ◽  
Graduate Seminars

One of the most powerful methods for generating similarity solutions to problems in fluid mechanics and heat transfer is the group-theory method; it is also one of the easiest to apply. However, because of the apparent difficulty and obscurity of the underlying mathematics it is rarely mentioned in anything but advanced graduate seminars in these areas. This is unfortunate, as it is actually one of the most physically based and computationally simple of the methods available for obtaining such solutions. In this paper we give a presentation of this method which will make these group-theoretic techniques accessible and useful to advanced undergraduates and beginning graduate students. Several examples, both standard and unusual, are also given.

Thermo/Fluids Curriculum Development in a New Mechanical Engineering Program

2010 ◽  
Author(s):  
Amir Jokar ◽  
Stephen Solovitz
Keyword(s):  
Heat Transfer ◽  
Graduate Students ◽  
Fluid Mechanics ◽  
Mechanical Engineering ◽  
Dual Approach ◽  
Engineering Programs ◽  
Engineering Research ◽  
Engineering Program ◽  
Research Activities ◽  
Hands On

This study describes a model for developing a thermo/fluids curriculum in a new mechanical engineering program. Hands-on experience and applied engineering research are the center of this development. The efforts in creating undergraduate, elective, and graduate level courses and laboratories in the fundamental topics of thermodynamics, fluid mechanics, and heat transfer are reviewed and explained in detail. A dual approach has been taken in developing the curriculum, so that both undergraduate and graduate students can utilize the facility in their research activities. This development has been revised and optimized since its initiation in 2005, and it has successfully been accredited by ABET. The good results obtained from this model can be used in developing mechanical engineering programs, especially for smaller-sized institutions.

Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Open Physics ◽  
2007 ◽  
Vol 5 (2) ◽  
Author(s):  
Piotr Potera ◽  
Ireneusz Stefaniuk ◽  
Marian Kuźma
Keyword(s):  
Group Theory ◽  
Group Action ◽  
Molecular State ◽  
Quantum States ◽  
Theory Method ◽  
Electron States ◽  
Factorization Scheme ◽  
Group Theory Method ◽  
The Subject

AbstractPentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.

The MIT Blowdown Turbine Facility

1984 ◽  
Author(s):  
A. H. Epstein ◽  
G. R. Guenette ◽  
R. J. G. Norton
Keyword(s):  
Heat Transfer ◽  
Fluid Mechanics ◽  
Short Duration ◽  
Three Dimensional ◽  
Inlet Pressure ◽  
Test Facility ◽  
Turbine Inlet ◽  
High Work

A short duration (0.4 sec) test facility, capable of testing 0.5-meter diameter, film-cooled, high work aircraft turbine stages at rigorously simulated engine conditions has been designed, constructed, and tested. The simulation capability of the facility extends up to 40 atm inlet pressure at 2500°K (4000°F) turbine inlet temperatures. The facility is intended primarily for the exploration of unsteady, three-dimensional fluid mechanics and heat transfer in modern turbine stages.

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