History of the Concept of Similarity in Natural Sciences

The concept of similarity has been discussed by many scientists and philosophers since ancient times. Thales of Miletus, Euclid, Aristotle, Galileo, Newton, Edgar Buckingham, and the modern philosopher of science Susan G. Sterrett are examples of intellectuals who perceived and examined the concept of similarity, while many scientists incorporated it in their scientific methodology. The wide range and variety of definitions of similarity could result in confusion regarding the meaning of the concept, the role the similarity mechanism plays in scientific methodology, and the identification of scientific fields to which similarity could be applied. The main aim of this paper was to enhance the understanding of the notion of similarity. To this end, we examined the historical evolution of the concept of similarity and the utilization of the mechanism of similarity in various eras of human intellectual activity, ranging from antiquity to the present day. In this context, the research hypothesis we investigated was the existence of specific and distinct stages of evolution within the long history of the concept of similarity in parallel with the evolution of scientific thought. A core question that motivated our work was when and under which conditions did the transition from the “technocratic” utilization of similarity (i.e., the use of similarity as a solution for practical problems) to its theoretical documentation and its conscious and systematic use as a significant experimental tool occurred. Another important question examined was whether there was a certain era that favored the development of the concept of similarity more than other historical periods. In order to address this hypothesis and respond to these questions, we sought to trace the evolution of conceptualizing and using similarity in different spatial and temporal contexts, formed by the corresponding historical, institutional, religious, and social conditions as well as the characteristics of the scientific methodology established during the period the similarity concept evolved

Modeling of flow and transport processes occurred in a typical polymer electrolyte membrane fuel cell (PEMFC)

Abstract. In the present work, a three dimensional model examining the fluid flow along with the fundamental transport phenomena occurring in a typical polymer electrolyte fuel cell (PEMFC), i.e. heat transfer, mass transport and charge transfer, has been developed. The flow field was simulated according to the well known Navier-Stokes equations, while the heat transfer was described by the typical conduction/convection equation and the mass transport by the convection/diffusion one. Furthermore, reaction kinetics were studied by the Butler-Volmer equation for the heterogeneous reactions occurring at the porous electrodes. The developed model was numerically solved by using the commercially available CFD package CFD-RC © , which is based on the multi-step finite volume method. The fuel cell performance in terms of velocity, temperature, mass fractions of active compounds and electric field has been investigated as well. Introduction Fuel cell systems are energy devices that directly convert the chemical energy of the feeding fuel into electricity without Carnot limitation, being suitable for stationary and mobile applications. Due to the high conversion efficiencies and the negligible environmental impact, fuel cell technology is considered as one of the most promising to contribute essentially to generation of electrical power in the near futur

On the Significance of Flow Regime for the Heat Transfer in Solid Oxide Fuel Cells

The steady state heat transfer that takes place in a hydrogen-fed tubular Solid Oxide Fuel Cell is considered here. The heat is produced due to the electrochemical reaction of the hydrogen that feds the cell with oxygen anions. An averaging technique is used to formulate a relatively simple one-dimensional heat transfer problem. The conduction-convection equation describing the heat transfer from the electrolyte’s surface to the moving gas that surrounds the cell’s cathode is solved analytically under the assumption of iso-thermal conditions. Three different cases are considered for the flow of the cathode gas: (a) plug flow, (b) fully developed incompressible laminar flow, and (c) compressible flow. Analytical expressions for the spatial distribution of gas and cell temperature along the cell's length are obtained. For constant mass flow rate, different flow regimes produce almost the similar spatial distributions for the gas temperature and, consequently, the consideration of the flow regime is of low importance in the design of fuel cell stacks.</jats:p

MASS TRANSPORT TO A SWARM OF ADSORBING SPHEROIDAL PARTICLES FROM A NEWTONIAN FLUID MOVING UNDER CREEPING FLOW CONDITIONS

MASS TRANSPORT FROM A LIQUID DILUTE SOLUTION TO A SWARM OF ADSORBING SOLID SPHEROIDAL PARTICLES STUDIED THEORETICALLY BY USING. THE SPHEROIDAL-IN-CELL MODEL (DASSIOS ET AL., 1994). FOR THE CASE OF HIGH PECLET NUMBERS AN ANALYTICAL SOLUTION IS OBTAINED FOR THE CONVECTIVE DIFFUSION EQUATION BOTH FOR THE PERFECT-SINK ADSORPTION AND FOR A REALISTIC ADSORPTION MODEL ACCORDING TO A SIMPLE CATALYTIC REACTION. SIMPLE EXPRESSIONS FOR THE LOCAL CONCENTRATION, THE LOCALAND OVERALL SHERWOOD NUMBER ETC, ARE ALSO OBTAINED. IT IS FOUND THAT OBLATE SPHEROIDS OF THE SAME SURFACE OR VOLUME. FOR THE CASE OF LOW PECLET A NUMERICAL SOLUTION IS PRODUCED FOR DESCRIBING THE MASS TRANSPORT ON THE OUTER SURFACEOF THE CELL. THE DIFFUSION FILM CUTS THE OUTER ENVELOPE FOR VERY LOW PECLET.THE INFUENCE OF THE SPHEROIDAL SHAPE IS LESS THAN THAT OBSERVED FOR THE HIGHPECLET, BUT REMAINS SIGNIFICANT.Η ΜΕΤΑΦΟΡΑ ΜΑΖΑΣ ΑΠΟ ΕΝΑ ΡΕΥΣΤΟ ΑΡΑΙΟ ΔΙΑΛΥΜΑ ΠΡΟΣ ΕΝΑ ΣΜΗΝΟΣ ΠΡΟΣΡΟΦΟΥΝΤΩΝ ΣΤΕΡΕΩΝ ΣΦΑΙΡΟΕΙΔΩΝ ΣΩΜΑΤΙΔΙΩΝ ΜΕΛΕΤΗΘΗΚΕ ΘΕΩΡΗΤΙΚΑ ΜΕ ΧΡΗΣΗ ΤΟΥ ΜΟΝΤΕΛΟΥ ΤΟΥ ΣΦΑΙΡΟΕΙΔΟΥΣ-ΣΕ-ΚΥΤΤΑΡΟ (DASSIOS ET AL, 1994) ΓΙΑ ΤΗΝ ΠΕΡΙΓΡΑΦΗ ΤΗΣ ΕΡΠΟΥΣΑΣ ΡΟΗΣΔΙΑΜΕΣΟΥ ΤΟΥ ΣΜΗΝΟΥΣ. ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΤΩΝ ΜΕΓΑΛΩΝ ΑΡΙΘΜΩΝ PECLET ΕΠΕΤΕΥΧΘΗ ΑΝΑΛΥΤΙΚΗ ΛΥΣΗ ΓΙΑ ΤΟ ΠΡΟΒΛΗΜΑ ΤΗΣ ΣΥΝΑΓΩΓΙΚΗΣ ΔΙΑΧΥΣΕΩΣ, ΤΟΣΟ ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΤΗΣ ΑΚΑΡΙΑΙΑΣ ΠΡΟΣΡΟΦΗΣΕΩΣ ΟΣΟ ΚΑΙ ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΟΠΟΥ ΘΕΩΡΕΙΤΑΙ ΕΝΑΣ ΡΕΑΛΙΣΤΙΚΟΤΕΡΟΣ ΜΗΧΑΝΙΣΜΟΣ ΠΡΟΣΡΟΦΗΣΕΩΣ Ο ΟΠΟΙΟΣ ΠΕΡΙΛΑΜΒΑΝΕΙ ΕΤΕΡΟΓΕΝΗ ΑΝΤΙΔΡΑΣΗ ΠΕΠΕΡΑΣΜΕΝΟΥ ΡΥΘΜΟΥ. ΠΑΡΗΧΘΗΣΑΝ ΑΠΛΕΣ ΕΚΦΡΑΣΕΙΣ ΓΙΑ ΤΗΝ ΣΥΓΚΕΝΤΡΩΣΗ ΤΗΣ ΔΙΑΛΥΜΕΝΗΣ ΟΥΣΙΑΣ ΚΑΘΩΣ ΚΑΙ ΓΙΑ ΤΑ ΠΑΡΑΓΩΓΑ ΤΗΣ ΜΕΓΕΘΗ (SHO, KO ΚΛΠ).ΒΡΕΘΗΚΕ ΟΤΙ ΤΟ ΟΡΙΑΚΟ ΣΤΡΩΜΑ ΠΟΥ ΕΜΦΑΝΙΖΕΤΑΙ ΕΙΝΑΙ ΕΞΑΙΡΕΤΙΚΑ ΜΙΚΡΟΥ ΕΥΡΟΥΣΕΝΩ ΠΑΡΑΤΗΡΗΘΗΚΕ ΑΥΞΗΜΕΝΗ ΙΚΑΝΟΤΗΤΑ ΚΑΤΑΝΑΛΩΣΕΩΣ ΤΗΣ ΔΙΑΛΥΜΕΝΗΣ ΟΥΣΙΑΣ ΟΤΑΝ ΤΟ ΣΦΑΙΡΟΕΙΔΕΣ ΕΙΝΑΙ ΠΕΠΛΑΤΥΣΜΕΝΟ ΣΕ ΣΧΕΣΗ ΜΕ ΑΥΤΗΝ ΠΟΥ ΠΑΡΟΥΣΙΑΖΟΥΝ ΟΙ ΣΦΑΙΡΕΣ ΚΑΙ ΤΑ ΕΠΙΜΗΚΗ ΣΦΑΙΡΟΕΙΔΗ. ΑΝΑΛΟΓΑ ΑΠΟΤΕΛΕΣΜΑΤΑ ΠΑΡΑΤΗΡΗΘΗΚΑΝ ΚΑΙ ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΤΩΝ ΜΙΚΡΩΝ ΑΡΙΘΜΩΝ PECLET. Η ΠΛΗΡΗΣ ΕΞΙΣΩΣΗ ΣΥΝΑΓΩΓΙΚΗΣ ΔΙΑΧΥΣΕΩΣΕΠΙΛΥΘΗΚΕ ΑΡΙΘΜΗΤΙΚΑ ΜΕ ΧΡΗΣΗ ΕΝΟΣ ΣΧΗΜΑΤΟΣ ΚΕΝΤΡΙΚΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΔΙΑΦΟΡΩΝ ΜΕΤΑΒΛΗΤΟΥ ΒΗΜΑΤΟΣ ΔΙΑΚΡΙΤΟΠΟΙΗΣΗΣ. ΠΡΟΤΑΘΗΚΕ ΜΙΑ ΝΕΑ ΣΥΝΟΡΙΑΚΗ ΣΥΝΘΗΚΗ ΠΑΝΩ ΣΤΟ ΕΞΩΤΕΡΙΚΟ ΣΥΝΟΡΟ ΤΟΥ ΚΥΤΤΑΡΟΥ ΔΙΟΤΙ ΟΙ ΥΠΑΡΧΟΥΣΕΣ ΕΙΤΕ ΠΑΡΗΓΑΓΑΝ ΛΑΝΘΑΣΜΕΝΕΣ ΤΙΜΕΣ ΓΙΑ ΤΟΝ ΡΥΘΜΟ ΠΡΟΣΡΟΦΗΣΕΩΣ ΕΙΤΕ ΕΚΑΝΑΝ ΜΗ ΦΥΣΙΚΕΣ ΥΠΟΘΕΣΕΙΣ (ΑΣΥΝΕΧΕΙΑ) ΓΙΑ ΤΗΝ ΣΥΓΚΕΝΤΡΩΣΗ. ΠΑΡΑΤΗΡΗΘΗΚΕ ΟΡΙΑΚΗ ΣΤΟΙΒΑΔΑ ΣΥΓΚΕΝΤΡΩΣΕΩΣ ΜΕΓΑΛΟΥ ΕΥΡΟΥΣ Η ΟΠΟΙΑ ΤΕΜΝΕΙ ΤΟ ΕΞΩΤΕΡΙΚΟ ΣΥΝΟΡΟ ΕΙΣΑΓΩΝΤΑΣ ΑΛΛΗΛΕΠΙΔΡΑΣΕΙΣ ΜΕΤΑΞΥ ΤΩΝΚΥΤΤΑΡΩΝ. (ΠΕΡΙΚΟΠΗ ΠΕΡΙΛΗΨΗΣ)