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Neste trabalho, estudamos alguns números e procedimentos que facilitam na solução de problemas no campo da contagem, sendo esses: O Princípio da Inclusão e Exclusão, Triângulo de Pascal, Binômios de Newton, números binomiais e multinomiais, números de funções, permutações, grafos, números de Stirling, lemas de Kaplansky e sequência de Fibonacci. / We studied some numbers and procedures that facilitate the solution of problems in the field of counting, these being: The Principle of Inclusion and Exclusion, Pascal\'s Triangle, Newton binomial, binomial and multinomial numbers, numbers of functions, permutations, graphs, Stirling numbers, slogans Kaplansky and the Fibonacci sequence.

Η παρούσα διπλωματική εργασία έχει ως θέμα τον ευφυή έλεγχο μιας μηχανής Stirling χαμηλής θερμοκρασιακής διαφοράς, με στόχο την πρακτική εφαρμογή σε οικιακούς καταναλωτές για την παραγωγή ηλεκτρικής ενέργειας. Έγινε διασύνδεση μιας σειρά αισθητήρων (μέτρηση θερμοκρασίας) και επενεργητών (αντλίες) σε ένα πρωτότυπο σύστημα, έτσι ώστε να προσομοιωθεί κατά το καλύτερο δυνατό τρόπο η λειτουργία της αύξησης της θερμοκρασίας του υγρού σε ένα ηλιακό θερμοσίφωνα και της τυπικής οικιακής ημερήσιας κατανάλωσης. Με βάση αυτό το πρότυπο παραγωγής και κατανάλωσης ενέργειας διαμορφώθηκε ένας ευριστικός έλεγχος έτσι ώστε να παραχθεί η περισσότερη ηλεκτρική ενέργεια χωρίς να παραβιασθούν μία σειρά από περιορισμούς που αφορούν στην χρήση του ηλιακού θερμοσίφωνα. Πειραματικά αποτελέσματα επιβεβαιώνουν την αποτελεσματικότητα της μηχανής Stirling και την ανάγκη προσαρμοστικοτητας της λειτουργίας της έτσι ώστε να ανταποκρίνεται στις ιδιάζουσες ανάγκες της κάθε οικογένειας. / This thesis is on the intelligent control of a Stirling engine with a low temperature difference in order to practice residential consumers for electricity production. An interface of a series of sensors (temperature measurement) and actuators (pumps) became in a prototype system in order to simulate as best as possible the function of warming the liquid in a solar water heater and the standard daily household consumption. Under this model of production and consumption was a Heuristic control order to generate more electricity without having violated a number of restrictions on the use of solar water heater. Experimental results confirm the effectiveness of the Stirling engine and the need for adaptability of its operation to meet the specific needs of each family.

Neste trabalho, estudamos alguns números e procedimentos que facilitam na solução de problemas no campo da contagem, sendo esses: O Princípio da Inclusão e Exclusão, Triângulo de Pascal, Binômios de Newton, números binomiais e multinomiais, números de funções, permutações, grafos, números de Stirling, lemas de Kaplansky e sequência de Fibonacci. / We studied some numbers and procedures that facilitate the solution of problems in the field of counting, these being: The Principle of Inclusion and Exclusion, Pascal\'s Triangle, Newton binomial, binomial and multinomial numbers, numbers of functions, permutations, graphs, Stirling numbers, slogans Kaplansky and the Fibonacci sequence.

This dissertation discusses Stirling’s cycle and its contribution using different approaches. There are calculation of Schmidt’s theory and distinctiveness between ideal and real cycle described. Based on my previous research, this work provides a detailed summary of different methods which are used to stimulate Stirling’s cycles as well as the motor as a whole. Attention is particularly dedicated to current utilization of this machine which is not broadly known within general public.

Thesis (MScIng( Mechanical Engineering)--University of Stellenbosch, 2007. / 121 Leaves printed single pages, preliminary pages a-l and numbered pages 1-81. / ENGLISH ABSTRACT:In the midst of the current non-renewable energy crises specifically with regard to fossil fuel, various research institutions across the world have turned their focus to renewable and sustainable development. Using our available non.renewable resources as efficiently as possible has been a focal point the past decades and will certainly be as long as these resources exist Various means to utilize the world's abundant and freely available renewable energy has been studied and some even introduced and installed as sustainable energy sources, Electricity generation by means of wind powered turbines, photo-voltaic cells, and tidal and wave energy are but a few examples. Modern photo-voltaic cells are known to have a solar to electricity conversion efficiency of 12% (Van Heerden, 2003) while wind turbines have an approximate wind to electricity conversion efficiency of 50% (Twele et aI., 2002). This low solar to electricity conversion efficiency together with the fact that renewable energy research is a relatively modern development, lead to the investigation into methods capable of higher solar to electricity conversion efficiencies. One such method could be to use the relatively old technology of the Stirling cycle developed in the early 1800's (solar to electricity conversion efficiency in the range of 20.24 % according Van Heerden, 2003). The Stirling cycle provides a method for converting thermal energy to mechanical power which can be used to generate electricity, One of the main advantages of Stirling machines is that they are capable of using any form of heat source ranging from solar to biomass and waste heat. This document provides a discussion of some of the available methods for the analysis of Stirling machines. The six (6) different methods considered include: the method of Beale, West, mean-pressurepower- formula (MPPF), Schmidt, idea! adiabatic and the simple analysis methods. The first three (3) are known to be good back-of-the-envelope methods specifically for application as synthesis tools during initialisation of design procedures, while the latter three (3) are analysis tools finding application during Stirling engine design and analysis procedures. These analysis methods are based on the work done by Berchowitz and Urieli (1984) and form the centre of this document. Sections to follow provide a discussion of the mathematical model as well as the MATlAB implementation thereof. Experimental tests were conducted on the Heinrici engine to provide verification of the simulated resutls. Shortcomings of these analyses methods are also discussed in the sections to follow. Recommendations regarding improvements of the simulation program, possible fields of application for Stirling technology, as well as future fields of study are made in the final chapter of this document. A review of relevanl literature regarding modern applications of Stirling technology and listings of companies currently manufacturing and developing Stirling machines and findings of research done at various other institutions are provided. / AFRIKAANSE OPSOMMING:Die tempo van uitputling van die wereld se nie-hernubare energiebronne die afgelope jare het aanleiding gegee daartoe dal daar loenemend fokus toegespits word op die ontwikkeling van hernubare alternatiewe. Meer doeltreffende benutting van die wereld se nie-hernubare energie is reeds 'n fokus punt, vir navorsers reg oor die wereld, vir die afgelope dekades. Die aarde se oorvloedryke hernubare energie bronne word reeds met verskeie metodes ontgin. Die omskakeling van wind-, son- en gety energie na elektrisieteids is net 'n paar voorbeelde. Die effektiwiteid van sonkrag na elektrisietyds omskakeling van moderne fotovo!la'iese selle is in die orde van 12% (Van Heerden, 2003) terwyl die doeltreffendeid van wind energie na elektrisiteit omskakelling in die orde van 50% (Twele et at, 2002) is. Hierdie relatief lae omskelings doeltreffendeid van sonkrag na elektrisietyd, tesame met die feit dat die hernubare industrie nag relatief jonk is, lei lot die soeke na ander meer doellreffende moontlikhede Die Stirling siklus is nie 'n mod erne beginsel nie, maar die toepassing daarvan veral in die hernubare energie industrie is wei 'n relatiewe nuwe beg rip, veral in teme van die omskakeling van sonkrag na elektriese energie (gemiddelde sonkrag na lektriese energie omskakelings doellreffendeid in die orde van 20-24% is gevind deur Van Heerden, 2003). Die omskakeling van lermiese energie na meganiese energie is sekerlik die hoof uitkomsle van die Stirling siklus, alhoewel dit ook toepassing vind in die verkoefingsindustrie. Die feit dat die Stirling siklus van enige vorm van termiese energie (bv. son. biomassa, asook hilte geproduseer as byproduk tydens sekere prosesse) gebruik kan maak. is een van die redes wat die tegnologie 56 aanloklik maak, spesifiek !.o,v. die hernubare energie sektor. Ses (6) metodes vir die analise van die Stirling siklus word in hierdie dokument bespreek. Dit slui! die volgnde in: Beale-, West-, die gemiddelde-druk-krag-metode (GDKM), Schmidt-, adiabatiese- en die eenvoudige analise melodes. Die eerste drie (3) metodes is handige berekenings metodes Iydens die aanvangs en sinlesefase van Stirling enjin ontwerp, lerwyl die laaste drie (3) meer loegespils is op die volledige ontwerps- en analisefases gedurende die Stirling eniin ontwerps proses. Die drie (3) analise melodes is gebaseer op die werk wat deur Berchowitz en Urieli (1984) gedoen is en maak die kern van die dokument uit. Die wiskundige model, implimentering daarvan in MATlAB, sowel as die eksperimentele verifieering van die resultate word bespreek. Tekortkominge van die analise metodes word ook aangespreek in elke hoofsluk. Moontlikke verbeterings len opsigte van die verskeie aannames word in die finale hoofsluk van die dokumenl aangespreek. Verskeie voorgestelde riglings vir toekomslige navorsings projekle word ook in die finale hoofstuk van die dokument genoem. 'n Kort oorsig van die relevanle lileraluur in verband mel huidige loepassings van die Stirling legnologie, asook die name van maatskappye wal tans hierdie tegnologiee ontwikkel en vervaardig, word genoem.

A single-stage pulse tube cryocooler was designed and fabricated to provide cooling at 50 K for a high temperature superconducting (HTS) magnet, with a nominal electrical input frequency of 50 Hz and a maximum mean helium working gas pressure of 2.5 MPa. Sage software was used for the thermodynamic design of the pulse tube, with an initially predicted 30 W of cooling power at 50 K, and an input indicated power of 1800 W. Sage was found to be a useful tool for the design, and although not perfect, some correlation was established. The fabricated pulse tube was closely coupled to a metallic diaphragm pressure wave generator (PWG) with a 60 ml swept volume. The pulse tube achieved a lowest no-load temperature of 55 K and provided 46 W of cooling power at 77 K with a p-V input power of 675 W, which corresponded to 19.5% of Carnot COP. Recommendations included achieving the specified displacement from the PWG under the higher gas pressures, design and development of a more practical co-axial pulse tube and a multi-stage configuration to achieve the power at lower temperatures required by HTS.

Small combined heat and power generators have the potential to reduce energy consumption and greenhouse gas emissions of residential buildings. Recently, much attention has been given to these units. To date, the majority of studies in this field have concentrated on the steady operational performance of a specific generator type, and the available computer models have largely been theoretical in nature. <br /><br /> The main goal of this study was to evaluate the performance of the latest combined heat and power generators, when integrated into Canadian residential homes. A fair comparison of four 1 kW (electrical) units was made. The combined heat and power units studied were based on PEM fuel cell, solid oxide fuel cell, Stirling Engine, and internal combustion engine energy converters. <br /><br /> This study utilized recent test data in an attempt to evaluate the most efficient method of integrating the combined heat and power units into residential houses. Start-up, shut down, and load change transients were incorporated into the simulations. The impact of load variations due to building thermal envelope differences and varying building heating system equipment was evaluated. The simulations were evaluated using TRNSYS software. The building heat demands were determined with eQuest hourly building simulation software. <br /><br /> All of the combined heat and power units under study were capable of providing a net annual benefit with respect to global energy and greenhouse gas emissions. The fuel cells offer the highest integrated performance, followed closely by the internal combustion engine and lastly the Stirling engine. Annual global energy savings up to 20%, and greenhouse gas savings up to 5. 5 tonnes per year can be achieved compared to the best conventional high efficiency appliances. <br /><br /> Heat demand influences performance greatly. As the thermal output of the generator unit approaches half of the average building thermal demand, the system design becomes critical. The system design is also critical when integrating with a forced air furnace. Only the PEM fuel cell unit produces clear global energy and emissions benefits when operating in the summertime.

Sustainable Built Environments Senior Capstone Project / This paper provides a study on the configuration of Stirling engines and the effect using a solar dish as a heat source on efficiency. The Stirling engine was based on the MIT 2.670 design - a Gamma configuration, low temperature differential Stirling engine. Temperature and speed were measured for the base model Stirling engine to determine the initial efficiency. Modifications were planned to add a parabolic mirror as a solar dish and compare the efficiency to the initial design, however, the completed solar Stirling engine testing and data collection is to be performed in the following summer. The work performed by the engine was to be calculated using the Schmidt formula to then find the power output. Results from the completion of this study would indicate how the solar dish effects the power output of the Stirling engine.

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