Modeliranje i simuliranje procesa izmjene topline te procjena parametara

undergraduate thesis

• Title (english): Modeling and simulation of heat exchange processes and parameter estimation
• Author: David Fabek
• Mentor: Željka Ujević Andrijić (mentor)
• Committee member: Željka Ujević Andrijić (predsjednik povjerenstva)
• Committee member: Nenad Bolf (član povjerenstva)
• Committee member: Marina Duplančić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2021-09-15, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Chemical Engineering

Abstract

Cilj ovog rada bio je razviti matematički model procesa prijenosa topline te izraditi računalni program u programskom paketu Matlab koji će računati profile temperatura po položaju tijekom određenog vremena i pritom procijeniti parametre procesa tj. toplinsku vodljivost i koeficijent prijenosa topline. Proces se analizirao na laboratorijskoj aparaturi za istraživanje prijenosa topline kroz kamenu ploču. Promatran je slučaj kada je kamena ploča jednom stranom naslonjena na grijač, dok se druga strana hladi zrakom iz okoline prirodnom konvekcijom. Ovakav nestacionarni proces se matematički opisuje pomoću parcijalnih diferencijalnih jednadžbi za čije je rješavanje primijenjena neposredna metoda konačnim razlikama. Određivanjem početnih i rubnih uvjeta te adekvatnog koraka iteracije po položaju i vremenu uz određene uvjete stabilnosti, izvedeni su modeli za raspodjelu temperatura u unutarnjim točkama ploče te na strani ploče koja se hladi zrakom. Za procjenu parametara korištena je ugrađena Matlab funkcija koja se temelji na Nelder-Mead metodi optimiranja, odnosno pronalazi minimum zadane funkcije cilja koja je u ovom slučaju bila korijen srednjeg kvadratnog odstupanja između eksperimentalnih i modelom dobivenih vrijednosti temperatura. Dobiveni rezultati pokazuju da se razvijenim računalnim programom mogu uspješno optimirati parametri procesa; toplinska vodljivost kamene ploče i koeficijent prijenosa topline s ispitivane ploče na okolni zrak. Također, dobiveni su grafički prikazi koji zorno opisuju promatrani fenomen prijenosa topline te potvrđuju vjerodostojnost razvijenog modela.

Abstract (english)

The main goal of this study was to develop a mathematical model of the heat transfer process and to create a computer program in the Matlab software package that will calculate temperature profiles per position over a certain period, while estimating the parameters of the process - thermal conductivity and heat transfer coefficient. The process was analyzed using the laboratory equipment for research of heat transfer through the stone plate. A stone plate leaned against the heater on one side was observed, while the other side was being cooled with environmental air by natural convection. A mathematical description of this non-stationary process includes partial differential equations. For solving the partial differential equations the explicit method of finite differences was used. Models for the temperature distribution in inner points and on the side of the plate which is being cooled with air were implemented by determining initial and border conditions and adequate iteration steps by place and time with specific conditions of stability. Matlab built-in function based on the Nelder-Mead optimization method was used for parameter estimation. This method finds the minimum of the objective function, in this case the root of the mean square deviation between the experimental and predicted temperatures. Results showed that the process parameters: thermal conductivity of the stone plate and heat transfer coefficient from the plate to the surrounding air, were successfully optimized with the developed computer program. The results are shown graphically and successfully describe the observed phenomenon and confirm the fidelity of the implemented model.

• Keywords: matematički model; prijenos topline; Matlab; optimiranje; Nelder-Mead; parcijalne diferencijalne jednadžbe
• Keywords (english): mathematical model; heat transfer; Matlab; optimization; Nelder-Mead; partial differential equations
• Language: croatian
• URN:NBN: urn:nbn:hr:149:861192
• Study programme: Title: Materials Science and Engineering - Undergraduate study; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka kemijskog inženjerstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka kemijskog inženjerstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2023-03-28 07:38:10