Politecnico di Torino  
Anno Accademico 2017/18  
01RMEND, 01RMEMW Introduction to computational heat transfer 

Corso di Laurea Magistrale in Ingegneria Energetica E Nucleare  Torino Corso di Laurea Magistrale in Ingegneria Chimica E Dei Processi Sostenibili  Torino 





Presentazione
The course focuses on the solution of 1D and 2D steadystate and transient heat conduction problems. These were chosen both as one of the fundamental classes of problems in energy applications and as a paradigm for the general case of elliptic and parabolic partial differential equations (PDE). Both problems are addressed using both the finite difference and the finite element approach. The fundamental tool for the solution of 1D heat conduction problems is MATLAB, to which the initial part of the lab classes is devoted. The chosen tool for the solution of 2D heat conduction problems is the Freefem++ freeware, to which the final part of the lab classes is devoted.

Risultati di apprendimento attesi
Through this course the student is expected to acquire:
 A feeling of the importance/relevance of the numerical, as opposed to analytical, solution of engineering problems such as that of heat conduction  A good knowledge of the finite difference and finite elements methods for solution of the abovementioned problems,  The ability to implement and solve them using MATLAB and Freefem++,  The ability to critically and quantitatively assess the accuracy of the results obtained with the computer (quality assurance). 
Prerequisiti / Conoscenze pregresse
The knowledge acquired in the following BSc courses (or equivalent ones) will be needed: Calculus (Analisi matematica I e II, Geometria), Computer science (Informatica), Applied thermodynamics and heat transfer (Termodinamica applicata e trasmissione del calore), with particular reference to vector and matrix algebra, to the solution of ordinary differential equations, to the basic elements of programming, and to steadystate and transient problems of heat conduction.

Programma
The 1D steadystate heat conduction problem
Finite difference approximation of derivatives Imposing boundary conditions Algebraic approximation of the original ordinary differential equation Concepts of accuracy and mesh independence Solution of 1D steady state problems in Cartesian and radial coordinates using MATLAB The 1D transient heat conduction problem Fundamental solution of the heat conduction problem The method of lines as a general approach to the solution of initialboundary value PDEs Numerical schemes for time marching Solution of 1D transient problems in Cartesian and radial coordinates using MATLAB The 2D heat conduction problem Weak formulation Imposing boundary conditions Finite element vs. finite difference approximation Concepts of mesh generation/triangulation Quadrature formulae Solution of 2D steady state and transient problems in Cartesian and cylindrical coordinates using Freefem++. 
Organizzazione dell'insegnamento
27 h of standard lectures, combined with a total of 53 h of computational lab (3+ h per week). Under the guidance of professor and teaching assistants, the students will address with an engineering pitch the solution of problems of increasing complexity.

Testi richiesti o raccomandati: letture, dispense, altro materiale didattico
 Notes by the teacher
 MATLAB and Freefem++ user manuals.  Selected chapters from: J. Cooper, "Introduction to Partial Differential Equations with MATLAB" (Springer, 2008) C. Johnson, "Numerical solutions of PDEs by the finite element method" (Cambridge UP, 1987) 
Criteri, regole e procedure per l'esame
The assessment is made by written exam. Each student works on a PC in the lab and is asked to: 1) solve different numerical problems, using Matlab and/or Freefem++, and summarizing the results in the form of suitable plots; 2) justify the choice of the methods used for the solution; 3) discuss the quality/accuracy of the obtained numerical solution. These three items, collected by the student in a short report (doc file), contribute as follows to the final grade: 1) 70%; 2) 10%; 3) 20%. If the mark in the written exam is ≥ 28, an oral followup is foreseen

Orario delle lezioni 
Statistiche superamento esami 
