34608 - Heat Transfer (Graduate Course)

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Affordable and clean energy

Academic Year 2021/2022

Learning outcomes

The aim of the course is to provide advanced knowledge on the following topics: analytical methods for the solution of heat conduction problems, thermoelectric effects, thermal behaviour of fins, problems of forced convection in ducts.

Course contents

Heat conduction
- The physical model of heat conduction
- Stationary two-dimensional heat conduction 
- Separation of variables in rectangular and cylindrical coordinates
- Unsteady one-dimensional heat conduction
- Steady-periodic regime
- Separation of variables in non-stationary problems

Heat Transfer in Fins
- Mathematical models of heat transfer in fins
- Examples and applications

Thermoelectric Effects
- Local entropy balance equation
- Phenomenological relationships
- Seebeck effect and Peltier effect

Laminar Forced Convection in Ducts
- Condition of hydrodynamically developed flow 
- Thermally-developed flow and thermal entrance region


Antonio Barletta: Introduzione Matematica alla Trasmissione del Calore, Pitagora Editrice, Bologna, 2005. 
Antonio Barletta: Applicazioni della Fisica Termica - Argomenti Complementari di Fluidodinamica e Termocinetica, Pitagora Editrice, Bologna, 2002.
David W. Hahn, M. Necati Ozisik: Heat Conduction, 3rd edition, John Wiley & Sons, 2012.

Teaching methods

Classroom lessons and guided solution of exercises

Assessment methods

Concerning the teaching unit Heat Transfer (Graduate Course) the exam consists in an oral test. The test is oriented to the evaluation of the achievement of the capability to formulate, from a physico-mathematical viewpoint, and solve problems of heat conduction. The test is also oriented to the evaluation of the achievement of an appropriate knowledge on the basic topics of the course under the theoretical perspective. The final mark, less or equal than 30 (positive outcome is greater or equal than 18), expresses the overall evaluation on the theoretical knowledge and on the practical ability with respect to problem solving. 

The final mark on the entire integrated course made of Heat Transfer (Graduate Course) and Heat and Fluid Flow (Graduate Course)  is the arithmetic mean of the marks obtained in the two separated exams: Heat Transfer (Graduate Course); Heat and Fluid Flow (Graduate Course). The partial mark in one of two modules of the integrated course is valid for twelve months. If within twelve months the student does not pass the exam on the whole integrated course, the mark on the single module loses its validity.

Teaching tools

Blackboard lessons, pc presentations, examples of numerical solutions 

Links to further information


Office hours

See the website of Antonio Barletta