75446 - Thermo-Fluid-Dynamics M

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 course is devoted to laminar and turbulent fluid mechanics, for both isothermal and convection flows. These subjects are important for the student to reach the ability of treating applied problems of heat and fluid flow also by means of computational techniques.

Course contents

Models of Fluid Dynamics and Convection: Elementary concepts of fluid mechanics - Reynolds transport theorem - Rigorous deduction of local balance equations for a fluid - Boussinesq approximation - Vorticity - Two-dimensional flows, streamfunction - Irrotational flow: velocity potential, unsteady Bernoulli equation - Irrotational two-dimensional flow, complex velocity potential, streamlines and potential lines.

Boundary Layer Theory: Prandtl hypothesis for two-dimensional incompressible flows - Order of magnitude method - Momentum boundary layer: simplification of local momentum balance equation - Thermal boundary layer: simplification of local energy balance equation.

Similarity Solutions for External Flows: Blasius solution for the flow around a plane: velocity field and drag coefficient - Evaluation of the temperature field and of the Nusselt number.
Compressible Flows and Waves in a Fluid: General description - One-dimensional case - Three-dimensional case. 

Stability of Laminar Flows and Introduction to Turbulence: Stability and instability, logistic equation, heat conduction equation - Linear stability analysis of flows: Poiseuille flow in a plane channel - Orr-Sommerfeld equation and stability diagram - Analysis of turbulent flows: average components and stochastic components - Reynolds equations for two-dimensional turbulent flows - Reynolds tensor - Boussinesq hypothesis: eddy viscosity, eddy diffusivity, turbulent Prandtl number - Closure problem of Reynolds equations and turbulence models - Algebraic turbulence model: mixing length, Prandtl relationship.

Heat and Fluid Flow in Porous Media: Description of fluid flow in a porous medium - Darcy's law - Permeability of a porous medium - Darcy-Forchheimer's law - Local mass and energy balance equations - Examples of fluid flow in porous media.

Natural and Mixed Convection: Mixed convection in a plane parallel channel - Flow reversal effect, special case of free convection - Rayleigh Bénard problem.


- Lecture notes.

- S. Kakaç, Y. Yener - Convective Heat Transfer - CRC Press, 1994. 

- V.S. Arpaci, P.S. Larsen - Convection Heat Transfer - Prentice-Hall, 1984. 

- A. Barletta - Applicazioni della Fisica Termica. Argomenti Complementari di Fluidodinamica e Termocinetica - Pitagora, Bologna, 2002. 

- A. Bejan - Convection Heat Transfer - Wiley, 1984.

Teaching methods

Classroom lessons and guided solution of exercises 

Assessment methods

Concerning the teaching unit Thermo-Fluid-Dynamics M the exam consists in an oral test. The oral test is oriented to the evaluation of the achievement of an appropriate knowledge on the basic topics of the course, both under the theoretical perspective and for the capability to formulate, from a physico-mathematical viewpoint, and solve elementary problems of heat and fluid flow. 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