Heat Transfer


Learn new concepts and become familiar with the analytical techniques in the three domains of heat transfer: conduction, convection and radiation.

Acquire skills to formulate and solve common problems concerning heat transfer in various engineer situations such as insulation and heat exchange.

 Learn to manage the limited time available at all moments of evaluation.

General characterization





Responsible teacher

Daniel Cardoso Vaz, José Fernando de Almeida Dias


Weekly - 5

Total - 90

Teaching language



It is assumed the knowledge of the matters dealt with in: «Física II», «Análises Matemáticas», «Dinâmica dos Fluidos» I and II.

The written and laboratory work evaluations have implicit that the student is able to express his/hers train of thought intelligibly, either in portuguese or english, and to apply the tools that were used in the course.


1. Carvalho, J. L. (2017), "Transferência de Calor e Eficiência Energética", NOVA Editorial - FCT/UNL.

2. Incropera e DeWitt (2011), "Fundamentals of Heat and Mass Transfer", John Wiley & Sons.

3. Holman, J. P. (2010), "Heat Transfer", McGraw-Hill.

4. Çengel, Yunus A. (2006), "Heat and Mass Transfer: A Practical Approach", McGraw‑Hill.

5. Bejan, Adrian (2013), "Heat Transfer", John Wiley & Sons.

6. Figueiredo, Rui (2015), "Transmissão de Calor - Fundamentos e Aplicações", Ed. Lidel.

Teaching method

The presentation of the subjects, using the board and audiovisual media, is made either in classes designated as theoretical (2h) or practices (3h), progressing the matter in a continuous method. That is, immediately after presentation, practical problems are presented by the teacher and solved by the students, with the help of teacher, which aims to consolidate the newly taught concepts.

Evaluation method

Continuous assessment is made by holding two tests, T1 and T2, contributing 45% and 40%, respectively. Additionally, an experimental work of group  in the laboratory, allows obtaining frequency.

In case the pandemic situation forbids the laboratory work, it shall be replaced by an individual work to be performed remotely.

If T1>=7,5 val. the student may opt for not do the laboratory work and then the final grade is NF=0,45*T1+0,40*T2+0,15*(T1+2,0). Otherwise the student must perform the laboratory work to get access to the exam.

In the exam route, if EX < 9,5 then the student fails with NF=EX, otherwise NF=0,85*EX + 0,15*TL if he/she did the laboratory work, or NF=EX otherwise.

The terms enter in this expression rounded to the first decimal place.

The short tests and exams, whenever presential, are closed-book. Formulae, or charts,  found  necessary will be given. Transgressions are subjected to what is foreseen in art. 9 of the RAC.

Subject matter

1- Heat transfer modes: Fourier, Newton and Stefan-Boltzmann laws. Heat diffusion equation. Thermal diffusivity. Isotherms and heat flux. Electrical analogy.

2- Uni and multi-dimensional steady-state conduction: mathematical and numerical methods (finite differences).

3- Dynamic conduction: Biot and Fourier numbers. The Heisler charts. Periodic regime.

4- Forced convection: differential energy conservation equation in the thermal boundary layer. Prandtl and Nusselt numbers. Turbulent regime. Empirical correlations.

5- Heat exchangers: thermal design by the LMTD and effectiveness methods.

6- Natural convection.  Local Grashof and  Nusselt numbers. Mean values . Empirical correlations for laminar and turbulent regimes.

7- Radiation: properties. The black body. Kirchhoff law. Wien''s displacement law. Gray bodies. Monochromatic and total emissivities. Shape factors. Fundamentals of environmental radiation and thermalsolarenergy.


Programs where the course is taught: