Conduction. - WPMECOD2

Goal(s)

Provide the necessary elements to enable students to carry out heat exchange calculations first using the concepts of thermal resistance before moving on to more sophisticated methods such as finite volumes.

Content(s)

In this heat conduction course, we will study the fundamental mechanisms of heat transfer, which corresponds to thermal energy in motion under the effect of a temperature gradient. This phenomenon, ubiquitous whenever there is a temperature difference within a medium or between several media, is manifested in particular by conduction: a mode of transfer where heat propagates through a stationary medium, whether solid or fluid, without macroscopic movement of matter. This process relies on the diffusion of molecular agitation, thus allowing for a gradual temperature equilibrium.
We will first discuss the heat equator in the stationary limit. In the absence of a heat source, we will introduce the concept of thermal resistance. Different types of boundary conditions will be applied, such as Robin's boundary conditions related to convection and Stefan's boundary conditions for radiation. A chapter will be devoted to the study of fins and their application in cooling an engine cylinder. To further explore these concepts, an opening will be made on the numerical resolution of the heat equation by the finite volume method. This approach, widely used in thermal simulation, makes it possible to discretize the study domain and to solve the energy conservation equations in a robust and precise manner, thus opening the way to various industrial and scientific applications.

Level M1 mathematics and a basis in python programming

Test

Written exam (1 hour). All document permitted, calculator permitted. Same for the second session.

Additional Information

Bibliography

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, et David P. DeWitt. Fundamentals of Heat and Mass Transfer. $8^e$ éd. Hoboken, NJ : John Wiley \& Sons, 2020. ISBN 978?1119722489

Çengel, Yunus A., and Afshin J. Ghajar. Heat and Mass Transfer: Fundamentals \& Applications. $6^e$ éd. New York : McGraw?Hill Education, 2019. ISBN 978?0073398198

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Taine, Jean, Franck Enguehard, et Estelle Iacona. Transferts thermiques: Introduction aux transferts d’énergie – Cours et exercices d’application. $6^e$ éd. Paris: Dunod, 2021.
ISBN 978-2100821662

Lienhard, John H. V., et John H. Lienhard IV. A Heat Transfer Textbook. $6^e$ éd. Cambridge, MA: Phlogiston Press, 2024. ISBN 978?0486837352

Marty, Philippe. Cours de transferts thermiques : Conduction et rayonnement. Licence L3, Université Joseph Fourier (Grenoble), version du 9 juillet 2012.