Lecture

Heat Transfer and Boundary Conditions

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In course

CH-250: Mathematical methods in chemistry

This course consists of two parts. The first part covers basic concepts of molecular symmetry and the application of group theory to describe it. The second part introduces Laplace transforms and Fourier series and their use for solving ordinary and partia ...

Description

This lecture covers the fundamental concepts of heat transfer, including Fourier's law and heat balance equations. It also discusses boundary conditions for heat conduction problems in 1D and 2D, such as Dirichlet and Neumann boundary conditions. The lecture further explores eigenvalue problems and steady-state temperatures in square plates, as well as solutions for particle confinement in a box. The presentation concludes with a practical application using Wolfram Mathematica to visualize wave functions in quantum mechanics.

Instructors (2)

Jiri Vanicek

Teaching & PhD PhD Students Liam Oliver Marsh, Yeha Lee, Davide Barbiero, Yannick Calvino Alonso, Manas Nagda Past EPFL PhD Students Cesare Mollica, Ray Marcel Marin Florez, Marius Wehrle, Aurélien Patoz, Konstantin Karandashev, Tomislav Begusic, Julien Roulet, Seonghoon Choi, Roya Moghaddasi Fereidani, Zhan Tong Zhang, Eriks Kletnieks, Alan Scheidegger, Fabian Kröninger Courses Mathematical methods in chemistry CH-250 This course consists of two parts. The first part covers basic concepts

Ulrich Lorenz

Teaching & PhD PhD Students Jakub Hruby Past EPFL PhD Students Pavel Olshin, Gabriele Bongiovanni, Chengcheng Yan, Oliver Florian Harder, Mowry Nathan Junior, Constantin Richard Krüger

Official source

Related concepts (32)

Thermal conduction

Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denoted k. Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it.

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer.

Convection (heat transfer)

Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow). Convection is usually the dominant form of heat transfer in liquids and gases. Note that this definition of convection is only applicable in Heat transfer and thermodynamic contexts.

Heat

In thermodynamics, heat is the thermal energy transferred between systems due to a temperature difference. In colloquial use, heat sometimes refers to thermal energy itself. An example of formal vs. informal usage may be obtained from the right-hand photo, in which the metal bar is "conducting heat" from its hot end to its cold end, but if the metal bar is considered a thermodynamic system, then the energy flowing within the metal bar is called internal energy, not heat.

Relativistic heat conduction

Relativistic heat conduction refers to the modelling of heat conduction (and similar diffusion processes) in a way compatible with special relativity. In special (and general) relativity, the usual heat equation for non-relativistic heat conduction must be modified, as it leads to faster-than-light signal propagation. Relativistic heat conduction, therefore, encompasses a set of models for heat propagation in continuous media (solids, fluids, gases) that are consistent with relativistic causality, namely the principle that an effect must be within the light-cone associated to its cause.

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Heat: Transport and Boundary Conditions

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Microscopic Heat Transport: Modes and Laws

Explores microscopic heat transport modes and laws, including Fourier's law and Newton's law, highlighting thermal conductivity principles.

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