Lecture

Heat Equation: Stationary Distribution

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In course

ME-212: Mechanical Design I: Manufacturing Processes

Application des principales catégories de procédés de production. Modèles physiques élémentaires décrivant le comportement des principaux procédés de production. Compréhension de base des aspects économiques des procédés de production. Méthodologie de ...

Description

This lecture covers the heat equation and the concept of stationary temperature distribution, exploring equilibrium equations, heat flux, thermal conductivity, and thermal diffusivity. It delves into harmonic functions in one and two dimensions, as well as cylindrical and spherical symmetry in heat distribution.

Instructor

Eric Boillat

Contact Microcity Phone: 41 21 69 54456 Teaching & PhD Past EPFL PhD Students as codirector Serguei Kolossov, Cédric André, Jamasp Jhabvala, Christoph Van Gestel, Tatiana Polivnikova, Nikola Kalentics Courses Industrial production processes ME-212 Application windows of the main manufacturing process categories. Implementation of simple models describing the behavior of the main manufacturing processes. Basic understanding of the economic aspects of production processes. Manufacturing proc

Official source

Related concepts (31)

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 coefficient

In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT ). It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2/K).

Thermal conductivity

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or . Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like mineral wool or Styrofoam.

Heat flux sensor

A heat flux sensor is a transducer that generates an electrical signal proportional to the total heat rate applied to the surface of the sensor. The measured heat rate is divided by the surface area of the sensor to determine the heat flux. The heat flux can have different origins; in principle convective, radiative as well as conductive heat can be measured. Heat flux sensors are known under different names, such as heat flux transducers, heat flux gauges, or heat flux plates.

Heat kernel

In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0.

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