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Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials

✍ Scribed by M. T. Laitinen; T. Tiihonen

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
289 KB
Volume
21
Category
Article
ISSN
0170-4214

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✦ Synopsis

In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions.

📜 SIMILAR VOLUMES

Solution of parabolic integro-differenti
Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He's variational iteration technique
✍ Mehdi Dehghan; Fatemeh Shakeri 📂 Article 📅 2010 🏛 Wiley (John Wiley & Sons) 🌐 English ⚖ 327 KB

## Abstract In this work, we present the solution of some parabolic integro‐differential equations, which naturally arise in many applications. He's variational iteration method is implemented to give the solution for this equation. This technique is based on the incorporation of a general Lagrange