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Analysis of an asymptotic thermo fluid-dynamic model for parabolic trough power plants

Giuseppe Maria Coclite, Ingenuin Gasser

Abstract

Parabolic trough power plants transform solar radiative energy into thermal energy which is then typically used to produce electricity. We consider a model derived in \cite{BGSP} to describe parabolic trough power plants. In particular, the thermo-fluid dynamics is studied in a single collector pipe where the solar radiation is concentrated. The model is the result of simplifying assumptions and asymptotic processes on the underlying mass, momentum and energy balance equations. { We show existence of solutions for the model. In addition we study the long-time behaviour and the stationary problem.

Analysis of an asymptotic thermo fluid-dynamic model for parabolic trough power plants

Abstract

Parabolic trough power plants transform solar radiative energy into thermal energy which is then typically used to produce electricity. We consider a model derived in \cite{BGSP} to describe parabolic trough power plants. In particular, the thermo-fluid dynamics is studied in a single collector pipe where the solar radiation is concentrated. The model is the result of simplifying assumptions and asymptotic processes on the underlying mass, momentum and energy balance equations. { We show existence of solutions for the model. In addition we study the long-time behaviour and the stationary problem.

Paper Structure

This paper contains 6 sections, 12 theorems, 95 equations.

Table of Contents

  1. Introduction
  2. Thermo-fluid dynamics in a single pipe
  3. Proof of Theorem \ref{['th:main']}
  4. Proof of Theorem \ref{['th:main02']}
  5. Conclusion
  6. A comment on the validity of assumption (\ref{['eq:ass3']})

Key Result

Theorem 2.2

Assume eq:ass1 and eq:ass3. The initial boundary value problem eq:CL admits an entropy solution $(\rho,\,p)$ in the sense of Definition def:sol.

Theorems & Definitions (26)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Remark 2.4
  • Theorem 2.5
  • Remark 2.6
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 16 more