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**On reachability of parallel-flow heat exchanger equations with boundary inputs.**
*(English)*
Zbl 1119.93015

This paper is concerned with the problem of reachability for parallel flow two-fluid heat exchanger equations with boundary inputs. It is shown that the boundary control system is well defined in the sense of [R. F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory. Texts in Applied Mathematics. 21. (New York), NY: Springer-Verlag. (1995; Zbl 0839.93001)] and that it is reachable. The proof gives a concrete expression of the corresponding controls. This is possible since the author obtains an explicit solution of the considered system through the method of characteristics. This representation of the solution allows a very clear analysis of the reachability problem. A reachable subspace is given for the case where only one boundary input is added to the system.

Reviewer: Martin Gugat (Erlangen)

### MSC:

93B03 | Attainable sets, reachability |

35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |

93C20 | Control/observation systems governed by partial differential equations |

### Keywords:

Parallel-flow heat exchanger equation; boundary input; reachability; characteristic differential equation; \(C_0\)-semigroup### Citations:

Zbl 0839.93001
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\textit{H. Sano}, Proc. Japan Acad., Ser. A 83, No. 1, 1--4 (2007; Zbl 1119.93015)

### References:

[1] | Journal of the Society of Instrument and Control Engineers, 19 (1980), no. 11. (in Japanese). |

[2] | R. F. Curtain and H. J. Zwart, An introduction to infinite-dimensional linear systems theory , Texts in Applied Mathematics, vol. 21, Springer-Verlag, New York, 1995. · Zbl 0839.93001 |

[3] | K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations , Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000. · Zbl 0952.47036 |

[4] | M. A. Jaswon and W. Smith, Countercurrent transfer processes in the non-steady state, Proc. Roy. Soc., Series A, 225 (1954), pp. 226-244. |

[5] | C. H. Li, Exact transient solutions of parallel-current transfer processes, ASME Journal of Heat Transfer, 108 (1986), pp. 365-369. |

[6] | L. Malinowski and S. Bielski, An analytical method for calculation of transient temperature field in the counter-flow heat exchanges, Int. Comm. Heat Mass Transfer, 31 (2004), no. 5, pp. 683-691. |

[7] | H. Sano, On observability and reachability of parallel-flow heat exchanger equations, Proceedings of Electronics, Information and Systems Conference 2005, Electronics, Information and Systems Society, I.E.E. of Japan, pp. 909-914. (in Japanese). |

[8] | Y. Takahashi, Transfer function analysis of heat exchange processes, in Automatic and Manual Control , A. Tustin (ed.), Butterworth Scientific Publications, London, 1952, pp. 235-248. |

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