Transfer-Matrix Method for Calculus of Long Cylinder Tube with Industrial Applications

Luminita Codrea, Mihai-Sorin Tripa, Daniel Opruţa, Robert Gyorbiro and Mihaela Suciu ()
Additional contact information
Luminita Codrea: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mihai-Sorin Tripa: Department of Design Engineering and Robotics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Daniel Opruţa: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Robert Gyorbiro: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mihaela Suciu: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2023, vol. 11, issue 17, 1-24

Abstract: The Transfer-Matrix Method (TMM) is an original and relatively simple mathematical approach for the calculus of thin-walled cylindrical tubes presented in this work. Calculation with TMM is much less used than calculation with the Finite Elements Method (FEM), even though it is much easier to apply in different fields. That is why it was considered imperative to present this original study. The calculus is based on Dirac’s and Heaviside’s functions and operators and on matrix calculation. The state vectors, the transfer-matrix, and the vector corresponding to the external efforts were defined, which were then used in the calculations. A matrix relation can be written, which gives the state vector of the last section depending on the state vector of the first section, a relation in which the conditions of the two end supports can be set. As an application, a heat exchanger was studied, with a large cylinder subjected to a uniformly distributed internal load, and from the inner cylinder bundle, a cylinder subjected to both uniform internal and external loads was considered. For the second cylinder, two possibilities of action for the external forces were considered, a successive action and a simultaneous action, achieving the same results in both situations. The TMM is intended to be used for iterative calculus in optimization problems where rapid successive results are required. In the future, we want to expand this method to other applications, and we want to develop related programs. This is an original theoretical study and is a complement to the research in the field on thin-walled cylinder tubes and their applications in heat exchangers.

Keywords: mathematical model of thin-walled cylindrical tube; load density; state vector; Transfer-Matrix Method; Dirac’s function; Heaviside’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/17/3756/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/17/3756/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:17:p:3756-:d:1230359

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().