Modeling of heat transfer process with the use of non integer order, discrete, transfer function models

2017 ◽  
pp. 425-433
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Edyta Gawin
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Integer Order ◽  
Function Models ◽  
Discrete Transfer Function ◽  
Transfer Function Models

scholarly journals A non integer order, state space model for one dimensional heat transfer process

2016 ◽  
Vol 26 (2) ◽  
pp. 261-275 ◽  
Author(s):  
Krzysztof Oprzedkiewicz ◽  
Edyta Gawin
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Transfer Process ◽  
State Space Model ◽  
State Equation ◽  
Heat Transfer Process ◽  
Order Model ◽  
One Dimensional ◽  
Integer Order ◽  
Proposed Model

Abstract In the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer order operator. The elementary properties of the state operator are proven. The solution of state equation is calculated with the use of Laplace transform. Results of experiments show, that the proposed model is more accurate than analogical integer order model in the sense of square cost function.

scholarly journals Modelling heat transfer in heterogeneous media using fractional calculus

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120146 ◽  
Author(s):  
Dominik Sierociuk ◽  
Andrzej Dzieliński ◽  
Grzegorz Sarwas ◽  
Ivo Petras ◽  
Igor Podlubny ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Flux ◽  
Transfer Function ◽  
Transfer Process ◽  
Heterogeneous Media ◽  
Heat Transfer Process ◽  
Order Partial Differential Equation ◽  
Partial Differential

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.

Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus

2011 ◽  
Author(s):  
Dominik Sierociuk ◽  
Andrzej Dzielin´ski ◽  
Grzegorz Sarwas ◽  
Ivo Petras ◽  
Igor Podlubny ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Flux ◽  
Transfer Function ◽  
Transfer Process ◽  
Heterogeneous Media ◽  
Heat Transfer Process ◽  
Order Partial Differential Equation ◽  
Partial Differential

The paper presents the results of modeling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in solid material (beam) can be described by integer order partial differential equation. However, in heterogeneous media it can be described by sub- or hyperdiffusion equation which results in fractional order partial differential equation. Taking into consideration that the part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in the new form. This leads to the transfer function which describes the dependency between the heat flux at the beginning of the beam and the temperature at the given distance. The article also presents the experimental results of modeling real plant in the frequency domain basing on the obtained transfer function.

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