Accuracy Estimation of the Fractional, Discrete-Continuous Model of the One-Dimensional Heat Transfer Process

2020 ◽  
pp. 1155-1166
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Klaudia Dziedzic
Keyword(s):  
Heat Transfer ◽  
Transfer Process ◽  
Continuous Model ◽  
Heat Transfer Process ◽  
Accuracy Estimation ◽  
One Dimensional ◽  
The One

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.

The One-equation Model for the Heat Transfer Process in an Oil Field

2013 ◽  
Vol 31 (1) ◽  
pp. 13-22 ◽  
Author(s):  
G. Espinosa-Paredes ◽  
A. Vázquez-Rodríguez ◽  
E.-G. Espinosa-Martínez ◽  
H. Romero-Paredes ◽  
R. Vázquez-Rodríguez ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Equation Model ◽  
Oil Field ◽  
The One

Design of the Blast Furnace Wall Structure Made of Efficient Materials. Part 4. Calculation Examples

2020 ◽  
Vol 786 (11) ◽  
pp. 30-34
Author(s):  
A.M. IBRAGIMOV ◽  
◽  
L.Yu. GNEDINA ◽  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Blast Furnace ◽  
Boundary Value Problems ◽  
Transfer Process ◽  
Rational Design ◽  
Boundary Value ◽  
Heat Transfer Process ◽  
Furnace Wall ◽  
Time Interval

This work is part of a series of articles under the general title The structural design of the blast furnace wall from efficient materials [1–3]. In part 1, Problem statement and calculation prerequisites, typical multilayer enclosing structures of a blast furnace are considered. The layers that make up these structures are described. The main attention is paid to the lining layer. The process of iron smelting and temperature conditions in the characteristic layers of the internal environment of the furnace is briefly described. Based on the theory of A.V. Lykov, the initial equations describing the interrelated transfer of heat and mass in a solid are analyzed in relation to the task – an adequate description of the processes for the purpose of further rational design of the multilayer enclosing structure of the blast furnace. A priori the enclosing structure is considered from a mathematical point of view as the unlimited plate. In part 2, Solving boundary value problems of heat transfer, boundary value problems of heat transfer in individual layers of a structure with different boundary conditions are considered, their solutions, which are basic when developing a mathematical model of a non-stationary heat transfer process in a multi-layer enclosing structure, are given. Part 3 presents a mathematical model of the heat transfer process in the enclosing structure and an algorithm for its implementation. The proposed mathematical model makes it possible to solve a large number of problems. Part 4 presents a number of examples of calculating the heat transfer process in a multilayer blast furnace enclosing structure. The results obtained correlate with the results obtained by other authors, this makes it possible to conclude that the new mathematical model is suitable for solving the problem of rational design of the enclosing structure, as well as to simulate situations that occur at any time interval of operation of the blast furnace enclosure.

Numerical Simulation for Microconvection Around Nano-Particle With Brownian Motion in Liquid

2003 ◽  
Author(s):  
B. X. Wang ◽  
H. Li ◽  
X. F. Peng ◽  
L. X. Yang
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Brownian Motion ◽  
Numerical Model ◽  
Temperature Gradient ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Nano Particles ◽  
Analytic Method ◽  
Nano Particle

The development of a numerical model for analyzing the effect of the nano-particles’ Brownian motion on the heat transfer is described. By using the Maxwell velocity distribution relations to calculate the most possible velocity of fluid molecules at certain temperature gradient location around the nano-particle, the interaction between fluid molecules and one single nano-particle is analyzed and calculated. Based on this, a syntonic system is proposed and the coupled effect that Brownian motion of nano-particles has on fluid molecules is simulated. This is used to formulate a reasonable analytic method, facilitating laboratory study. The results provide the essential features of the heat transfer process, contributed by micro-convection to be considered.

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