scholarly journals Метод восстановления моделей тепломассопереноса по пространственно-временным распределениям параметров

2021 ◽  
Vol 47 (24) ◽  
pp. 9
Author(s):  
Н.Ю. Быков ◽  
А.А. Хватов ◽  
А.В. Калюжная ◽  
А.В. Бухановский
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Phase Transitions ◽  
Laser Radiation ◽  
High Efficiency ◽  
Design Method ◽  
Temperature Dependent ◽  
Partial Differential ◽  
Correct Structure

An algorithm of the generative design method for reconstruction of heat transfer models from the available data is proposed. The method is applied to generate a partial differential equation describing the process of heating and evaporation of a metal, the surface of which is heated by laser radiation. The high efficiency of the method was demonstrated for the purpose of reconstructing the correct structure of the equation, indicating additional processes accompanying heating as phase transitions, and also for determining the values of the temperature-dependent coefficients of the derivatives.

Invariance, Conservation Laws, and Exact Solutions of the Nonlinear Cylindrical Fin Equation

2014 ◽  
Vol 69 (5-6) ◽  
pp. 195-198 ◽  
Author(s):  
Saeed M. Ali ◽  
Ashfaque H. Bokhari ◽  
Fiazuddin D. Zaman ◽  
Abdul H. Kara
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Exchange ◽  
Thermal Diffusivity ◽  
Conservation Laws ◽  
Cylindrical Shape ◽  
Method Of Multipliers ◽  
Double Reduction ◽  
Temperature Dependent

Fins are heat exchange surfaces which are used widely in industry. The partial differential equation arising from heat transfer in a fin of cylindrical shape with temperature dependent thermal diffusivity are studied. The method of multipliers and invariance of the differential equations is employed to obtain conservation laws and perform double reduction.

scholarly journals A Numerical Well-Balanced Scheme for One-Dimensional Heat Transfer in Longitudinal Triangular Fins

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
I. Rusagara ◽  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Transfer Coefficients ◽  
Partial Differential ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Highly Nonlinear ◽  
Triangular Fin

The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution in a one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile.

A Two-Temperature Model of the Regenerative Solid-Vapor Heat Pump

1994 ◽  
Vol 116 (4) ◽  
pp. 297-304 ◽  
Author(s):  
T. A. Fuller ◽  
W. J. Wepfer ◽  
S. V. Shelton ◽  
M. W. Ellis
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Pump ◽  
Flow Direction ◽  
Time And Space ◽  
Partial Differential ◽  
Thermodynamic Performance ◽  
Heat Regeneration ◽  
Two Temperature

A thermally driven heat pump using a solid/vapor adsorption/desorption compression process is thermodynamically analyzed. Heat regeneration between the two adsorbent beds is accomplished through the use of a circulating heat transfer (HX) fluid. Effective heat regeneration and system performance requires that steep thermal profiles or waves be established in the beds along the path of the HX-fluid flow direction. Previous studies by Shelton, Wepfer, and Miles have used square and ramp profiles to approximate the temperature profiles in the adsorbent beds, which, in turn, enable the thermodynamic performance of the heat pump to be computed. In this study, an integrated heat transfer and thermodynamic model is described. The beds are modeled using a two-temperature approach. A partial differential equation for the lumped adsorbent bed and tube is developed to represent the bed temperature as a function of time and space (along the flow direction), while a second partial differential equation is developed for the heat transfer fluid to represent the fluid temperature as a function of time and space (along the flow direction). The resulting differential equations are nonlinear due to pressure and temperature-dependent coefficients. Energy and mass balances are made at each time step to compute the bed pressure, mass, adsorption level, and energy changes that occur during the adsorption and desorption process. Using these results, the thermodynamic performance of the heat pump is calculated. Results showing the heat pump’s performance and capacity as a function of the four major dimensionless groups, DR, Pe, Bi, and KAr, are presented.

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.

scholarly journals Investigation of High-Efficiency Iterative ILU Preconditioner Algorithm for Partial-Differential Equation Systems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1461 ◽  
Author(s):  
Yan-Hong Fan ◽  
Ling-Hui Wang ◽  
You Jia ◽  
Xing-Guo Li ◽  
Xue-Xia Yang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Systems ◽  
High Efficiency ◽  
Iterative Scheme ◽  
Processing Unit ◽  
Matrix Equations ◽  
Partial Differential ◽  
Central Processing ◽  
Ilu Factorization

In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used. The ILU preconditioners of linear systems are performed on the different computation nodes of multi-central processing unit (CPU) cores. Firstly, the preconditioner of general tridiagonal matrix equations is tested on supercomputers. Then, the effects of partial-differential equation systems on the speedup of parallel multiprocessors are examined. The numerical results estimate that the parallel efficiency is higher than in other algorithms.

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