scholarly journals Graph Theory-Based Mathematical Calculation Modeling for Temperature Distribution of LED Lights’ Convective Cooled Heat Sinks under Moisture Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Bei-xuan Lyu ◽  
Yu-ren Chen ◽  
Yong Li
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Graph Theory ◽  
Transfer Process ◽  
Heat Sink ◽  
Heat Transfer Process ◽  
Heat Sinks ◽  
Junction Temperature ◽  
Model Based ◽  
Led Lights

In this paper, a mathematical model based on graph theory is proposed to calculate the heat distribution of LED lights’ convective cooled heat sink. First, the heat and mass transfer process of a single fin under moisture environment is analyzed. Then, the heat transfer process is characterized by a digraph, defining fins and joints of a heat sink as edges and vertices in graph theory. Finally, the whole heat transfer process is described by two criteria achieved based on graph theory. Therefore, the temperature-heat calculation equations of the whole heat sink are deduced. The accuracy of this model is verified by testing the junction temperature of different LED chips mounted on the same heat sink under moisture environment, and the relative errors between the calculated value and the experimental data are all within 5%, and it is also concluded from the model that heat sinks with an identical heat digraph but different types have close cooling performance and are verified by two typical heat sinks, cylindrical heat sink and rectangular plate-fin heat sink, under the same conditions. The mathematical model based on group theory developed in this paper combined with computer technology is convenient for the performance analysis among a large number of heat sink fin arrangement schemes.

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.

The Research on the Heat Transfer Process of Low Temperature Hot Water Radiant Heating Phase Change Wallboard

2013 ◽  
Vol 800 ◽  
pp. 18-21
Author(s):  
Quan Ying Yan ◽  
Li Hang Yue ◽  
Ran Huo
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Low Temperature ◽  
Phase Change ◽  
Physical Model ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Hot Water ◽  
Radiant Heating ◽  
Heating Phase

In this paper, physical model and mathematical model of the hot water radiant heating phase change wallboard were built. The heat transfer process of wallboard was simulated to analyze different influencing factors and optimize the design of the hot water heating phase change wallboard. The research results can provide reference and basis to the optimization of low temperature hot water radiant heating phase change wallboard.

Modeling Cooling Process of High Temperature Sinter

2011 ◽  
Vol 71-78 ◽  
pp. 2411-2415 ◽  
Author(s):  
Guo Feng Lou ◽  
Zhi Wen ◽  
Xun Xiang Liu ◽  
Xin Zhang ◽  
Kun Chan Zheng ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
High Temperature ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Measured Data ◽  
Cooling Process ◽  
Temperature Sinter ◽  
High Temperature Sinter ◽  
Operation Parameters

In the paper, a 1-D unsteady mathematical model for the Gas-Solid heat transfer process of high temperature sinter has been developed, and is used to analyse the cooling process of high temperature sinter. A set of measured data is used to verify the modeling result. The agreement between the measured and the modeling is good. The effect of operation parameters on the cooling process of the annular cooler has been investigated.

scholarly journals A proposal method for reducing the order of general heat conduction equation

2018 ◽  
Vol 20 ◽  
pp. 02014
Author(s):  
Thanh-Phong Tran
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Transfer Process ◽  
Heat Conduction Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Heat Transfer Process ◽  
Unknown Parameters ◽  
Simulation Experiments ◽  
Three Dimensional Space

In the context of investigating methods dedicated to identifying unknown parameters of the system described by partial differential equations, particularly in the field of heat transfer, it has been realized that the heat transfer process in particular three-dimensional features is really complex and takes longer to calculate. Therefore, an equivalent mathematical model which is simpler proposed to reduce the calculation time and the costs of experimental activities. We observe that the mathematical models of the diffusion equation can be minimized in three-dimensional space into a similar two-dimensional pattern within certain limits did not change the physical properties of heat transfer process. A mathematical model and the numerical results of simulation experiments in order to prove effectiveness the proposed method will be presented in detail in this article.

Effect of Synthetic Jets Over Natural Convection Heat Sinks

2008 ◽  
Author(s):  
Mehmet Arik ◽  
Yogen Utturkar ◽  
Murat Ozmusul
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Sink ◽  
Heat Dissipation ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Operating Conditions ◽  
Heat Sinks ◽  
Junction Temperature ◽  
Allowable Limit

In moderate power electronics applications, the most preferred way of thermal management is natural convection to air with or without heat sinks. Though the use of heat sinks is fairly adequate for modest heat dissipation needs, it suffers from some serious performance limitations. Firstly, a large volume of the heat sink is required to keep the junction temperature at an allowable limit. This need arises because of the low convective film coefficients due to close spacing. In the present computational and experimental study, we propose a synthetic jet embedded heat sink to enhance the performance levels beyond two times within the same volume of a regular passive heat sink. Synthetic jets are meso-scale devices producing high velocity periodic jet streams at high velocities. As a result, by carefully positioning of these jets in the thermal real estate, the heat transfer over the surfaces can be dramatically augmented. This increase in the heat transfer rate is able to compensate for the loss of fin area happening due to the embedding of the jet within the heat sink volume, thus causing an overall increase in the heat dissipation. Heat transfer enhancements of 2.2 times over baseline natural convection cooled heat sinks are measured. Thermal resistances are compared for a range of jet operating conditions and found to be less than 0.9 K/W. Local temperatures obtained from experimental and computational agreed within ± 5%.

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