scholarly journals Effects of the Solder Phase Transformation on the Optimization of Reflow Soldering Parameters and Temperature Profiles

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Yongze Xu ◽  
Yu Liu ◽  
Lei Zhang
Keyword(s):  
Heat Transfer ◽  
Transfer Problem ◽  
Linear Equations ◽  
Transition Process ◽  
Coefficient Matrix ◽  
Temperature Profiles ◽  
Conduction Model ◽  
Reflow Soldering ◽  
Heat Transfer Theory ◽  
Convection Model

In this study, a heat convection model of the reflow oven and a heat conduction model of the soldering area are proposed based on heat transfer theory, and a dynamic Thomas algorithm is developed for solving linear equations with coefficient matrix evolving over time in the tridiagonal system, which is derived from a heat transfer problem with moving boundaries in the solder phase transition process. We have also carried out numerical simulations for investigating the accuracy of the mathematical model, in which the temperature profiles are calculated and compared for different cases with considering or ignoring phase transformations, respectively. Parameters of reflow soldering, such as the conveyor speed, the set temperature in each zone, and a part of the heating factor, are optimized by the use of the nondominated sorting genetic algorithm II. By comparing the temperature profile and optimal solutions in the two cases, numerical results show that phase transitions of the solder have great impacts on optimal parameters and the slope of temperature profiles. Moreover, the phenomenon that the heating factor varies with the maximum set temperature in a banded distribution is investigated and analyzed, which is an important part of this work.

Analysis of Heat Distributing to Ensure Energy Saving

2013 ◽  
Vol 724-725 ◽  
pp. 880-884
Author(s):  
Xiao Chang ◽  
Tian Chi Li ◽  
Yu Bo Xian ◽  
Xin Chao Zhao
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Heat Conduction ◽  
Outer Edge ◽  
Heat Distribution ◽  
Order Partial Differential Equation ◽  
Conduction Model ◽  
Heat Transfer Theory ◽  
Different Shapes ◽  
Save Energy

In this paper, we present a mathematical model which aims to save energy of household appliances, take the brownie pan as example we take advantage of the heat conduction and draw the conclusion that the pan in shape with more edges has more even distribution of heat. In most cases, the shape of rectangle is the best choice to save energy when bake. In Heat conduction model, We raise a conception of doneness to accurately measure how hard the food is being baked, and we handle a second-order partial differential equation based on the heat transfer theory, considering both evenly heating vertically and heat transferring horizontally. We focus on the ratio of how well roasted the edges and the corners are shows the distribution of heat across the outer edge of a pan for pans of different shapes. The variance of all points heating level on the pan shows the evenness of the heat distribution.

scholarly journals Linear computational cost implicit solver for elliptic problems

2020 ◽  
Vol 21 (3) ◽  
Author(s):  
Grzegorz Gurgul ◽  
Marcin Los ◽  
Maciej Paszynski ◽  
Victor Calo
Keyword(s):  
Heat Transfer ◽  
Transfer Problem ◽  
Linear Equations ◽  
Computational Cost ◽  
Basis Functions ◽  
Implicit Method ◽  
Time Step ◽  
B Spline ◽  
Spline Basis ◽  
Intermediate Time

In this paper, we use the alternating direction method for isogeometric finite elements to simulate implicit dynamics. Namely, we focus on a parabolic problem and use B-spline basis functions in space and an implicit marching method to fully discretize the problem. We introduce intermediate time steps and separate our differential operator into a summation of the blocks, acting along a particular coordinate axis in the intermediate time steps. We show that the resulting stiffness matrix can be represented as a multiplication of two (in 2D) or three (in 3D) multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. As a result of this algebraic transformations, we get a system of linear equations that can be factorized in linear $O(N)$ computational cost in every time step of the implicit method. We use our method to simulate the heat transfer problem. We demonstrate theoretically and verify numerically that our implicit method is unconditionally stable for heat transfer problems (i.e., parabolic). We conclude our presentation with a discussion on the limitations of the method.

Thermal Behavior of Aluminum Rolling

1990 ◽  
Vol 112 (2) ◽  
pp. 301-308 ◽  
Author(s):  
A. A. Tseng ◽  
S. X. Tong ◽  
S. H. Maslen ◽  
J. J. Mills
Keyword(s):  
Heat Transfer ◽  
Aluminum Alloys ◽  
Hot Rolling ◽  
High Speed ◽  
Critical Factor ◽  
Work Roll ◽  
Operating Parameters ◽  
Temperature Profiles ◽  
Rolling Mills ◽  
Heat Transfer Theory

Proper roll cooling has been identified as a critical factor in the problems of excessive roll spalling and poor thermal crowning in modern, high-speed rolling mills. In this paper, an analytical model has been developed to determine the temperature profiles of the roll and the strip. This model uses basic heat transfer theory and provides the capability of studying the influence of operating parameters on both the work-roll and workpiece temperatures. Examples on cold and hot rolling of aluminum alloys are given to demonstrate the feasibility and capability of the model developed. Previous work on thermal modeling of rolling processes is also briefly reviewed.

Numerical Simulation Research of Velocity and Temperature Fields in High Temperature Flow of Liquid Lend-Bismuth Eutectic

2014 ◽  
Vol 541-542 ◽  
pp. 1333-1337
Author(s):  
Yun Bo Li ◽  
Tao Zhou ◽  
Qin Jun Huo ◽  
Xu Yang
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Gas Injection ◽  
Temperature Fields ◽  
Temperature Profiles ◽  
Two Phase ◽  
Simulation Research ◽  
Heat Transfer Theory ◽  
Velocity And Temperature Fields ◽  
Section Analysis

On basis of two-phase flow and the heat transfer theory, the velocity and temperature of the liquid lend-bismuth eutectic were calculated with gas-injection and without gas-injection by FLUENT code, in the calculation segment. The radial velocity profiles and temperature profiles were acquired at different cross section. Analysis results show that: no matter the argon is existence or not, the velocity distribution and the temperature distribution have a good symmetry. Temperature rise of the liquid lend-bismuth eutectic with gas injected is larger than without argon. It is shown that the gas-injection is good for heat transfer of liquid lend-bismuth in the calculation segment.

Experiments on the Onset of Longitudinal Vortices in Horizontal Blasius Flow Heated from Below

1978 ◽  
Vol 100 (1) ◽  
pp. 71-77 ◽  
Author(s):  
R. R. Gilpin ◽  
H. Imura ◽  
K. C. Cheng
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Surface Temperature ◽  
Flat Plate ◽  
Transfer Rate ◽  
Thermal Instability ◽  
Transition Process ◽  
Temperature Profiles ◽  
Longitudinal Vortices ◽  
Turbulent Transition

Experiments were performed to confirm the occurrence and growth of longitudinal vortices in a laminar boundary layer developing in water over a heated horizontal flat plate with uniform surface temperature. Photographs of the vortices, measurements of the conditions of their onset, and measurements of their wavelength are presented. Comparisons are made with theoretical instability results for the critical Grashof number and wavelength. Temperature profiles across the boundary layer were measured for flows with and without vortices to show qualitatively the effect that the longitudinal vortices have on the heat transfer rate at the plate. Under conditions of thermal instability the longitudinal vortices were found to be the first stage of the laminar-turbulent transition process in a boundary layer heated from below.

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