A heat-flux based “building block” approach for solving heat conduction problems

Monte, Filippo de; Beck, James V.; Amos, Donald E.

doi:10.1016/j.ijheatmasstransfer.2011.02.060

Cited by 27 publications

(6 citation statements)

References 11 publications

(28 reference statements)

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“…Another important researching direction is to use a heatflux based "building block" approach to control temperature in our system. In the method, it can use a sequential numerical form of the two-dimensional transient Green's function solution equation based on a heat-flux formulation, thus achieving the function of temperature prediction and regulation (see, e.g., [12]).…”

Section: Resultsmentioning

confidence: 99%

“…Meanwhile, a heat-flux based "building block" approach is also available; this method gives a sequential numerical form of the twodimensional transient Green's function solution equation based on a heat-flux formulation. It is appropriate for solving forward and inverse linear heat conduction problems and gives us guidance to our work [12]. Following the research line, plenty of possible control strategies or methods to control the laser power to track some target temperature curves have been developed.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Thermodynamic Model and Temperature Control Method of Laser Soldering Systems

Chen

Zheng

et al. 2015

Mathematical Problems in Engineering

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Laser technology is vital in production of precision electronic components and has been widely used in modern industry. In laser soldering systems, accurate temperature control remains a challenging problem, since the temperature is highly sensitive to laser power and thermodynamic parameters of solder joints. In this paper, a good solution is proposed to solve the problem by controlling the temperature based on a novel thermodynamic model. In the model, many of the major factors are taken into account, such as laser energy, flux influence, and solder joints with different parameters. Aimed at the thermodynamic process and the influence of solder fluxes, a mixed mode control method is used to track the designed target temperature curve; this method can produce a solder joint with good quality. As a result, a model-based feed-forward and proportional, integral, and derivative (PID) mixed control method is developed. In practice, the proposed method is verified to have a wider product capability and production size; and a rate of good products of 99.94% is achieved with consuming approximately half of the energy comparing with manual soldering and constant laser power soldering.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Thermodynamic Model and Temperature Control Method of Laser Soldering Systems

Chen

Zheng

et al. 2015

Mathematical Problems in Engineering

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“…The infinite summation appearing in Equation ( 23) exhibits an exponential convergence and, hence, very fast. A conservative convergence criterion for this summation may be defined following the procedure given in [16]. In particular, by using (m − 1/2)π as a conservative estimate for β m , the maximum number of required terms m max in order to get a truncation error of 10 −A (A = 2, 3, .…”

Section: Maximum Number Of Termsmentioning

confidence: 99%

Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids

D'Alessandro

Monte

2020

Energies

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Boundary conditions of high kinds (fourth and sixth kind) as defined by Carslaw and Jaeger are used in this work to model the thermal behavior of perfect conductors when involved in multi-layer transient heat conduction problems. In detail, two- and three-layer configurations are analyzed. In the former, a thin layer modeled as a lumped body is subject to a surface heat flux on the front side while it is in perfect (fourth kind) or in imperfect (sixth kind) thermal contact with a semi-infinite or finite body on the back side. When dealing with a semi-infinite body in imperfect contact, the temperature solution is derived by means of the Laplace transform method. Green’s function approach is also used but for solving the companion case of a finite body in perfect contact with the thin film. In the latter, a thin layer with internal heat generation is located between two semi-infinite or finite bodies in perfect/imperfect contact. For the sake of thermal symmetry, such a three-layer structure reduces to a two-layer configuration. Results are given in both tabular and graphical forms and show the effect of heat capacity and thermal resistance on the temperature distribution of conductive layers.

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“…(19a) are quite difficult to treat, particularly the integration over cotime, the short-time temperature solution T S may also be obtained at any point (x,y) of the considered domain by "using" the simple 1D semiinfinite solution for a constant surface temperature [ [10], p. 186, Eq. (6.16)], that is, 20) where, in view of Eqs. (1) and (2), the partition time t p has to be taken as …”

Section: Examplementioning

confidence: 99%

Solving two-dimensional Cartesian unsteady heat conduction problems for small values of the time

Monte

Beck

Amos

2012

International Journal of Thermal Sciences

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A heat-flux based “building block” approach for solving heat conduction problems

Cited by 27 publications

References 11 publications

A Novel Thermodynamic Model and Temperature Control Method of Laser Soldering Systems

A Novel Thermodynamic Model and Temperature Control Method of Laser Soldering Systems

Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids

Solving two-dimensional Cartesian unsteady heat conduction problems for small values of the time

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