A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Coronel, Aníbal; Huancas, Fernando; Lozada, Esperanza; Tello, Alex

doi:10.3390/axioms11080422

Cited by 3 publications

(8 citation statements)

References 29 publications

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“…The results of numerous studies on heat transfer through single-and double-chamber windows are presented in previous works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Gan [1] studied heat transfer through a double-glazed window.…”

Section: Analysis Of Known Research Resultsmentioning

confidence: 99%

Heat Transfer through Double-Chamber Glass Unit with Low-Emission Coating

Koshlak,

Basok,

Davydenko

2024

Energies

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The numerical modeling of radiation and convective heat transfer through a double-chamber glass unit was carried out to substantiate the increase in the heat transfer resistance of this unit via the application of low-emission coatings to glass surfaces. In the space between the panes of a window without low-emission coatings, the amount of heat transferred via radiation exceeds the amount of heat transferred via thermal conductivity and convection. The question of the effect of low-emissivity coatings on reducing heat loss through a window has not yet been sufficiently studied. This problem is also not sufficiently reflected in the literature. In this regard, this paper presents the results of numerical simulation aimed at studying the effect of low-emissivity coatings on heat transfer through a double-chamber glass unit. Simulation is carried out by numerically solving a system of equations of fluid dynamics and energy for the air gap and glass. Boundary conditions of the fourth kind are set on the internal surfaces of the chambers, taking into account the radiation and conduction components of the total heat flux emanating from the glass. The results of modeling heat transfer through a glass unit with ordinary glass show that about 60% of the heat is transferred by radiation. Therefore, an effective measure to reduce heat loss through windows is to reduce the radiation component of the total heat flux by applying a low-emissivity coating to the internal surfaces of the glass unit. This allows for the reduction of the overall heat flux (and, accordingly, heat loss to the environment) by 20–34%, depending on the number of glass surfaces with such a coating.

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Section: Analysis Of Known Research Resultsmentioning

confidence: 99%

Heat Transfer through Double-Chamber Glass Unit with Low-Emission Coating

Koshlak,

Basok,

Davydenko

2024

Energies

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“…; α 1 and α 2 are some coefficients; K 1 and K 2 are the Knudsen numbers; ψ 1 and ψ 2 are the initial conditions; φ 1 and φ 2 are two provided functions modelling the boundary conditions; and the bracket • is defined by G(x, t) = G(x − 0, t) − G(x + 0, t). The relationship between K n and k is provided by K 2 n CL 2 c = 3kτ q with L c a characteristic length, boundary conditions ( 12) and ( 13) are a consequence of assuming a temperature-jump condition, and the model is not in dimensionless form; see [40,41,45] for details.…”

Section: A Mathematical Model For Heat Conduction In a Three-phase-la...mentioning

confidence: 99%

“…We rewrite (L 1 ∆ u) 1/2 j and (D 1 ∆ u) 1/2 j in notation (41). We begin by (L 1 ∆ u) 1/2 j , from (21) and the initial condition (11), and we deduce that…”

Section: Numerical Approximation Of the Systemmentioning

confidence: 99%

“…Meanwhile, to rewritte (D 2 ∆ u) n j in notation (41), we begin by rewriting (33)-(35) using notation (41), i.e.,…”

Section: The Numerical Scheme and Propertiesmentioning

confidence: 99%

“…Then, the scheme is easy to implement. Then, we invite the arduous computations provided in [40,41], where the authors considered a change in the variable, a semi-discrete finite difference scheme for the new variable, a fully finite difference scheme for the new variable, and then approximated the original variable. Moreover, we show that the scheme is unconditionally stable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Coronel,

Lozada,

Berres

et al. 2024

Energies

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In this article, we propose a mathematical model for one-dimensional heat conduction in a three-layered solid considering that an interfacial condition is present for the temperature and heat flux conditions between the layers. The numerical approach is developed by constructing a finite difference scheme to solve the initial boundary–interface problem. The numerical scheme is designed by considering the accuracy of the model on the inner part of each layer, then extending to the interfaces and boundaries by incorporating the continuous interfacial conditions. The finite difference scheme is unconditionally stable, convergent, and easy to implement since it consists of the solution of two algebraic systems. We provide three numerical examples to confirm that our numerical approximation is consistent with the analytical solution and the physical phenomenon.

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Reduced Heat Loss Through Window Structures

Basok,

Davydenko,

Pavlenko

et al. 2023

Energ. Tech. & Res. Sav.

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The results of theoretical and experimental studies of heat transfer through the window structures of the building are presented, the thermal characteristics of the windows are established and the level of heat loss realized through them is estimated. To determine the heat transfer resistance of two-chamber double-glazed units, numerical modeling of radiative-convective heat transfer is performed, taking into account the thermal conductivity of the gas layer between the glasses. Natural free convection of the gaseous medium in the double-glazed chambers occurs as a result of the temperature difference between the side glass surfaces of the chamber. Modeling is performed by numerically solving the system of fluid dynamics and energy equations for the air layer and glass. On the inner surfaces of the chambers, conditions of the fourth kind are set, which take into account the radiation and conductive components of the total heat flow coming from the glass surface. The results of simulation of heat transfer through double-glazed windows with ordinary glass indicate that about 60 % of heat is transferred by radiation. Therefore, an effective measure to reduce heat loss through windows is to reduce the radiation component of the total heat flow by applying a low-emissivity coating to the inner surfaces of the glass unit. This makes it possible to reduce the total heat flow (and, accordingly, heat loss to the environment) by 20–34 %, depending on the number of glass surfaces with this coating. Conducted independent experimental studies confirm the modeling results. In order to comply with the current requirements of state building regulations and to achieve the energy efficiency class of type C buildings (specific heat consumption for heating 1 sq. m of usable area is less than 75 kWh), for the climatic conditions of Kyiv, it is recommended to use double-chamber windows with two low-emission coatings with the formula of the glass unit: 4M1-10-i4M1-10-i4M1. Bibl. 22, Fig. 8.

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A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Cited by 3 publications

References 29 publications

Heat Transfer through Double-Chamber Glass Unit with Low-Emission Coating

Heat Transfer through Double-Chamber Glass Unit with Low-Emission Coating

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Reduced Heat Loss Through Window Structures

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