Modeling of heat and mass transfer in multilayer heat- and fire-insulating coatings under interaction with a high-temperature gas flow

Isakov, G. N.; Kuzin, A. Ya.

doi:10.1007/bf02672820

Cited by 3 publications

(2 citation statements)

References 1 publication

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“…Systems of nonlinear difference equations with threediagonal matrices were solved by the marching method [5] with iterations by the coefficients with a prescribed accuracy. Special difference equations allowing for the difference in the thermophysical characteristics of the materials of the subdomains [6] were used at the internal boundaries of the domain d.…”

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confidence: 99%

Heat Transfer in a Plane Three-Layer System with a Not-Through Cross Connection

Khutornoi

Цветков

Kuzin

et al. 2005

J Eng Phys Thermophys

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The regularities of formation of temperature fields in a plane three-layer system with a not-through cross connection (connector) are considered with boundary conditions of the second kind on one exterior surface of the system. The character of distribution of the temperature fields in the zone of influence of the steel connector is investigated experimentally. The results of the experiment are compared to the numerical solution of the problem with boundary conditions of the second and third kind on the interior surface of the wall. Their satisfactory agreement is shown.The regularities of heat transfer in a plane three-layer system with a not-through heat-conducting connection (connector) have been investigated theoretically in [1]. To extend this investigation it became necessary to solve the problem of heat conduction in a plane three-layer system with a not-through cross connection in the case of boundary conditions of the second kind on one exterior surface of the system for optimum designing of energy-saving enclosing structures of buildings and development of systems of their external thermal protection (warmth-keeping).The present work seeks to develop an efficient numerical method of solution of the problem, which is rapidly adaptable to different configurations of multilayer external enclosures with cross connections, to compare results of numerical solution of the problem of heat transfer in a three-layer exterior wall with a connector in the case of boundary conditions of the second and third kind on its interior surface, to experimentally investigate the character of distribution of temperature fields in the zone of influence of a steel connector, and to compare the results of numerical solution to experimental data.Physicomathematical Formulation and Method of Solution of the Problem. Heat transfer through a plane multilayer system with a cross connection will be considered using a brick three-layer exterior wall with a cylindrical connector as an example (Fig. 1). The internal and external layers of the enclosure represent the brickwork and the central layer is a warmth-keeping jacket. The ends of the connector are embedded in the internal and external layers of the enclosure. The geometric dimensions of the layers of the enclosure and the connector are prescribed. The thermophysical characteristics of the wall material (λ i , ρ i , and c i , i = 1, 4 ___ ), which are generally dependent on temperature, are known. The temperature of the medium t g,e and the heat-transfer coefficient α w are prescribed on the exterior surface of the enclosure, and the heat-flux density q 0 is prescribed on the interior surface. The temperature profile over the enclosure thickness t 0 , t 12 , t 23 , and t w outside the zone of influence of the connector is determined from the known value of q 0 from the analytical solution of a one-dimensional stationary heat-conduction problem [2].We will solve the problem formulated in a cylindrical coordinate system (Fig. 1). The origin of coordinates will be located on the inte...

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confidence: 99%

Heat Transfer in a Plane Three-Layer System with a Not-Through Cross Connection

Khutornoi

Цветков

Kuzin

et al. 2005

J Eng Phys Thermophys

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“…(iv) From the earliest papers on modeling of intumescent coatings by Cagliostro et al [10], researchers [11][12][13][14][15][16][17][18][19] have shown that the amount the coating expands has a major impact on the thermal resistance of the material. However, in modeling the expansion process virtually all researchers resort to using an 'expansion factor' method; an experimentally measured, post-intumescence, coating thickness is used to calculate a factor used to predict the developing thickness of the coating as a function of the coating temperature [3,4,11] or conversion of gas-producing component (or fractional mass loss) in the coating [10,[12][13][14][15][16][17][18][19][20][21][22][23] (The model of Asaro et al [24] went to the extreme of basing the heat transfer calculations on only the post-intumesence thickness, without taking account of the affect of variation in thickness during heating, with consequent poor agreement between theoretical predictions and experimental data.) It has been noted [25] that the use of an expansion factor can produce predictions that do not agree with experimental observations.…”

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The Modeling of Heat Transfer across Intumescent Polymer Coatings

Griffin

2009

Journal of Fire Sciences

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The use of mathematical models to predict the thermal resistance of polymer-based, intumescent coatings are reviewed and their limitations are discussed. A mathematical model is derived to describe the developing temperature profile across an intumescent coating when exposed to a radiant heat source. The model includes the effects of: the endothermic and exothermic reactions; convective heat transfer as degradation gases are transported through the coating; radiation heat transfer across the developing porous solid; and the increase in thermal resistance as gases are formed and the coating expands. The model predictions are compared with experimental data from the heating of epoxy-based and vinyl acetate-based intumescent coatings in a cone calorimeter. A sensitivity analysis is performed to show the effect of the thermal characteristics of the coating on the thermal resistance of the material. The application of the model to newly developed intumescent coatings is discussed.

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Assessing the performance of intumescent coatings using bench‐scaled cone calorimeter and finite difference simulations

Bartholmai

Schartel

2006

Fire and Materials

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SUMMARYA method was developed to assess the heat insulation performance of intumescent coatings. The method consists of temperature measurements using the bench-scaled experimental set-up of a cone calorimeter and finite difference simulation to calculate the effective thermal conductivity dependent on time/temperature. This simulation procedure was also adapted to the small scale test furnace, in which the standard time-temperature curve is applied to a larger sample and thus which provides results relevant for approval. Investigations on temperature and calculated effective thermal conduction were performed on intumescent coatings in both experimental set-ups using various coating thicknesses. The results correspond to each other as well as showing the limits of transferability between both fire tests. It is shown that bench-scaled cone calorimeter tests are a valuable tool for assessing and predicting the performance of intumescent coatings in larger tests relevant for approval. The correlation fails for processes at surface temperatures above 7508C, which are not reached in the cone calorimeter, but are attained in the small scale furnace set-up.

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Modeling of heat and mass transfer in multilayer heat- and fire-insulating coatings under interaction with a high-temperature gas flow

Cited by 3 publications

References 1 publication

Heat Transfer in a Plane Three-Layer System with a Not-Through Cross Connection

Heat Transfer in a Plane Three-Layer System with a Not-Through Cross Connection

The Modeling of Heat Transfer across Intumescent Polymer Coatings

Assessing the performance of intumescent coatings using bench‐scaled cone calorimeter and finite difference simulations

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