Model of Complex Heat Transfer in the Package of Rectangular Steel Sections

Wyczółkowski, R.; Gała, M.; Bagdasaryan, Vazgen

doi:10.3390/app10249044

Cited by 5 publications

(8 citation statements)

References 13 publications

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“…It was also demonstrated that above 300 • C, thermal radiation is essential for the whole phenomenon. In the next article [41,42], the complex heat transfer in the packages of rectangular steel sections was analyzed in turn. It was established that the heat transfer intensity in such systems mostly depends on the thermal contact resistance R ct between adjacent layers of the package.…”

Section: Resultsmentioning

confidence: 99%

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Experimental Investigations of Effective Thermal Conductivity of the Selected Examples of Steel Porous Charge

Wyczółkowski

2021

Solids

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In many cases of heat treatment of steel products, the heated charge has a porous structure. The examples of such charges include bundles of long steel components e.g., bars. The basic thermal property of the charge in this form is effective thermal conductivity kef. This paper presents the results of experimental examinations of effective thermal conductivity of the porous charge, which is composed from various types of steel long components. Due to the specific nature of the samples, a special measurement stand was constructed based on the design of a guarded hot plate apparatus. The measurements were performed for sixteen different samples across a temperature range of 70–640 °C. The porosity of the samples, depending on the type of components used, ranged from 0.03 to 0.85. Depending on these factors, the effective thermal conductivity ranged from 1.75 to 8.19 W·m−1·K−1. This accounts for 0.03 to 0.25 of the value of thermal conductivity of the solid phase of the charge, which in the described cases was low-carbon steel. It was found that the effective thermal conductivity rises linearly with temperature. The intensity of this increase and the value of coefficient kef depend on the transverse dimension of the components that form the charge. The results may represent the basis for the validation of various models of effective thermal conductivity with respect to the evaluation of thermal properties of the porous charge.

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Section: Resultsmentioning

confidence: 99%

“…At a temperature of 675 • C, this value ranges from 0.09 to 0.25. The increase in Kr with temperature can be explained by the effect of thermal radiation that takes place in the area of the porous charge between the surfaces of individual components (bars or sections) [42,48].…”

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Experimental Investigations of Effective Thermal Conductivity of the Selected Examples of Steel Porous Charge

Wyczółkowski

2021

Solids

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“…In order to prepare the samples, bars from low-carbon steel with the carbon content of 0.2% were used. The change in the thermal conductivity of such steel in the temperature function (where temperature is expressed in • C) is described by the following relationship [36]: The results of the measurement of effective thermal conductivity are presented in the form of diagrams. Figure 4a presents the results obtained for samples made of 5 × 20 mm bars, whereas Figure 4b shows the results for samples made of 10 × 40 mm bars.…”

Section: Methodsmentioning

confidence: 99%

Experimental Investigation of Thermal Contact Conductance in a Bundle of Flat Steel Bars

2022

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The phenomenon of thermal contact conduction in two-phase (fluid-solid) media determines many technological processes. An example of such a process is heat treatment of steel bars, when a heated charge has a form of a packed bundle. In order to determine the optimal heating curve it is necessary to have knowledge about the intensity of transfer through contact areas of the bars. This phenomenon is quantified by the thermal contact conductance hct. The article describes the methodology of determining the hct coefficient for bundles of flat steel bars. The starting point for the analysis is the measurement of the effective thermal conductivity kef performed for 5 × 20 mm and 10 × 20 mm bars. Individual samples of the same bars differed in arrangement. The analytical investigation used the concept of an elementary cell. This approach consisted in analysing resistances for individual heat transfer types: conduction, contact conduction and radiation. Based on the performed calculations it has been established that the value of the hct coefficient for the analysed samples is within the range 128–472 W/(m2 K). Changes of the hct coefficient in the temperature range 25–700 °C can be described with a second degree polynomial. It has been established that hct assumes maximum values in the temperature range from 300 °C to 400 °C.

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“…For this purpose, the concept of an elementary cell has been used. It is a commonly used approach in which the effective thermal conductivity is calculated based on the analysis of thermal resistances (the so-called electrical analogy) [ 19 , 20 , 21 , 22 , 23 ]. The coefficient k ef for a defined elementary cell has been calculated from the Equation (18)

where: l cell —characteristic dimension of the elementary cell, R cell —total thermal resistance of the cell.…”

Section: Methodsmentioning

confidence: 99%

“…Values of the coefficients A1-A3 from Equation(21) and characteristic dimension of the elementary cell lcell obtained for particular samples.…”

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Analysing the Contact Conduction Influence on the Heat Transfer Intensity in the Rectangular Steel Bars Bundle

et al. 2021

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Bundles of steel bars, besides metal foams, are an example of cellular solids. Such bundles constitute a charge during the heat treatment of bars. The paper presents a mathematical model of transient heat transfer in a bundle of rectangular steel bars based on the energy balance method. The key element of this model is the procedure of determining the effective thermal conductivity using the electrical analogy. Different mechanisms of heat transfer occurring within the analysed medium (conduction in steel and contact conduction) are assigned corresponding thermal resistances. The discussed procedure involves expressing these resistances with the use of arithmetic relationships describing their changes in the temperature function. Thermal contact resistance has been described with the use of the relationships determined experimentally. As a result of the performed calculations, the influence of contact conduction between the adjacent bars and bundle arrangement on its heating time was established. The results of the calculations show that the heating time of bundles can be lowered by 5–40% as a result of a decrease in the thermal contact resistance. This effect depends on the bar size and bundle arrangement. From the practical point of view, the analysed problem is connected with the optimization of the heat treatment processes of steel bars.

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Model of Complex Heat Transfer in the Package of Rectangular Steel Sections

Cited by 5 publications

References 13 publications

Experimental Investigations of Effective Thermal Conductivity of the Selected Examples of Steel Porous Charge

Experimental Investigations of Effective Thermal Conductivity of the Selected Examples of Steel Porous Charge

Experimental Investigation of Thermal Contact Conductance in a Bundle of Flat Steel Bars

Analysing the Contact Conduction Influence on the Heat Transfer Intensity in the Rectangular Steel Bars Bundle

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