On Determination of the Effective Thermal Conductivity of a Bundle of Steel Bars Using the Krischer Model and Considering Thermal Radiation

Abstract

Cellular solid materials are commonly found in industrial applications. By definition, cellular solids are porous materials that are built of distinct cells. One of the groups of such materials contains metal foams. Another group of cellular metals contains bundles of steel bars, which create charges during the heat treatment of the bars. A granular structure connected by the lack of continuity of the solid phase is the main feature that distinguishes bundles from metal foams. The boundaries of the bundle cells are made of adjacent bars, with the internal region taking the form of an air cavity. In this paper, we discuss the possibility of using the Krischer model to determine the effective thermal conductivity of heat-treated bundles of steel bars based on the results of experimental tests and calculations. The model allows the kef coefficient to be precisely determined, although it requires the weighting parameter f to be carefully matched. It is shown that the value of f depends on the bar diameter, while its changes within the examined temperature range (25–800 °C) can be described using a third-degree polynomial. Determining the coefficients of such a polynomial is possible only when the effective thermal conductivity of the considered charge is known. Moreover, we analyze a simplified solution, whereby a constant value of the f coefficient is used for a given bar diameter; however, the kef values obtained thanks to this approach are encumbered with inaccuracy amounting to several dozen percentage points. The obtained results lead to the conclusion that the Krischer model cannot be used for the discussed case.

Correlations for the thermal conductivity of selected steel grades as a function of temperature in the range of 0–800°C

“…Therefore, the developed equations can be successfully used in engineering calculations connected with transient thermal conductivity through steel elements within the temperature range 0-800 • C. Moreover, the developed equation can be used in modelling the effective thermal conductivity of a steel porous charge. Such models have been described in [36,37].…”

Measurement of thermal conductivity of the cortical bone: experimental studies and comparative analysis

“…Linear energy flow is assumed, and homogeneity of the bone structure and the samples must take the same shape and size. The measured temperature changes can be substituted into the formula for the thermal conductivity of the test sample [22]:…”

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

“…The problem of heat transfer in round bar bundles has been widely analysed by the authors. The works published in this field concerned: determination of the effective thermal conductivity [13][14][15], heat conduction [16], thermal radiation [17][18][19] and free convection [20]. The present article is concerned with the problem of heat transfer in a bundle of flat bars.…”