thermal conductivity, porosity, electron beam heating, sintering, contact between particles


Background. Development of the consolidation processes of powder products using highly concentrated energy sources is impossible without a detailed analysis of the processes of thermal conditions arising in these products.

Objective. The aim of the study is to select a method for calculating the thermal conductivity of a porous body, which will be established under various conditions of electron-beam sintering of molybdenum compacts, and to study the effect of the parameters of the porous structure on the thermal conductivity.

Methods. An analysis of the sintering process in finite element calculations, in problems of thermal conductivity for two-dimensional and three-dimensional domains, simulating the real porous structure of molybdenum compaction and a regular porous structure with dense packing of spheres is proposed.

Results. Mathematical analysis of the contribution of re-radiation to the total thermal conductivity of the porous material is performed. The obtained dependences of the relative thermal conductivity on the porosity of the material and the relative radius of contacts between its particles are presented.

Conclusions. According to the results of the mathematical analysis of the conditions of heat transfer in a porous compact of molybdenum for the case of electron-beam heating, it was found that the radiant component of the thermal conductivity of a porous body with pores of the order of 2.5 μm is four orders of magnitude less than the conductive component of its thermal conductivity. Based on the results of finite element modeling of two-dimensional and three-dimensional porous objects, a significant effect of the contact area between particles on their integral thermal conductivity has been established, especially at small sizes of these contacts. At the same time, almost linear effect of porosity on thermal conductivity was established at contact radii between particles > 0.1 Rparticles. A significant influence of the uniformity of the distribution of contacts in aporous material on the uniformity of the temperature field in it is shown.


E.S. Huetter et al., “Determination of the effective thermal conductivity of granular materials under varying pressure conditions,” J. Geophys. Res., vol. 113, no. E12, pp. 286–296, 2008. doi: 10.1029/2008je003085

J. Mo and H. Ban, “Measurements and theoretical modeling of effective thermal conductivity of particle beds under compression in air and vacuum,” Case Stud. Thermal Eng., vol. 10, pp. 423–433, 2017. doi: 10.1016/j.csite.2017.10.001

D. Moser et al., “Computation of effective thermal conductivity of powders for selective laser sintering simulations,” J. Heat Transf., vol. 138, no. 8, pp. 977–988, 2016. doi: 10.1115/1.4033351

N. Sakatani et al., “Thermal conductivity model for powdered materials under vacuum based on experimental studies,” AIP Advances, vol. 7, no. 1, p. 015310, 2017. doi: 10.1063/1.4975153

C.K. Chan and C.L. Tien, “Conductance of packed spheres in vacuum,” J. Heat Transf., vol. 95, no. 3, pp. 302–308, 1973. doi: 10.1115/1.3450056

W. Schotte, “Thermal conductivity of packed beds,” AIChE J., vol. 6, no. 1, pp. 63–67, 1960. doi: 10.1002/aic.690060113

D. Shah and A.N. Volkov, “Calculation of effective thermal conductivity of powder bed systems using smoothed particle hydrodynamics method,” in The 16th Annual Early Career Technical Conf., Birmingham, 2016.

G. Weidenfeld et al., “A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression,” Granul. Matter, vol. 6, no. 2–3, pp. 121–129, 2004. doi: 10.1007/s10035-004-0170-1

D. de Moraes and A. Czekanski, “Parametric thermal FE analysis on the laser power input and powder effective thermal conductivity during selective laser melting of SS304L,” J. Manuf. Mater. Process., vol. 2, no. 3, p. 47, 2018. doi: 10.3390/jmmp2030047

M.R. Alkahari et al., “Thermal conductivity of metal powder and consolidated material fabricated via selective laser melting,” Key Eng. Mater., vol. 523–524, pp. 244–249, 2012. doi: 10.4028/www.scientific.net/KEM.523-524.244

Kh. Uong, Basic formulae and data on heat transfer for engineers. Мoscow, Russia: Atomizdat, 1979.

V.E. Zinovev, Thermophysical properties of metals at high temperatures. Мoscow, Russia: Metallurgy, 1989.