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In the simulations, the distribution of solid propellant grain is represented by the volume fraction of solid phase αp, which is determined from the distribution of representative particles.
These particles have the information of the burnup fraction, the volume and temperature of solid grains, and solid phase velocity.
The rate of mass decomposition and the linear burning rate on each grain surfaces are respectively given by () r V S m p p pρα−= 1& , r = a ⋅ pn (7) The resistant force due to the friction between the projectile and the launch tube wall acts on the projectile.
In the calculation, the number of the computational grid points is 341x31, and that of the representative particles is 20x20.

On the other hand up to date enormous numbers of experimental studies for the creep behaviour of MMCs have been performed, in which constitutive relations of steady state creep for the composites are mainly empirically derived [1].
This value is lower than that of grain-boundary diffusion of Ni, which is reported with 115kJmol -1[6].
The effective sectional area of a diffusion path, S, which usually seems a unknown parameter, was decided through the comparison of tangent modulus between experimental and simulated stress-strain curves of 10vol. % ZrO2/ Ni composites at 900 C o , and the pre-exponential term and activation energy for the interface diffusion were used with those of grain-boundary diffusion of Ni polycrystalline.
Young's modulus /GPa 207 200 Poisson's ratio 0.31 0.3 σ0 /MPa 25 Grain-boundary diffusion parameters for Ni [6] D0 (Pre-exp. term) / m 3s-1 : 3.5×10-7 , Activation energy / kJmol-1 : 115 Atomic volume / 1.09×10 -29m 3 : , Effective area of diffusion path S: 6.0 ×10 -11 m 2 .

Vickers hardness number (HV) is the ratio of the applied load to the surface area of the indent.
For Trial 4 and from Sample 1, Sample 2, Sample 3 and Sample 4 we observe a refinement in the grain structure coupled with the formation and presence of “onion rings”.
The technique has the advantage of producing welds with (a) low heat input, (b) a low degree of distortion, (c) a smaller grain size in the weld, (d) a narrow thermally-affected zone, and (e) properties closer to that of the parent metal.
The formation of fine equiaxed grains coupled with uniformly distributed fine strengthening precipitates in the region of the weld are reasons for superior tensile properties of friction stir welded joints. 6.

However, the degree of compaction is affected by various factors such as mechanical properties of soil, water content, compaction thickness, number of compactions, compacting machinery, test equipment, test operators and so on [1].
The compaction characteristics of fine-grained soil and coarse-grained soil are different, and the compaction effect of sandy soil is better than that of cohesive soil [5].
As the sediments are mainly silts, loess belongs to fine-grained soil.

The intrinsic thermal conductivity can be expressed as follows[8]: (2) where χ is the adjustable parameter, μ is the shear modulus, Vm is the unit cell volume per molecular, γ is the Grüneisen anharmoncity parameter, N is the number of atoms per molecular unit, ρ is the density, T is the temperature, A is the parameter independent of the temperature.
As we know, the mean path of the phonon which predominate the thermal conductivity of the dielectric solid is composed of three parts: (15) here li, lp and lb represent the phonon mean free path corresponding to Umklapp scattering, point defect scattering, and grain-boundary scattering processes, respectively.
Since the mean free path of the phonon is usually in the nanometer scale and the grain size of the ceramic is in the microm scale, the grain boundary scattering can be omitted.

They, as a rule, are located on grain boundaries as chains.
Unlike the hot cracks, cold cracks evolve along the grains themselves rather than along the grain boundaries; they are detected mainly is the zones of stress concentration
Since it is virtually impossible to produce a mold casting without defects, the issue of ultimate permissible number and size of defects in the mold is of great importance. 2.

Final characteristics of the diamond layer, such as grain size, thickness, hardness, are depending on the pre-treatment parameters.
In this paper investigations have been done in order to find an optimal configuration of pre-treatment function of carbide grade with a minimum number of tests.
Experiments have been performed on H10F carbide rods from Sandvick, which is a tungsten carbide with fine grain size (between 1 and 1.3 µm) bound by 10wt% of cobalt.
Pure abrasive wear is obtained instead of breakage of the grains and no blasting particles are embedded in the treated surface.

Results of the X-ray pointwise microanalysis (regions of analysis are marked with numbers in Fig. 3 a) Element, at. % Region of analysis 1 2 3 4 5 C (K) 0.00 0.00 17.61 0.00 0.00 O (K) 0.00 7.44 0.00 0.00 0.00 Al (K) 3.77 4.30 6.08 9.95 12.42 S (K) 0.00 0.00 0.00 0.00 2.52 Ti (K) 41.73 46.83 45.17 66.28 78.81 V (K) 1.46 2.21 2.92 3.60 4.51 Cr (K) 0.90 0.00 0.00 0.74 0.87 Fe (K) 0.93 0.00 0.00 0.00 0.86 Nb (L) 51.22 39.22 28.22 19.42 0.00 Based on the results of elemental analysis, it can be assumed that the formed coating is multiphase and should contain, along with the Ti-Nb alloy, carbide and oxide phases.
The surface layer has a grain-subgrain structure, with grain size varying within 150-200 nm.
The structure of the coating revealed by the methods of transmission electron microscopy of thin foils. a– grain-subgrain structure, b– second phase particles in the volume of crystallites Table 2.

Mathematical models present a number of useful aspects from the scientific point of view.
As a final comment we notice that the proposed mathematical model is versatile and can be used in different operating conditions, different geometries and types of materials without nature restrictions (fruits, vegetables, grains, clay products, wood, etc) with constant, impermeable or convective boundary conditions, and also with other boundary conditions, under small modifications.
Hall, Drying and storage of grains and oilseeds.
Parti, Selection of mathematical models for drying grain in thin-layers.

The material composition of these rocks does not allow them to be used to obtain ceramic materials, Portland cement, but due to the optimal ratio between clay minerals (aggregates) and quartz grains in the rock on their basis it is possible to obtain highly efficient silicate materials, including non-autoclave hardening [13-14].
According to the number of plasticity related to sandy loam.
Analysis of the samples’ microstructure showed that at low magnifications the obtained composites have a dense structure, individual grains are indistinguishable (refer with: Fig. 3).
Tolstoy, Fine-grained high-strength concrete, Construction Materials and Products. 3 (1) (2020) 39– 43 [2] L.H.