_{1}

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Goal: Formulation of empiric formula, which establishes relations between major matrix parameters of ceramic materials and composites and the coefficient of resistance to material thermogradient. Method: Harcpurt’s method of cooling of water in boiling regime till disappearance of water. Results: It is proved that work-pieces reveal maximum thermal resistance and preservation of exploitation properties, when total closed porosity is within 2% - 8%, and pore sizes vary within 1 - 6 mcm. Besides, they are more or less of spherical form and are spread equally in the matrix. Conclusion: Thermogradient effect formula was defined for complex form work-pieces, when surfaces in the pieces are transacted several times by angles of various curvature radii.

It is known that resistance to thermal- and air-thermal aggression and respectively to thermogradient of composite work-pieces made on ceramic matrix depends greatly not only on the value of the gradient at the mechanical stresses, which are mainly conditioned by the phases present in the material, thermal-processing regime and physical-chemical processes going on in the material during synthesis but also together with other factors, on their form [

If we take into consideration the fact that, when the nature of distribution of local mechanical stresses in solid bodies depends substantially on the form of a body, it is apparent that neglect of the form of a piece to thermogradient, will be associated with a big inaccuracy while determining the resistance of any specific work-piece [

As far as it is known for us, in technical literature available up to now impact of the form of any work-piece on the resistance of thermogradient of pieces has not been elucidated yet. The known Weibull’s formula [

In most cases these are spherical, cylinder and infinitely flat plates, that is, simple forms. We considered necessary to define formula of thermogradient effect for relatively complex forms, that is, when the piece surfaces are intersections by various curvature radius angle. For determination of a piece resistance to thermal aggression the value of this angle has determining significance. Although we will repeat that in the complex material structure, the composition, texture and many factors have important impact on thermal resistance. Besides, we have to take into consideration that selection of adequate parameter for evaluation of methodology of thermal resistance and its assessment is rather difficult [

It is known from practice [

K = r ⋅ σ b ( 1 − μ ) / a ⋅ d T / d y ⋅ d 1 / 2 ⋅ E ⋅ a t

r―is for the work-piece curvature radius for selected surface element, σ_{bend} is mechanics at bending, MPa; μ―Poisson coefficient; a_{t}―temperature conductivity; E―Young’s module; a―coefficient of linear expansion, dT/dy―thermal gradient for the selected y axis, along which thermogradient occurs, d_{1/2}―half of piece wall thickness. It is necessary to allow some empiric assumptions, thus, e.g. that the piece from the side of heating should be flat, while the angle of joining of any two planes should be determined by curvature radius, which equals or exceeds

r ≥ 0.3 cm

Spot of joining of two planes of a piece is computed according to the design, empirically, at 30% maximum angle. As to the thermal expansion and thermal stress, it is considered that expansion of the work-piece is free, that is, mechanically unlimited, while the stress can be formed not only due to abrupt alteration but also at gradual changes, since at one and the same thermal gradient and at various curvature radii, various stresses will be formed in the piece.

In our case, to test the formula we used the properties of celsian electro-ceramic piece synthesized in BaO-Al_{2}O_{3}-SiO_{2} system [

K = 0.3 × 69 × ( 1 − 0.282 ) / 282 × 75 × 3 × 10 − 6 × 140 × 0.4 = 0.28 cm / sec

Thus, if we determine universal connection between mechanical and thermal properties of the material, and alongside with it, we’ll take into consideration the piece design and wall thickness, we’ll be able to compute resistance of a piece to thermal gradient.

The formula enables us to determine numerical value, which will conform to the resistance of the given work-piece to thermogradient. This latter is computed by the provision of numerical values of the characteristics of the main ceramic materials (composites) used in practice which are given in the formula [

The author declares no conflicts of interest regarding the publication of this paper.

Kovziridze, Z. (2018) Formula of Thermogradient Effect. Journal of Electronics Cooling and Thermal Control, 8, 49-54. https://doi.org/10.4236/jectc.2018.84004