The article proposed a general research scheme of heat transfer process in multilayer constructions for three basic geometric forms in order to simulate fire distribution. The scheme is based on linear differential equations, the Fourier method and the modified method of Eigen functions. The work considers five different layers' design and does not take into account internal heat sources. In this regard, a one-parameter family of boundary problems were solved. The authors simulated heat transfer for the Cartesian, cylindrical and spherical coordinates. Structures comprised several materials each having thermal properties varying with temperature.
Purpose. To develop an algorithm for calculating the problem of determining the nonstationary temperature field through the thickness of a multilayered structure, taking into account changes in the thermophysical characteristics and geometric dimensions (fluctuations) of the applied fire protection coating. Methodology. Application of the direct method for solving the differential equation of heat conduction using the method of reduction, the concept of quasiderivatives, the method of separation of variables and the modified method of eigenfunctions of Fourier. findings. An algorithm for determining the nonstationary temperature field in a multilayered flat structure is proposed, taking into account changes in the thermophysical characteristics and geometric dimensions (bursting expansion process) of the fire protection coating. This is achieved by solving a sequence of two tasks (the temperature field before the swelling and after the swell ing of the coating). originality. For the first time, using the direct method, in solving the problem of nonstationary heat conductivity, an algo rithm for determining the temperature field in multilayer elements with variable thickness of a layer on the example of building structures with flame retardant systems based on intumescent coatings is proposed. Practical value. Further, this approach can be implemented for approximation of solutions of heat conduction problems and it will allow catalyzing studies on fire retardant properties of intumescent coatings.
Purpose. Characteristics of heat transfer processes in multilayer bodies of basic geometric shapes simultaneously under conditions of convective heat transfer on its surfaces and taking into account imperfect thermal contact between the layers. Methodology. A direct method was applied to solve a one-parameter family of boundary value problems in the theory of heat conduction. This method is based on the reduction method, the concept of quasiderivatives, a system of differential equations with impulse action, the method of separation of variables, and the modified method of eigenfunctions of Fourier. It is worth noting that the application of the concept of quasiderivatives allows you to circumvent the well-known problem of multiplication of generalized functions, which arises when using the differentiation procedure of the coefficients of a differential equation. Such a procedure, in our opinion, casts doubt on the equivalence of the transition to the differential equation obtained in this way with generalized coefficients. Findings. The solution to the problem is obtained in a closed form. The proposed algorithm does not contain a solution to volume conjugation problems. It includes only: a) finding the roots of the corresponding characteristic equations; b) the multiplication of a finite number of known (2 2) matrices; c) the calculation of certain integrals; d) summing the required number of members of the series to obtain the specified accuracy. As an illustration, we consider model examples of heating eight-layer structures in a fire. Originality. For the first time, the direct method has been applied to solving the problem of the distribution of an unsteady temperature field over the thickness of multilayer structures of basic geometric shapes simultaneously, in the presence of imperfect thermal contact between the layers. Practical value. The implementation of the research results allows us to effectively study the heat transfer processes in multilayer structures, which are found in a number of applied problems.
The article deals with the current problem of determining the fire resistance of protected steel elements of building structures. Based on the analysis of literary sources, the main methods for increasing the fire resistance of steel structures are considered, as well as the use of fire retardant coatings based on polymetallophenylsiloxane. Analytical studies were conducted to determine the time of fire protection of the coating, compared to unprotected structures. The results show that the limit of fire resistance of protected steel constructions is increased 2-4 times, depending on the thickness of the application.
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