Abstract
The research paper is devoted to protection of structures against heat and temperature effects. The necessity of improving the calculation of multilayered fence structures is shown. The solution of a one-dimensional unsteady heat conduction equation with constant and variable coefficients allowing to use of inhomogeneous and anisotropic materials as the fence material is given. An example of the solution of a fence made of inhomogeneous and anisotropic material is given. Solution of heat conduction equation is obtained by the recurrence-operator method. The solution of one-dimensional unsteady heat conduction equation with variable coefficients is obtained using the recurrence-operator method. The possibility of using the solution of the equation for multilayered inhomogeneous anisotropic fence materials is indicated.
Highlights
The object of investigation is the protection of structures from heat influence by means of bone up of the process of heat flow and correspondent temperature through covering thickness of outer parts, consisting of layers of different thermal protective materials.In construction thermal physics, such problems are investigated mainly by solving a one-dimensional nonstationary nonlinear heat conduction equation
The cases when the heat transfer coefficient is variable and the heat capacity coefficient is constant are discussed in detail, and it is pointed out that it is in principle possible to obtain solutions when the heat transfer coefficient and the specific heat capacity coefficient changes c
The purpose of this paper is to develop a simpler algorithm for solving the heat conduction equation when both coefficients are variable, using the recurrence-operated method
Summary
In construction thermal physics, such problems are investigated mainly by solving a one-dimensional nonstationary nonlinear (more precisely quasi-linear) heat conduction equation. These characteristics depend on the material properties, its temperature, humidity and can be a given function of the envelope thickness within each envelope layer in the case of continuously heterogeneous material. Partial cases of this transformation allow us to solve the heat conduction equation in the Bessel functions of the complex argument with various laws of variation of the variable coefficients In this case, such solutions can be used that are expressed in terms of the constructed functions. The cases when the heat transfer coefficient is variable and the heat capacity coefficient is constant are discussed in detail, and it is pointed out that it is in principle possible to obtain solutions when the heat transfer coefficient and the specific heat capacity coefficient changes c
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