scholarly journals Enhancement of methodology for protection of structures in contradiction of thermal effects

2021 ◽  
Vol 264 ◽  
pp. 02033
Author(s):  
Еlena Rojkova ◽  
Nodira Ruzieva ◽  
Zuxritdin Ergashev
Keyword(s):  
Heat Conduction ◽  
Anisotropic Material ◽  
Thermal Effects ◽  
Temperature Effects ◽  
Heat Conduction Equation ◽  
Operator Method ◽  
Variable Coefficients ◽  
Conduction Equation ◽  
One Dimensional ◽  
Unsteady Heat Conduction

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.

Some Algebraically Explicit Analytical Solutions of Unsteady Nonlinear Heat Conduction

2001 ◽  
Vol 123 (6) ◽  
pp. 1189-1191 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Heat Conduction ◽  
Analytical Solutions ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Conduction Equation ◽  
Nonlinear Heat Conduction ◽  
One Dimensional ◽  
Nonlinear Heat Conduction Equation ◽  
Conduction Theory ◽  
Unsteady Heat Conduction

The analytical solutions of nonlinear unsteady heat conduction equation are meaningful in theory. In addition, they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes, grid generation methods and so forth. However, very few explicit analytical solutions have been known for the unsteady nonlinear heat conduction. In order to develop the heat conduction theory, some algebraically explicit analytical solutions of nonlinear heat conduction equation have been derived in this paper, which include one-dimensional and two-dimensional unsteady heat conduction solutions with thermal conductivity, density and specific heat being functions of temperature.

scholarly journals Non-linear unsteady inverse boundary problem for heat conduction equation

2017 ◽  
Vol 38 (2) ◽  
pp. 81-100 ◽  
Author(s):  
Magda Joachimiak ◽  
Michał Ciałkowski
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Linear Problem ◽  
Conduction Equation ◽  
Direct And Inverse Problems ◽  
Heat Conduction Coefficient ◽  
Nitrification Process ◽  
Non Linear ◽  
Unsteady Heat Conduction ◽  
Inverse Boundary Problem

AbstractDirect and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff’s substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.

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