scholarly journals Variational principle for unsteady heat conduction equation

2014 ◽  
Vol 18 (3) ◽  
pp. 1045-1047 ◽  
Author(s):  
Zhijuan Jia ◽  
Mingsheng Hu ◽  
Qiaoling Chen
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Heat Conduction Equation ◽  
Inverse Method ◽  
Conduction Equation ◽  
Unsteady Heat Conduction

The semi-inverse method is used to establish a variational principle for an unsteady heat conduction equation.

scholarly journals Remark on a constrained variational principle for heat conduction

2013 ◽  
Vol 17 (3) ◽  
pp. 951-952 ◽  
Author(s):  
Zhao-Ling Tao ◽  
Guo-Hua Chen
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Heat Conduction Equation ◽  
Inverse Method ◽  
Separation Of Variables ◽  
Conduction Equation ◽  
Variable Separation

The heat conduction equation is re-studied by the semi-inverse method combined with separation of variables; a new variational principle for the heat conduction equation is obtained. Equivalence of the existed two in literature is shown. The significance of variable separation is confirmed once more.

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.

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.

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