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.

Algebraically Explicit Analytical Solutions of Unsteady Conduction With Variable Thermal Properties in Spheroidal Coordinates

2004 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Spherical Coordinates ◽  
Rectangular Coordinates ◽  
Conduction Theory ◽  
Unsteady Heat Conduction ◽  
Spheroidal Coordinates

The analytical solutions of unsteady heat conduction with variable thermal properties (thermal conductivity, density and specific heat are functions of temperature or coordinates) 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. Such solutions in rectangular coordinates have been derived by the authors; some other solutions for unsteady point symmetrical heat conduction in spherical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.

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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