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.

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