Inverse problems for the heat-conduction equation in a domain with a moving boundary

1976 ◽  
Vol 27 (5) ◽  
pp. 568-572 ◽  
Author(s):  
I. G. Malyshev
Keyword(s):  
Heat Conduction ◽  
Inverse Problems ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Conduction Equation

The Method of Fundamental Solutions for the Moving Boundary Problem of the One-Dimension Heat Conduction Equation

2014 ◽  
Vol 1039 ◽  
pp. 59-64 ◽  
Author(s):  
Xin Jiang ◽  
Xiao Gang Wang ◽  
Yue Wei Bai ◽  
Chang Tao Pang
Keyword(s):  
Heat Conduction ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Metal Wire ◽  
Moving Boundary Problem ◽  
Conduction Equation ◽  
Temperature Function

The melting of the material is regarded as the moving boundary problem of the heat conduction equation. In this paper, the method of fundamental solution is extended into this kind of problem. The temperature function was expressed as a linear combination of fundamental solutions which satisfied the governing equation and the initial condition. The coefficients were gained by use of boundary condition. When the metal wire was melting, process of the moving boundary was gained through the conversation of energy and the Prediction-Correlation Method. A example was given. The numerical solutions agree well with the exact solutions. In another example, numerical solutions of the temperature distribution of the metal wire were obtained while one end was heated and melting.

Fuel Droplet Heating and Evaporation: New Hydrodynamic and Kinetic Models

2010 ◽  
Author(s):  
Sergei S. Sazhin ◽  
Irina N. Shishkova ◽  
Ivan G. Gusev ◽  
Ahmed Elwardany ◽  
Pavel Krutitskii ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Traditional Approach ◽  
Kinetic Modelling ◽  
Conduction Equation ◽  
Fuel Droplet ◽  
Transient Heating ◽  
Explicit Analytical Solution

Recently developed approaches to the hydrodynamic and kinetic modelling of fuel droplet heating and evaporation are reviewed. Two new solutions to the heat conduction equation, taking into account the effect of the moving boundary during transient heating of an evaporating droplet, are discussed. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterra integral equation of the second kind. It has been pointed out that the new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution of the species diffusion equation inside droplets, is discussed. A new algorithm, based on simple approximations of the kinetic results for droplet radii and temperatures, suitable for engineering applications, is discussed.

Sign in / Sign up

Export Citation Format

Share Document