An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped two-dimensional and axisymmetric ducts without flow

1978 ◽  
Author(s):  
S. CHAKRAVARTHY
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Sound Propagation ◽  
Two Dimensional

The Simplified Method to Calculate Two-Dimensional Heat Conduction Equations of Heating Slab

2011 ◽  
Vol 79 ◽  
pp. 105-110
Author(s):  
Guo Jun Li ◽  
Xiao Ting Li ◽  
Hai Geng Chen
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Thermal Flux ◽  
Computational Time ◽  
Fourth Power ◽  
Heating Process ◽  
Two Dimensional ◽  
Simplified Method

The most effective way of determining the whole billet temperature field is to use a simulation model. Large amount of calculation as well as computational time is consumed to employ two-dimensional finite difference method since the heating process is extremely complex, then it’s necessary to simplify the calculation process. In this paper, a simplified method in one-dimension format was presented to calculate two-dimensional heat conduction equations of heating slab. The billet simulated was placed in a changeable thermal flux boundary environment, in which the thermal flux was proportional to fourth power of temperature. During the heating process, the changeable parameters were taken into account: i. e different billet dimensions, different billet thermal conduction, different specific heat, etc. The comparision between results of two-dimensional finite difference method and the simplified method verified that the simplified method can satisfy accuracy requirement as well as calculation time saving, which enable the simplified method online using.

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