Control of an Error of a Finite-Difference Solution of the Heat-Conduction Equation by the Conjugate Equation

2004 ◽  
Vol 77 (1) ◽  
pp. 177-184 ◽  
Author(s):  
A. K. Alekseev
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Conjugate Equation ◽  
Finite Difference Solution ◽  
Difference Solution

Numerical Modelling of Nanocomposites Using GA and FD Techniques

2019 ◽  
Vol 969 ◽  
pp. 478-483 ◽  
Author(s):  
Siddhartha Kosti ◽  
Jitender Kundu
Keyword(s):  
Genetic Algorithm ◽  
Heat Conduction ◽  
Finite Difference ◽  
Numerical Modelling ◽  
Structural Properties ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Weight Percentage ◽  
Finite Difference Technique ◽  
Finite Difference Techniques

Use of nanocomposites is increasing rapidly due to their enhanced thermal and structural properties. In the present work, the numerical modelling of nanocomposites is conducted with the help of the (GA) genetic algorithm and (FD) finite difference techniques to find out a set of nanocomposites with best thermal and structural properties. The genetic algorithm is utilized to find out the best set of nanocomposites on the basis of thermal and structural properties while the finite difference technique is utilized to solve the heat conduction equation. Different nanocomposites considered in the present work are Al-B4C, Al-SiC and Al-Al2O3. The weight percentage of these nanocomposites is varied to see its effect on the nanocomposites properties. In the end, the solidification curve for all the nanocomposites is plotted and analysed. Result reveals that GA helps in identifying the best set of nanocomposites while FD technique helps in predicting the solidification curve accurately. Increment in the wt. % of nanocomposites makes the solidification curve steeper.

scholarly journals METHOD OF LINES AND FINITE DIFFERENCE SCHEMES WITH THE EXACT SPECTRUM FOR SOLUTION THE HYPERBOLIC HEAT CONDUCTION EQUATION

2011 ◽  
Vol 16 (1) ◽  
pp. 220-232 ◽  
Author(s):  
Harijs Kalis ◽  
Andris Buikis
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Difference Scheme ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Method Of Lines ◽  
Numerical Results ◽  
Conduction Equation ◽  
Finite Difference Schemes ◽  
Hyperbolic Heat Conduction

This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third kind is solved by the spectral method. Method of lines and the Fourier method are considered for the time discretization. Finite difference schemes with central difference and exact spectrum are analyzed. A novel method for solving the discrete spectral problem is used. Special matrix with orthonormal eigenvectors is formed. Numerical results are obtained for steel quenching problem in the plate and in the sphere with holes. The hyperbolic heat conduction problem in the sphere with holes is reduced to the problem in the plate. Some examples and numerical results for two typical problems related to hyperbolic heat conduction equation are presented.

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