A finite difference scheme for the heat conduction equation

1985 ◽  
Vol 58 (1) ◽  
pp. 59-66 ◽  
Author(s):  
E Livne ◽  
A Glasner
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Heat Conduction Equation ◽  
Conduction Equation

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.

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.

Truncation Error Estimates for Numerical and Analog Solutions of the Heat-Conduction Equation

1961 ◽  
Vol 83 (3) ◽  
pp. 382-383 ◽  
Author(s):  
N. H. Freed ◽  
C. J. Rallis
Keyword(s):  
Heat Conduction ◽  
Heat Flow ◽  
Finite Difference ◽  
Error Estimates ◽  
Heat Conduction Equation ◽  
Truncation Error ◽  
Mesh Size ◽  
Practical Method ◽  
Conduction Equation ◽  
One Dimensional

A practical method is presented for obtaining a meaningful estimate of the truncation error associated with fully finite-difference forms of the heat-conduction equation. The analysis is applied in this instance to the Liebmann analog equations. It may also be used with other manual and analog methods of computation, where the error due to mesh size is relatively large. An example is given deriving error estimates for a case of one-dimensional heat flow.

An Unconditionally Stable Method for Solving the Heat Conduction Equation Using Laguerre Polynomials

2016 ◽  
Vol 13 (10) ◽  
pp. 6649-6653
Author(s):  
Di Zhang ◽  
Xiao-Ping Miao
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Heat Conduction Equation ◽  
Transfer Problem ◽  
Laguerre Polynomials ◽  
Conduction Equation ◽  
Stable Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
Comparison Results

In this work, an unconditionally stable method for solving the heat conduction equation is proposed. In the equation, the temperature field and its first order time derivatives are expanded by the Laguerre polynomials and weighting functions. By applying a Galerkin temporal testing procedure to the finite difference format, the time-step limitation can be eliminated in the process of computation and one can obtain an equation under no convergent conditions. To verify the efficiency and the accuracy of this presented method, we compare the numerical results of the presented method with the finite difference method (FDM) and the alternating direction implicit (ADI) method. The comparison results show that the proposed method has great advantage in efficiency while maintaining high accuracy when solving a heat transfer problem in a complex media with fine structure.

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