Solution of a plane steady heat conduction problem with boundary conditions of the third kind for regions of special type

1966 ◽  
Vol 10 (6) ◽  
pp. 428-433
Author(s):  
B. A. Vasil'ev
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
The Third ◽  
Steady Heat Conduction ◽  
Steady Heat

Inverse Determination of Boundary Conditions and Sources in Steady Heat Conduction With Heat Generation

1996 ◽  
Vol 118 (3) ◽  
pp. 546-554 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Analytic Solutions ◽  
Heat Sources ◽  
Two Dimensional ◽  
Simple Modification ◽  
Ill Posed ◽  
Steady Heat Conduction ◽  
Steady Heat

A Boundary Element Method (BEM) implementation for the solution of inverse or ill-posed two-dimensional Poisson problems of steady heat conduction with heat sources and sinks is proposed. The procedure is noniterative and cost effective, involving only a simple modification to any existing BEM algorithm. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object while the heat sources can be partially or entirely unknown. Overspecified boundary conditions or internal temperature measurements are required in order to compensate for the unknown conditions. The weighted residual statement, inherent in the BEM formulation, replaces the more common iterative least-squares (L2) approach, which is typically used in this type of ill-posed problem. An ill-conditioned matrix results from the BEM formulation, which must be properly inverted to obtain the solution to the ill-posed steady heat conduction problem. A singular value decomposition (SVD) matrix solver was found to be more effective than Tikhonov regularization for inverting the matrix. Accurate results have been obtained for several steady two-dimensional heat conduction problems with arbitrary distributions of heat sources where the analytic solutions were available.

A Plane steady heat conduction problem

1966 ◽  
Vol 10 (2) ◽  
pp. 163-166 ◽  
Author(s):  
Yu. Ya. Iossel ◽  
R. A. Pavlovskii
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Steady Heat Conduction ◽  
Steady Heat

scholarly journals Local fractional Euler’s method for the steady heat-conduction problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 735-738 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Relaxation Equation ◽  
Euler’S Method ◽  
Steady Heat Conduction ◽  
First Time ◽  
Steady Heat

In this paper, the local fractional Euler?s method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.

Steady heat-conduction problem for a double cylinder

1974 ◽  
Vol 26 (2) ◽  
pp. 238-245 ◽  
Author(s):  
I. E. Zino ◽  
Yu. A. Sokovishin
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Steady Heat Conduction ◽  
Steady Heat

scholarly journals Local fractional functional decomposition method for solving local fractional Poisson equation in steady heat-conduction problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 785-788
Author(s):  
Xiao-Ying Wang
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Poisson Equation ◽  
Decomposition Method ◽  
Heat Conduction Problem ◽  
Functional Decomposition ◽  
Steady Heat Conduction ◽  
Steady Heat ◽  
Fractional Functional

The steady heat-conduction problem via local fractional derivative is investigated in this paper. The analytical solution of the local fractional Poisson equation is obtained. The local fractional functional decomposition method is proposed to find the analytical solution of the partial differential equation in the steady heat-conduction problem.

A Least-Squares Finite Element Formulation for Inverse Detection of Unknown Boundary Conditions in Steady Heat Conduction

2008 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Unknown Boundary ◽  
Unknown Boundary Conditions ◽  
Steady Heat Conduction ◽  
Steady Heat ◽  
Element Method

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in steady heat conduction is presented. The method is capable of determining temperatures and heat fluxes in locations where such quantities are unknown provided such quantities are sufficiently overspecified in other locations. In several finite element and boundary element inverse implementations, the resulting system of equations becomes become rectangular if the number of overspecified conditions exceeds the number of unknown conditions. In the case of the finite element method, these rectangular matrices are sparse and can be difficult to solve efficiently. Often we must resort to the use of direct factorizations that require large amounts of core memory for realistic geometries. This difficulty has prevented the solution of large-scale inverse problems that require fine meshes to resolve complex 3-D geometries and material interfaces. In addition, the Galerkin finite element method (GFEM) does not provide the same level of accuracy for both temperature and heat flux. In this paper, an alternative finite element approach based on LSFEM will be shown. The LSFEM formulation always results in a symmetric positivedefinite matrix that can be readily treated with standard sparse matrix solvers. In this approach, the differential equation is cast in first-order form so equal order basis functions can be used for both temperature and heat flux. Enforcement of the overspecified boundary conditions is straightforward in the proposed formulation. The methods allows for direct treatment of complex geometries composed of heterogeneous materials.

Sign in / Sign up

Export Citation Format

Share Document