scholarly journals A Recursive Estimate of Transitional Boundary Conditions in Heat Conduction Problem

1998 ◽  
Vol 1 ◽  
pp. 83-90
Author(s):  
Katsuyuki NIIMI ◽  
Makoto SUZUKI ◽  
Minoru UEDA ◽  
Masatoshi SATO
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Recursive Estimate

scholarly journals Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Aghili
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Heat Conduction Problem ◽  
Complete Solution ◽  
Mixed Boundary Conditions ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Two Dimensions ◽  
Operational Method

AbstractIn this study, we present some new results for the time fractional mixed boundary value problems. We consider a generalization of the Heat - conduction problem in two dimensions that arises during the manufacturing of p - n junctions. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.

ADDITIONAL SOUGHT-FOR FUNCTIONS AND LOCAL COORDINATE SYSTEMS APPLIED IN THE HEAT CONDUCTIVITY PROBLEMS FOR MULTILAYERED BUILDING STRUCTURES

2018 ◽  
Vol 8 (3) ◽  
pp. 29-32
Author(s):  
Ol’ga Yu. KURGANOVA
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Balance ◽  
Integral Method ◽  
Approximate Analytical Solution ◽  
Heat Conduction Problem ◽  
Erential Equation ◽  
Building Structures ◽  
Coordinate Systems ◽  
Partial Diff

The solution problems of the additional the sought-for function and additional boundary conditions based when using local coordinate systems, an approximate analytical solution of the heat conduction problem for a double-layer plate is obtained for symmetric boundary conditions of the fi rst kind. The use of the additional sought-for function in the integral method of heat balance makes it possible to reduce the solution of the partial diff erential equation to the integration of an ordinary diff erential equation.

scholarly journals A spacetime collocation Trefftz method for solving the inverse heat conduction problem

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986127 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang ◽  
Yan Su
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Heat Conduction Problem ◽  
Domain Boundary ◽  
Inverse Heat Conduction Problem ◽  
Test Problems ◽  
Inverse Heat Conduction ◽  
Trefftz Method ◽  
Base Functions

In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted to solve the inverse heat conduction problem by approximating numerical solutions using Trefftz base functions satisfying the governing equation. The validity of the proposed method is established for a number of test problems. We compared the accuracy of the proposed method with that of the Trefftz method based on exponential basis functions. Results demonstrate that the proposed method obtains highly accurate numerical solutions and that the boundary data on the inaccessible boundary can be recovered even if the accessible data are specified at only one-fourth of the overall spacetime boundary.

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