Unsteady Heat Conduction Problem for a Plane with a Crack at the Interface between Two Inhomogeneous Materials

2021 ◽  
Vol 61 (11) ◽  
pp. 1800-1810
Author(s):  
A. V. Glushko ◽  
E. A. Loginova
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inhomogeneous Materials ◽  
Unsteady Heat Conduction

An Application of Conformal Mapping to a Three-Dimensional Unsteady Heat Conduction Problem

1965 ◽  
Vol 16 (3) ◽  
pp. 221-230 ◽  
Author(s):  
Patricio A. Laura ◽  
M. Chi
Keyword(s):  
Heat Conduction ◽  
Conformal Mapping ◽  
Cross Section ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Unsteady State ◽  
Numerical Techniques ◽  
Prismatic Body ◽  
Unsteady Heat Conduction

SummaryThis paper deals with an unsteady-state three-dimensional heat conduction problem in a prismatic body which has a complicated boundary shape. Numerical techniques such as a relaxation method must be used to solve a problem of this type; this method, however, requires unusually large amounts of labour. The method used in this paper consists of the application of conformal mapping and numerical solution of a partial differential equation and is applied first to a prismatic body of square cross section for which the exact solution is well known. As a second application, the approximate solution for a problem involving a star-shaped cross section is presented.

scholarly journals The mixed unsteady heat conduction problem for a half-infinite hollow cylinder

2019 ◽  
pp. 222-225
Author(s):  
I. M. Turchyn ◽  
G. V. Vasylko ◽  
O. Ya. Ivaskevych
Keyword(s):  
Heat Conduction ◽  
Integral Transformation ◽  
Mixed Boundary ◽  
Heat Conduction Problem ◽  
Laguerre Polynomials ◽  
Operating Conditions ◽  
Temperature Fields ◽  
Algebraic Equations ◽  
Dual Integral Equations ◽  
Unsteady Heat Conduction

Analysis of temperature fields is important for many engineering applications. The account of actual operating conditions of these structures frequently leads to mixed heating condition. The authors of this paper developed a new effective method of solutions derivation for mixed boundary-value unsteady heat conduction problems. This paper considers the cylinder with at the part of surface of which the temperature distribution is known. Outside this area the heat transfer by Newton's law is performed. To the heat conductivity problem it is applied the Laguerre integral transformation in time variables and integral Fourier transformation in spatial variable. As a result the triangular sequence of ordinary differential equations is obtained. The general solution of these sequences is obtained in the form of algebraic convolution. Taking into account the mixed boundary conditions leads to dual integral equations. For solution of this problem it is proposed the method of Neumann's series. By this method the problem is reduced to the infinite system of algebraic equations, for which the convergence of reduction procedure is proved. Finally, the unknown temperature is submitted as a series of Laguerre polynomials. The coefficient of these series is Fourier integrals.

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