A New Approximate Analytic Solution for Finite-Conductivity Vertical Fractures

1986 ◽  
Vol 1 (01) ◽  
pp. 75-88 ◽  
Author(s):  
Sheng-Tai Lee ◽  
John R. Brockenbrough
Keyword(s):  
Analytic Solution ◽  
Finite Conductivity ◽  
Approximate Analytic Solution ◽  
Vertical Fractures

scholarly journals An approximate analytic solution of a particular boundary value problem

2001 ◽  
Vol 27 (8) ◽  
pp. 513-520
Author(s):  
Ugur Tanriver ◽  
Aravinda Kar
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Equation ◽  
Analytic Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Welding Process ◽  
Approximate Analytic Solution ◽  
Analytic Expression ◽  
Steady State Heat ◽  
Laser Welding Process

This note is concerned with the three-dimensional quasi-steady-state heat conduction equation subject to certain boundary conditions in the wholex′y′-plane and finite inz′-direction. This type of boundary value problem arises in laser welding process. The solution to this problem can be represented by an integral using Fourier analysis. This integral is approximated to obtain a simple analytic expression for the temperature distribution.

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