Evaluation of a Diffusion Coefficient Based on Proper Solution Space

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuanlong Wang ◽  
Abdalkaleg Hamad ◽  
Mohsen Tadi
Keyword(s):  
Diffusion Coefficient ◽  
Steady State ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Solution Space ◽  
Initial Guess ◽  
Proper Solution ◽  
Numerical Examples ◽  
Steady State Heat ◽  
Unknown Diffusion Coefficient

Abstract This note is concerned with the evaluation of the unknown diffusion coefficient in a steady-state heat conduction problem. The proposed method is iterative and, starting with an initial guess, updates the assumed value at every iteration. The updating stage is achieved by generating a set of functions that satisfy some of the required boundary conditions. The correction to the assumed value is then computed by imposing the remaining boundary conditions. Numerical examples are used to study the applicability of this method.

Inverse Scattering Based on Proper Solution Space

2019 ◽  
Vol 27 (03) ◽  
pp. 1850033
Author(s):  
A. Hamad ◽  
M. Tadi
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Unknown Function ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Solution Space ◽  
Initial Guess ◽  
Proper Solution ◽  
New Approach ◽  
Numerical Examples

This paper is concerned with an inverse scattering problem in frequency domain, when the scattered field is governed by the Helmholtz equation. The algorithm is iterative in nature. It introduces a new approach which we refer to as proper solution space. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. The updating stage is accomplished by generating a set of functions that satisfy some of the required boundary conditions. We refer to this space as proper solution space. The correction to the assumed value can then be obtained by imposing the remaining boundary conditions. A number of numerical examples are used to study the applicability and effectiveness of the new approach.

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

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