A one-dimensional solution of the homogeneous diffusion equation

1989 ◽  
Vol 32 (4) ◽  
pp. 454-456
Author(s):  
G. Fabricatore ◽  
F. Gasparini ◽  
G. Miano
Keyword(s):  
Diffusion Equation ◽  
Dimensional Solution ◽  
One Dimensional

Corrosion initiation time of steel reinforcement in a chloride environment—A one dimensional solution

1997 ◽  
Vol 39 (4) ◽  
pp. 739-759 ◽  
Author(s):  
P. Arora ◽  
B.N. Popov ◽  
B. Haran ◽  
M. Ramasubramanian ◽  
S. Popova ◽  
...  
Keyword(s):  
Steel Reinforcement ◽  
Initiation Time ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Corrosion Initiation ◽  
Corrosion Initiation Time ◽  
Chloride Environment

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

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