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Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data

Bullo Tesfaye Aga, Degla Guy Aymard, Duressa Gemechis File

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

5-16

A uniformly convergent higher-order finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with non-smooth data. This scheme involves an average non-standard finite difference with the Richardson extrapolation method for space variables and second-order finite difference approximation for time direction on uniform meshes. The scheme is shown to be second-order convergent in both temporal and spatial directions. Further, the scheme is proven to be uniformly convergent and also confirmed by numerical experiments. Wide numerical experiments are conducted to support the theoretical results and to demonstrate its accuracy. Concisely, the present scheme is stable, convergent, and more accurate than existing methods in the literatur

Heat transfer in thin porous fibrous material: mathematical modelling and experimental validation using active thermography

Banerjee D., Zhao S, Schabel S.

Autex Research Journal

2010

Vol. 10, no. 4

95--99

This paper deals with the modelling of the heat transfer process in a thin porous fibrous material such as a paper sheet when it is subjected to an incident heat flux introduced by a laser beam. A mathematical model based on the control volume principle is developed for numerical estimation of radial temperature distribution which is validated experimentally by infrared thermography. Here the heat flux is introduced by a CO2 laser beam of 10.6 μm wavelength and an infrared image sequence is recorded as a function of time with a high resolution infrared camera. The preliminary validation results indicate that the simulation model can predict the transient development of sheet temperature very accurately under the specified heating conditions. The model can enhance our understanding and insights of the heat transfer process in such media, which is of great interest for many drying and thermal applications. Though the application shown here is on a 0.1 mm thick paper sheet, the model can be extended to any thin porous fibrous media such as textiles and nonwovens.