Journal of Scientific and Technical Research (Sharda University, Noida)

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Computational Solution Of One Dimensional Diffusion Equation With Fixed Limits


Affiliations
1 Department Of Mathematics, SBSR Sharda University, Greater Noida, Uttar Pradesh, India
     

   Subscribe/Renew Journal


This paper presents a model for the mathematical description of the diffusion process, as well as an attempt to use Green’s function approach to solve the one-dimensional diffusion equation within the necessary bounds. By studying the initial condition for, we will be able to obtain the appropriate solution to this diffusion equation. With a constant diffusion coefficient, this equation represents the rate of change of concentrations of substances in their own lattice or in separate substances. Finally, numerical answers will be obtained via a computational approach. Because we consider t = 0 throughout the equation, the result can also be applied to an isothermal diffusion.

Keywords

Diffusion Process, Fick’s Law, Green’s Function Method, Mathematical Modelling Of Diffusion Process, Thermal Diffusion.
User
Subscription Login to verify subscription
Notifications
Font Size

  • M. Suchecka, A. Borisovich, and W. Serbimnski, “Green’s function methods for mathematical modeling of unidirectional diffusion process in isothermal metal bonding process,” Advances in Materials Science, vol. 5, no. 3, 2005.

  • J. N. Kapur, Mathematical Models in Biology and Medicine. East West Press Private Limited, 2000.

  • P. Shewmon, Diffusion in Solids, 2nd ed. The Minerals Metals and Materials Society, 1989.

  • R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomenon. John Wiley and Sons (Asia) Pvt. Ltd., India, 2002.

  • NATO Science Series, “Mathematical modeling and research for diffusion process in multilayer and nonporous media,” Fluid Transport in Nanoporous Materials, vol. 219, Springer Netherlands, 2006, pp. 639-655.

  • M. Petryk, S. Leclerc, D. Canet, and J. Fraissard, “Mathematical modeling and visualization of gas transport in a Zeolite bed using a slice selection procedure,” Diffusion Fundamentals, vol. 4, no. 11, pp. 1-23, 2007.

  • M. R. Petryk, “Mathematical modeling of mass transfer in symmetric heterogeneous and non-porous media with a system of n-interface interactions,” Cybernetics and Systems Analysis, vol. 43, pp. 94-111, 2007.

  • I. S. Ike, L. E. Aneke, and G. O. Mbah, “Mathematical modeling and simulation of a diffusion process in the human bloodstream,” AMSE Journals - 2014-Series: Modelling C, vol. 75, no. 1, pp. 1-12, 2014.

  • S. Mungkasi, “Modelling and simulation of topical drug diffusion in the dermal layer of human body,” Journal of Advances Research in Fluid Mechanics and Thermal Sciences, vol. 86, no. 2, pp. 39-49, 2021.


Abstract Views: 250

PDF Views: 0




  • Computational Solution Of One Dimensional Diffusion Equation With Fixed Limits

Abstract Views: 250  |  PDF Views: 0

Authors

Alpna Mishra
Department Of Mathematics, SBSR Sharda University, Greater Noida, Uttar Pradesh, India

Abstract


This paper presents a model for the mathematical description of the diffusion process, as well as an attempt to use Green’s function approach to solve the one-dimensional diffusion equation within the necessary bounds. By studying the initial condition for, we will be able to obtain the appropriate solution to this diffusion equation. With a constant diffusion coefficient, this equation represents the rate of change of concentrations of substances in their own lattice or in separate substances. Finally, numerical answers will be obtained via a computational approach. Because we consider t = 0 throughout the equation, the result can also be applied to an isothermal diffusion.

Keywords


Diffusion Process, Fick’s Law, Green’s Function Method, Mathematical Modelling Of Diffusion Process, Thermal Diffusion.

References