Numerical solutions to a fractional diffusion equation used in modelling dye-sensitized solar cells

Benjamin J. Maldon; Bishnu Lamichhane; Ngamta Thamwattana

doi:10.21914/anziamj.v63.15944

Authors

Benjamin J. Maldon University of Newcastle http://orcid.org/0000-0001-8746-7575
Bishnu P. Lamichhane University of Newcastle https://orcid.org/0000-0002-9184-8941
Ngamta Thamwattana University of Newcastle https://orcid.org/0000-0001-9885-3287

DOI:

https://doi.org/10.21914/anziamj.v63.15944

Keywords:

dye-sensitized solar cells, electron density, efficiency, fractional diffusion, finite-difference methods, finite-element methods

Abstract

Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.

doi:10.1017/S1446181121000353

Author Biographies

Benjamin J. Maldon, University of Newcastle

PhD Student, School of Mathematical and Physical Sciences, University of Newcastle, Callagham NSW 2308, Australia.

Bishnu P. Lamichhane, University of Newcastle

School of Mathematical and Physical Sciences, University of Newcastle, Callagham NSW 2308, Australia.

Ngamta Thamwattana, University of Newcastle