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NUMERICAL SOLUTIONS TO A FRACTIONAL DIFFUSION EQUATION USED IN MODELLING DYE-SENSITIZED SOLAR CELLS

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  16 November 2021

BENJAMIN MALDON Open the ORCID record for BENJAMIN MALDON [Opens in a new window] ,
BISHNU PRASAD LAMICHHANE Open the ORCID record for BISHNU PRASAD LAMICHHANE [Opens in a new window]  and
NGAMTA THAMWATTANA Open the ORCID record for NGAMTA THAMWATTANA [Opens in a new window]
BENJAMIN MALDON*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW2308, Australia; e-mail: [email protected] and [email protected].
BISHNU PRASAD LAMICHHANE
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW2308, Australia; e-mail: [email protected] and [email protected].
NGAMTA THAMWATTANA
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW2308, Australia; e-mail: [email protected] and [email protected].
*
e-mail: [email protected]
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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.

Keywords

dye-sensitized solar cellselectron densityefficiencyfractional diffusionfinite-difference methodsfinite-element methods

MSC classification

Primary: 35R11: Fractional partial differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 4 , October 2021 , pp. 420 - 433
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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