Next Article in Journal
A Novel Counterfeit Feature Extraction Technique for Exposing Face-Swap Images Based on Deep Learning and Error Level Analysis
Next Article in Special Issue
Stability Analysis of the Explicit Difference Scheme for Richards Equation
Previous Article in Journal
The Self-Simulation Hypothesis Interpretation of Quantum Mechanics
Previous Article in Special Issue
Spherically Restricted Random Hyperbolic Diffusion
Article

Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells

1
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan NSW 2308, Australia
2
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, Australia
*
Author to whom correspondence should be addressed.
Current address: University Drive, Callaghan, NSW 2308 Australia.
Entropy 2020, 22(2), 248; https://doi.org/10.3390/e22020248
Received: 14 January 2020 / Revised: 11 February 2020 / Accepted: 19 February 2020 / Published: 21 February 2020
(This article belongs to the Special Issue Applications of Nonlinear Diffusion Equations)
Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells. Under linear diffusion and recombination, this paper provides analytical solutions to the diffusion equation. Further, Lie symmetry analysis is adopted in order to explore analytical solutions to physically relevant special cases of the nonlinear diffusion equations. While analytical solutions may not be possible, we provide numerical solutions, which are in good agreement with the results given in the literature. View Full-Text
Keywords: dye-sensitized solar cells; electron density; efficiency; nonlinear diffusion; Lie symmetry dye-sensitized solar cells; electron density; efficiency; nonlinear diffusion; Lie symmetry
Show Figures

Figure 1

MDPI and ACS Style

Maldon, B.; Thamwattana, N.; Edwards, M. Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells. Entropy 2020, 22, 248. https://doi.org/10.3390/e22020248

AMA Style

Maldon B, Thamwattana N, Edwards M. Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells. Entropy. 2020; 22(2):248. https://doi.org/10.3390/e22020248

Chicago/Turabian Style

Maldon, Benjamin, Ngamta Thamwattana, and Maureen Edwards. 2020. "Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells" Entropy 22, no. 2: 248. https://doi.org/10.3390/e22020248

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop