Dr. R. Usha Rani
@mce.edu.in
Assistant Professor and Mathematics
Meenakshi College of Engineering
3
Scopus Publications
31
Scholar Citations
1
Scholar h-index
1
Scholar i10-index
Scopus Publications
- Understanding the nonlinear reactive transport model in porous catalysts
D. Sujatha, R.Usha Rani, G. Vennila, A. Marimuthu, M. Renugadevi, and L. Rajendran
Elsevier BV - Analytical and numerical solutions of nonlinear heat diffusion model for the thermal energy storage problem
Vannathamizhan Silambuselvi, Karuppiah Angaleeswari, Sekar Rekha, Lakshmanan Rajendran, and Ramu Usha Rani
AIP Publishing - Theoretical analysis of the enzyme reaction processes within the multiscale porous biocatalytic electrodes: Akbari–Ganji's and Taylor's series method
S. Krishnakumar, R. Usha Rani, K. Lakshmi Narayanan, and L. Rajendran
Elsevier BV - A theoretical and computational analysis of the concentration of substrate and product in enzyme-based electrochemical biosensors: Akbari-Ganji's method
R. Usha Rani, Navnit Jha, and Lakshmanan Rajendran
Elsevier BV - Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential
Ramu Usha Rani, Lakshmanan Rajendran, and Marwan Abukhaled
Springer Science and Business Media LLC - Theoretical analysis of amperometric response towards PPO-based rotating disk bioelectrodes: Taylors series and hyperbolic function method
Vannathamizhan Silambuselvi, Sekar Rekha, Ramu Usha Rani, Lakshmanan Rajendran, Karuppiah Angaleeswari, and Michael E.G. Lyons
Elsevier BV - Analytical Expressions for Steady-State Current and Estimation of Kinetic Parameters in an Amperometric Biosensor with The Product Inhibition: Power Series Method
J. Saranya, R. Usha Rani, M. E. G. Lyons, M. Abukhaled, and L. Rajendran
AIP Publishing - Mathematical Modelling of Amperometric Glucose Biosensor Based on Immobilized Enzymes: New Approach of Taylors Series Method
K. Lakshmi Narayanan, J. Kavitha, Ramu Usha Rani, Michael E.G. Lyons, and Lakshmanan Rajendran
Elsevier BV
An amperometric glucose biosensor's theoretical model is discussed. The glucose oxidase enzyme in this model is immobilized in conducting polypyrrole.This model includes a nonlinear term that corresponds with the kinetics of enzyme reactions. The solution of coupled nonlinear reaction diffusion equations is obtained using new approach of Taylor method . Additionally, a comparison of numerical simulation and analytical approximation is provided. There is an agreement between numerical results and analytical expressions. - A New Method to Study the Nonlinear Reaction-Diffusion Process in the Electroactive Polymer Film using Hyperbolic Function Method
Sekar Rekha and
Elsevier BV
A mathematical model developed by Lyons and co-workers (Analyst, 121, (1996) 715–731) describes a substrate to form a complex with the immobilized catalyst is discussed. The hyperbolic function method is applied to solve the nonlinear equations in the electroactive polymer film. The resulting analytical expression of the substrate concentration is compared to the numerical results and previously available results. A satisfactory agreement is noted. The innovative method yields a compact set of analytical approximations that are easy to compute and simple to validate - Transport and Kinetics in Biofiltration Membranes: New Analytical Expressions for Concentration Profiles of Hydrophilic and Hydrophobic VOCs Using Taylor’s Series and Akbari- Ganji methods
Singaravel Anandhar Salai Sivasundari and
Elsevier BV
The mathematical models of biofiltration of mixtures of hydrophilic (methanol) and hydrophobic ( pinene) volatile organic compounds (VOCs) are explored in this paper. This model is based on diffusion equations that contain a nonlinear term linked to the enzymatic reaction's Michaelis-Menten kinetics. An approximate analytical expression of methanol and pinene concentration profiles in the air and biofilm phase were derived using Taylor's series and Akbari-Ganji's methods. In addition, the numerical simulation of the problem using the Matlab programme to investigate the system's dynamics is reported in this work. Graphic results are presented to illustrate the solution, and numerical data is analyzed. The analytical and numerical data are in good agreement. - Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji's Methods
Ramu UshaRani, Lakshmanan Rajendran, and Marwan Abukhaled
International Information and Engineering Technology Association
A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations. - Diffusion indicator for hemispheroidal and ring ultramicroelectrode geometries for E and ECʹ reactions
R. Usha Rani and L. Rajendran
Elsevier BV - Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method
Ramu Usha Rani, Lakshmanan Rajendran, and Michael E.G. Lyons
Elsevier BV - Nonlinear Mass Transfer at the Electrodes with Reversible Homogeneous; Reactions:Taylor’s Series and Hyperbolic Function Method
Lilly Clarance Mary and
Elsevier BV
The mathematical model for mass transfer with reversible homogeneous reactions is discussed. Estimation of mass transfer to and from electrodes for this reaction needs the analytical solution of nonlinear reaction-diffusion equations. Taylor's series method and hyperbolic function method are used to solve the system of nonlinear reaction-diffusion equations. Approximate closed-form of analytical expression of the concentration of substrate, reactant and product are derived for all values parameters. The empirical results are compared with the simulation results, and there is noticeable agreement. The effect of various parameter on aqueous carbonate-species concentration are also discussed. The current density and homogeneous equilibrium constant are also obtained. - Approximate analytical solution of nonlinear equations in cubic auto-catalytic reaction-diffusion process
R. Usha Rani and L. Rajendran
AIP Publishing - Taylor's series method for solving the nonlinear reaction-diffusion equation in the electroactive polymer film
R. Usha Rani and L. Rajendran
Elsevier BV
RECENT SCHOLAR PUBLICATIONS
- Understanding the nonlinear reactive transport model in porous catalysts
D Sujatha, RU Rani, G Vennila, A Marimuthu, M Renugadevi, ...
International Journal of Electrochemical Science 19 (12), 100852 2024 - Analytical and numerical solutions of nonlinear heat diffusion model for the thermal energy storage problem
V Silambuselvi, K Angaleeswari, S Rekha, L Rajendran, RU Rani
AIP Conference Proceedings 3160 (1) 2024 - Theoretical analysis of the enzyme reaction processes within the multiscale porous biocatalytic electrodes: Akbari–Ganji's and Taylor’s series method
S Krishnakumar, RU Rani, KL Narayanan, L Rajendran
International Journal of Electrochemical Science 19 (4), 100527 2024 - A theoretical and computational analysis of the concentration of substrate and product in enzyme-based electrochemical biosensors: Akbari-Ganji’s method
RU Rani, N Jha, L Rajendran
Journal of Electroanalytical Chemistry 956, 118077 2024 - Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential
RU Rani, L Rajendran, M Abukhaled
Reaction Kinetics, Mechanisms and Catalysis 136 (3), 1229-1242 2023 - Theoretical analysis of amperometric response towards PPO-based rotating disk bioelectrodes: Taylors series and hyperbolic function method
V Silambuselvi, S Rekha, RU Rani, K Angaleeswari
International Journal of Electrochemical Science 18 (4), 100083 2023 - A New Method to Study the Nonlinear Reaction-Diffusion Process in the Electroactive Polymer Film using Hyperbolic Function Method
* Sekar Rekha1 , Ramu Usha Rani2 , Lakshmanan Rajendran1,*, Michael E.G. Lyons3
International Journal of ELECTROCHEMICAL SCIENCE 17, 221261 2022 - Analytical expressions for steady-state current and estimation of kinetic parameters in an amperometric biosensor with the product inhibition: Power series method
J Saranya, RU Rani, MEG Lyons, M Abukhaled, L Rajendran
AIP Conference Proceedings 2516 (1) 2022 - Mathematical modelling of amperometric glucose biosensor based on immobilized enzymes: new approach of taylors series method
KL Narayanan, J Kavitha, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (10), 221064 2022 - Mathematical modelling of forced convection in a porous medium for a general geometry: Solution of thermal energy equation via Taylor’s series with Ying Buzu algorithms
KL Narayanan, R Shanthi, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (6), 220623 2022 - Transport and Kinetics in Biofiltration Membranes: New Analytical Expressions for Concentration Profiles of Hydrophilic and Hydrophobic VOCs Using Taylor’s Series and Akbari
SAS Sivasundari, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (4), 220447 2022 - Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods
MA Ramu Usha Rani 1 , Lakshmanan Rajendran 1*
Mathematical Modelling of Engineering Problems 8 (4), 527-537 2021 - Diffusion indicator for hemispheroidal and ring ultramicroelectrode geometries for E and ECʹ reactions
RU Rani, L Rajendran
Electrochemistry Communications 128, 107071 2021 - Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method
RU Rani, L Rajendran, MEG Lyons
Journal of Electroanalytical Chemistry 886, 115103 2021 - Taylor’s Series Solution of a Singular BVP of Reaction cum Diffusion in a Biocatalyst
LR • R. Usha Rani
Emerging Technologies and Innovative Research in Science, Engineering and 2021 - Nonlinear Mass Transfer at the Electrodes with Reversible Homogeneous; Reactions: Taylor'sSeries and Hyperbolic Function Method
LC Mary, RU Rani, A Meena, L Rajendran
International Journal of Electrochemical Science 16 (1), 151037 2021 - Approximate analytical solution of nonlinear equations in cubic auto-catalytic reaction-diffusion process
RU Rani, L Rajendran
AIP Conference Proceedings 2277 (1), 130006 2020 - Taylor’s series method for solving the nonlinear reaction-diffusion equation in the electroactive polymer film
RU Rani, L Rajendran
Chemical Physics Letters 754, 137573 2020
MOST CITED SCHOLAR PUBLICATIONS
- Taylor’s series method for solving the nonlinear reaction-diffusion equation in the electroactive polymer film
RU Rani, L Rajendran
Chemical Physics Letters 754, 137573 2020
Citations: 55 - Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method
RU Rani, L Rajendran, MEG Lyons
Journal of Electroanalytical Chemistry 886, 115103 2021
Citations: 38 - Nonlinear Mass Transfer at the Electrodes with Reversible Homogeneous; Reactions: Taylor'sSeries and Hyperbolic Function Method
LC Mary, RU Rani, A Meena, L Rajendran
International Journal of Electrochemical Science 16 (1), 151037 2021
Citations: 23 - Transport and Kinetics in Biofiltration Membranes: New Analytical Expressions for Concentration Profiles of Hydrophilic and Hydrophobic VOCs Using Taylor’s Series and Akbari
SAS Sivasundari, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (4), 220447 2022
Citations: 14 - Mathematical modelling of forced convection in a porous medium for a general geometry: Solution of thermal energy equation via Taylor’s series with Ying Buzu algorithms
KL Narayanan, R Shanthi, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (6), 220623 2022
Citations: 12 - Mathematical modelling of amperometric glucose biosensor based on immobilized enzymes: new approach of taylors series method
KL Narayanan, J Kavitha, RU Rani, MEG Lyons, L Rajendran
International Journal of Electrochemical Science 17 (10), 221064 2022
Citations: 10 - A New Method to Study the Nonlinear Reaction-Diffusion Process in the Electroactive Polymer Film using Hyperbolic Function Method
* Sekar Rekha1 , Ramu Usha Rani2 , Lakshmanan Rajendran1,*, Michael E.G. Lyons3
International Journal of ELECTROCHEMICAL SCIENCE 17, 221261 2022
Citations: 9 - Diffusion indicator for hemispheroidal and ring ultramicroelectrode geometries for E and ECʹ reactions
RU Rani, L Rajendran
Electrochemistry Communications 128, 107071 2021
Citations: 7 - Theoretical analysis of amperometric response towards PPO-based rotating disk bioelectrodes: Taylors series and hyperbolic function method
V Silambuselvi, S Rekha, RU Rani, K Angaleeswari
International Journal of Electrochemical Science 18 (4), 100083 2023
Citations: 6 - Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods
MA Ramu Usha Rani 1 , Lakshmanan Rajendran 1*
Mathematical Modelling of Engineering Problems 8 (4), 527-537 2021
Citations: 6 - Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential
RU Rani, L Rajendran, M Abukhaled
Reaction Kinetics, Mechanisms and Catalysis 136 (3), 1229-1242 2023
Citations: 5 - Approximate analytical solution of nonlinear equations in cubic auto-catalytic reaction-diffusion process
RU Rani, L Rajendran
AIP Conference Proceedings 2277 (1), 130006 2020
Citations: 4 - Theoretical analysis of the enzyme reaction processes within the multiscale porous biocatalytic electrodes: Akbari–Ganji's and Taylor’s series method
S Krishnakumar, RU Rani, KL Narayanan, L Rajendran
International Journal of Electrochemical Science 19 (4), 100527 2024
Citations: 3 - Understanding the nonlinear reactive transport model in porous catalysts
D Sujatha, RU Rani, G Vennila, A Marimuthu, M Renugadevi, ...
International Journal of Electrochemical Science 19 (12), 100852 2024
Citations: 1 - Analytical expressions for steady-state current and estimation of kinetic parameters in an amperometric biosensor with the product inhibition: Power series method
J Saranya, RU Rani, MEG Lyons, M Abukhaled, L Rajendran
AIP Conference Proceedings 2516 (1) 2022
Citations: 1