Kamalesh Kumar
Verified @gmail.com
Scopus Publications
- Numerical simulation of cobalt coated ferrite nanoparticle flow and exponential heat transfer over an expanding cylinder
D. Bhavya, M.S. Sarvajith, K.R. Vasanth, K. Ganesh Kumar
Next Materials, 2026 - An efficient numerical approach for time-fractional singularly perturbed Burger-Huxley equation
Pramod Chakravarthy Podila, Rahul Mishra, Kamalesh Kumar, Higinio Ramos
Computational and Applied Mathematics, 2026 - A comparative mathematical framework for strontium Stannate nanoparticle flow over a stretching sheet with Forchheimer effect
D.B. Anitha, K.R. Vasanth, K. Ganesh Kumar
International Communications in Heat and Mass Transfer, 2026 - Thermophoresis and Brownian motion effect on hybrid nanoparticles flow over a wedge surface by considering double stratification effects
D. G. Prakasha, K. Ganesh Kumar, Waseem Sharaf Saeed, Aqeel Afzal
Numerical Heat Transfer Part A Applications, 2026
This research looks at the flow of hybrid nanoparticles across a wedge-shaped surface. In addition to this, Brownian motion and thermal stratification are used to model how heat moves through a system. The mass expression also deals with the thermophoresis effect and mass stratification. The governing equations involve the continuity, momentum, energy, and mass equation of hybrid nanofluids that are modified into ODE's by applying similarity transformation. The solutions are obtained from two well-known numerical routines, RKF-45 and the profiles embodying f′(η),θ(η), and P(η) are interpreted under the influence of several physical parameters. The results showed that as the Prandtl number goes up, temperature profiles of fluid flow go down, and as Brownian motion factors go up, temperature profiles go up. It is found that the fluid's thermal flow rate slows down as the Brownian motion and thermophoretic elements get stronger. On the other hand, the thermal flow rate of fluid goes up as the thermal stratification parameter goes up. - A new stable finite difference scheme and its error analysis for two-dimensional singularly perturbed convection–diffusion equations
Kamalesh Kumar, Pramod Chakravarthy Podila
Numerical Methods for Partial Differential Equations, 2022
Abstract This work focuses on the numerical solution of two‐dimensional singularly perturbed convection–diffusion equations via a new stable finite difference (NSFD) scheme on a tensor product of two piecewise‐uniform Shishkin meshes. First, we convert the two‐dimensional equation into two one‐dimensional equations using the alternating direction implicit technique. A NSFD scheme has been developed using Taylor's series and the one‐dimensional equations. Here the truncation of Taylor's series is different from the classical finite difference scheme. The convergence analysis is also studied on a tensor product of two piecewise‐uniform Shishkin meshes. Numerical simulations confirm the theory. Moreover, from the numerical illustrations, it is also observed that the method is parameter uniform convergent. - A stable finite difference scheme and error estimates for parabolic singularly perturbed PDEs with shift parameters
Kamalesh Kumar, P. Chakravarthy, H. Ramos, J. Vigo-Aguiar
Journal of Computational and Applied Mathematics, 2022 - A graded mesh refinement approach for boundary layer originated singularly perturbed time-delayed parabolic convection diffusion problems
Kamalesh Kumar, Pramod Chakravarthy Podila, P. Das, H. Ramos
Mathematical Methods in the Applied Sciences, 2021
In this work, we consider a graded mesh refinement algorithm for solving time‐delayed parabolic partial differential equations with a small diffusion parameter. The presence of this parameter leads to boundary layer phenomena. These problems are also known as singularly perturbed problems. For these problems, it is well‐known that one cannot achieve a convergent solution to maintain the boundary layer dynamics, on a fixed number of uniform meshes irrespective of the arbitrary magnitude of perturbation parameter. Here, we consider an adaptive graded mesh generation algorithm, which is based on an entropy function in conjunction with the classical difference schemes, to resolve the layer behavior. The advantage of the present algorithm is that it does not require to have any information about the location of the layer. Several examples are presented to show the high performance of the proposed algorithm. - A Novel Method for Singularly Perturbed Delay Differential Equations of Reaction-Diffusion Type
P. Chakravarthy, Kamalesh Kumar
Differential Equations and Dynamical Systems, 2021
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction–diffusion type. A fitted operator finite difference scheme based on Numerov’s method is constructed. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method. - Numerical solution of time-fractional singularly perturbed convection–diffusion problems with a delay in time
Kamalesh Kumar, P. Chakravarthy, J. Vigo-Aguiar
Mathematical Methods in the Applied Sciences, 2021
This work is concerned with the development of a stable finite difference method (SFDM) for time‐fractional singularly perturbed convection–diffusion problems with a delay in time. The fractional derivative is considered in the Caputo sense. The SFDM is constructed based on the stability of the analytical solution. Unlike the other classical numerical methods for singular perturbation problems, this method works nicely on a uniform mesh. The method is easily adaptable on Shishkin mesh and also on any graded mesh in space. Error estimates are presented to show the convergence of the numerical scheme. To support the theory, numerical results are presented in tables for different values of the fractional derivative parameter and perturbation parameter. - A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs
Pramod Chakravarthy Podila, Kamalesh Kumar
Computational and Applied Mathematics, 2020
In this study, we consider the time-delayed singularly perturbed parabolic PDEs (SPPPDEs). We know that the classical finite difference scheme will not produce good results for singular perturbation problems on a uniform mesh. Here, we propose a new stable finite difference (NSFD) scheme, which produces good results on a uniform mesh and also on an adaptive mesh. The NSFD scheme is constructed based on the stability of the analytical solution. Results are compared with the results available in the literature and observed that the proposed method is efficient over the existing methods for solving SPPPDEs. - An adaptive mesh method for time dependent singularly perturbed differential-difference equations
P. Pramod Chakravarthy, Kamalesh Kumar
Nonlinear Engineering, 2019 - A class of finite difference schemes for singularly perturbed delay differential equations of second order
Pramod Chakravarthy Podila, Kamalesh Kumar
Turkish Journal of Mathematics, 2019 - An adaptive mesh selection strategy for solving singularly perturbed parabolic partial differential equations with a small delay
Kamalesh Kumar, Trun Gupta, P. Chakravarthy, R. Rao
Trends in Mathematics, 2019 - MHD flow and heat transfer (PST and PHF) of dusty fluid suspended with alumina nanoparticles over a stretching sheet embedded in a porous medium under the influence of thermal radiation
M. R. Krishnamurthy, K. Ganesh Kumar, B. J. Gireesha, N. G. Rudraswamy
Journal of Nanofluids, 2018 - Scrutinization of joule heating and viscous dissipation on MHD flow and melting heat transfer over a stretching sheet
K.G. Kumar, B.J. Gireesha, S. Manjunatha
International Journal of Applied Mechanics and Engineering, 2018 - Enhancement of radiation on hydromagnetic Casson fluid flow towards a stretched cylinder with suspension of liquid-particles
G.K. Ramesh, K. Ganesh Kumar, S.A. Shehzad, B.J. Gireesha
Canadian Journal of Physics, 2018 - Effect of viscous dissipation on three dimensional flow of a nanofluid by considering a gyrotactic microorganism in the presence of convective condition
Bijjanal Jayanna Gireesha, K. Ganesh Kumar, N.G. Rudraswamy, S. Manjunatha
Defect and Diffusion Forum, 2018 - Non linear thermal radiation effect on Williamson fluid with particle-liquid suspension past a stretching surface
K. Ganesh Kumar, N.G. Rudraswamy, B.J. Gireesha, S. Manjunatha
Results in Physics, 2017
