Jayalatha Gopal

A linear stability analysis of thermal convection in variable viscosity Newtonian ferromagnetic liquid by considering all possible boundary combinations is studied. The importance of this problem lies in the interesting possibility of regulating convection using heat source (sink). Using Galerkin technique the critical eigenvalue and wave number for stationary convection are obtained. These critical values are then improved upon by the shooting method. The influence of various parameters on the onset of convection has been analyzed. � 2017, Springer India Pvt. Ltd.

The linear and weakly nonlinear stability analysis of the quiescent state in a viscoelastic fluid subject to vertical solute concentration and temperature gradients is investigated. The non-Newtonian behavior of the viscoelastic fluid is characterized using the Oldroyd model. Analytical expressions for the critical Rayleigh numbers and corresponding wave numbers for the onset of stationary or oscillatory convection subject to cross diffusion effects is determined. A stability diagram clearly demarcates non-overlapping regions of finger and diffusive instabilities. A Lorenz system is obtained in the case of the weakly nonlinear stability analysis. The effect of Dufour and Soret parameters on the heat and mass transports are determined and discussed. Due to consideration of dilute concentrations of the second diffusing component the route to chaos in binary viscoelastic fluid systems is similar to that of single-component (thermal) viscoelastic fluid systems. � 2013 Elsevier Inc..

The influence of heat sources on instability in rotating viscoelastic liquids is studied. Linear stability analysis is done using normal modes. Computations are done for 10 boundary combinations and the results reveal that convection manifests via the oscillatory mode in this case. The critical values of the oscillatory and stationary instability have been studied. The results indicate individual stabilizing influences of rotation and strain retardation along with heat source in the case of free isothermal boundary conditions. It has quite unpredictable influences on the system stability in all the other boundary conditions for the chosen parameters. By suitable limiting processes, results pertaining to Oldroyd liquid B will lead to those of Maxwell, Newtonian, and Rivlin�Ericksen liquids. The problem finds applications in a working media consisting of viscoelastic liquids with nonisothermal systems. � 2021 Wiley Periodicals LLC

Oscillatory onset of convection is studied numerically for Rivlin-Ericksen, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and the destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to the Jeffreys description whereas the Rivlin-Ericksen liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. � 2010 Elsevier Ltd.

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter is greater than unity. When the ratio is less than unity then the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Maxwell and Jeffreys liquids by considering free-free, rigid-rigid and rigid-free isothermal/adiabatic boundaries. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen liquid is comparatively more stable. Free-free adiabatic boundary combination is found to give rise to a most unstable system, whereas the rigid isothermal rigid adiabatic combination gives rise to a most stable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media. � 2009 Elsevier Masson SAS. All rights reserved.

The non-linear instability of weakly electrically conducting viscoelastic liquid with the modulated rotational speed heated from below is studied. Fourier series with a minimal representation has been used for the study. Rotational speed varying sinusoidally and time periodic is considered. Adaptive grid numerical method of Runge�Kutta�Fehlberg is used to obtain the solution of the resulting Khayat�Lorenz model and the solution is made use of for the heat transport quantification. On the buoyancy-driven convection, for various modulation amplitude values, Chandrasekhar number and Taylor number, rotational modulation effect is examined. It is shown that the combined effect of magnetic field and modulation in rotation leads to diminishment of heat transport. The three types of liquids, namely Newtonian, Rivlin�Ericksen and Maxwell, as particular cases are compared with available results and are found to be in agreement with the results available. � 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

The present work considers time-periodic-temperature modulation effect on non-linear convection in a viscoelastic ferromagnetic fluids (VFF). For finite amplitude perturbation, minimal representation of Fourier series is used to obtain a non-autonomous system of generalized Khayat-Lorenz model. This model is numerically integrated to determine heat-transfer. The buoyancy and non-buoyancy magnetic parameters, Prandtl number, elastic parameters and modulation parameter effects on heat-transfer are considered. There is reduction in heat-transfer due to temperature modulation. In comparison with stabilizing effect of elastic ratio and modulation amplitude, Deborah number has antagonistic influence. The results pertaining to those of Rivlin-Ericksen, Newtonian and Maxwell fluids are obtained from the present work. Temperature modulation is shown to facilitate sub-critical motions. � 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

In this study, the analysis of nonlinear stability with viscoelastic ferromagnetic fluids as working media is performed by finite-amplitude perturbations. The solution of the resulting nonautonomous system of the Lorenz model (generalized Khayat�Lorenz model of four modes) is obtained numerically to measure the amount of heat transport. The effects of elastic parameters, Prandtl number, modulation parameters, buoyancy magnetic parameter, and nonbuoyancy magnetic parameter on heat transport are studied. Heat transport is quantified through the average Nusselt number, which is determined by solving the scaled Lorenz model. As limiting cases of the study, the results of Newtonian, Maxwell, Rivlin�Ericksen fluids are determined. The results obtained have been presented graphically. � 2021 Wiley Periodicals LLC

Real-world problems are addressed effectively and safely using simulation modeling. Simulation modeling gives highly appreciable solutions by providing a clear picture of complex systems. The reason for the same is that nonlinear structure of real-world problems with complexities cannot be handled by linearized models. Further, computational complexities of large-scale dynamical system simulations occurring in such situations will be reduced by model order reduction (MOR). This is further improved with the use of artificial neural networks (ANNs). In this paper, the generalized neural network modeling of nonlinear autonomous dissipative system using machine learning and proper orthogonal decomposition (POD) has been addressed, which is a novel one. The fluid mechanical model considered here is trained with multiple temporal swatches evolved on different parametric variations and trialed out at different time instances. Machine learning tries to learn such models by analyzing snapshot observations from active systems. The neural network developed by machine learning is able to make better prediction for validating data which is different from the training data set. The complexity of the data set generated by nonlinear autonomous dissipative system is reduced by applying the POD on the original data set. This demonstrates that the neural network is successfully utilized to macromodel the autonomous dynamical system. � 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

In this study, heat transport in thermal convection of rotating viscoelastic liquids heated from below with temperature modulation is analyzed. The study is performed using Fourier series with a minimal representation. The constitutive relationship of the Oldroyd liquid B model is taken into consideration. The resulting Khayat�Lorenz model in the generalized form is solved using the numerical technique of Runge�Kutta�Fehlberg 45 with the adaptive grid method, and this solution is used to quantify the heat transport. The combined effect of the temperature modulation and Coriolis force on the thermal convection is investigated for various values of the amplitude of modulation and Taylor number. It is shown that the temperature modulation and Coriolis force lead to the enhancement of heat transport. As particular cases, the results of three liquids, namely Maxwell, Newtonian, and Rivlin�Ericksen, are obtained in the current study, which are found to have a good agreement with the available results. � 2020 Wiley Periodicals LLC