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An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions
The Rayleigh-Benard situation in Boussinesq-Stokes suspensions is investigated using both linear and non-linear stability analyses. The linear and non-linear analyses are based on a normal mode solution and minimal representation of double Fourier series, respectively. The effect of suspended particles on convection is delineated against the background of the results of the clean fluid. The realm of non-linear convection warrants the quantification of heat transfer and this has been achieved on the Rayleigh-Nusselt plane. Possibility of aperiodic convection is discussed. 2003 Elsevier Science Ltd. All rights reserved. -
Effect of temperature/gravity modulation on the onset of magneto-convection in electrically conducting fluids with internal angular momentum
The effect of time-periodic temperature/gravity modulation on the onset of magneto-convection in electrically conducting fluids with internal angular momentum is investigated by making a linear stability analysis. The results of the present study are presented against the background of the results of weak electrically conducting fluids. The qualitative findings of Siddheshwar and Pranesh are found to be true in the present case also except that the eigenvalue is found to be magnitudewise less than that obtained in the case of a weak electrically conducting fluid. -
Magnetoconvection in a micropolar fluid
The problem of Rayleigh-Bard convection in an electrically conducting micropolar fluid layer permeated by a uniform, vertical magnetic field is investigated with free-free, isothermal, spin-vanishing boundaries. The influence of the various micropolar fluid parameters and magnetic field on the onset of stationary convection has been analysed. It is observed that the electrically conducting micropolar fluid layer heated from below is more stable as compared with the classical electrically conducting Newtonian fluid. The critical wave number is found to be insensitive to the changes in the micropolar fluid parameters, but sensitive to the Chandrasekhar number. 1998 Elsevier Science Ltd. All rights reserved. -
Suction-injection effects on the onset of Rayleigh-Bard-Marangoni convection in a fluid with suspended particles
The effect of Suction-Injection-Combination (SIC) on the linear stability of Rayleigh-Bard Marangoni convection in a horizontal layer of an Boussinesq fluid with suspended particles confined between an upper free adiabatic boundary and a lower rigid isothermal/adiabatic boundary is considered. The Rayleigh-Ritz technique is used to obtain the eigenvalues. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pre-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles. The problem has possible applications in microgravity situations. -
Effect of temperature/gravity modulation on the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum
The effect of time-periodic temperature/gravity modulation at the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum is investigated by making a linear stability analysis. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitude temperature/gravity modulation. The temperature modulation is shown to give rise to sub-critical motion and gravity modulation leads to delayed convection. An asymptotic analysis is also presented for small and large frequencies. 1999 Elsevier Science B.V. -
Effect of gravity modulation on linear, weakly-nonlinear and local-nonlinear stability analyses of stationary double-diffusive convection in a dielectric liquid
The paper deals with the study of effect of gravity modulation on double-diffusive convection in a dielectric liquid for the cases of rigid-rigid and free-free boundaries. Using a modified Venezian approach, expressions for the Rayleigh number and its correction are determined. FourierGalerkin expansion is employed for a weakly nonlinear stability analysis and this results in a fifth-order Lorenz system that retains the structure of the classical one in the limiting case. A local nonlinear stability analysis using the method of multiscales leads to the time-periodic GinzburgLandau equation from the time-periodic generalized Lorenz system and the numerical solution of this simpler equation helps in quantifying unsteady heat and mass transports. Influence of various non-dimensional parameters (Lewis number, solutal Rayleigh number, electrical Rayleigh number and Prandtl number), amplitude and frequency of gravity modulation on onset of convection and heat and mass transports is discussed. The study reveals that the influence of gravity modulation is to stabilize the system and enhance heat and mass transports. The results from free-free boundaries are qualitatively similar to that of rigid-rigid boundaries. Further, it is shown that in the case of free-free boundaries the heat and mass transports are less compared to those of rigid-rigid boundaries. 2020, Springer Nature B.V. -
Effect of rotation on Brinkman-Bard convection of a Newtonian nanoliquid using local thermal non-equilibrium model
Rayleigh-Bard-Taylor convection in a Newtonian, nanoliquid-saturated high porous medium using the local thermal non-equilibrium model (LTNE) is studied analytically using the single term Galerkin technique. The Bousinessq approximation is considered to be valid and the exerted centrifugal force due to rotation is taken. A high porosity porous material glass reinforced fiber with porosity 0.88% is considered and hence the Brinkman model is adopted. The rate of rotation is quantified by the Taylor number and the stability of the system is controlled by thermal Rayleigh number. The expression for the critical eigenvalue (Rayleigh number) is obtained for both idealistic and realistic boundary conditions, that is, stress-free, isothermal and rigid-rigid, isothermal boundary conditions. The presumption of LTNE advances the inception of convection and increases the transport of heat in comparison with that of the local thermal equilibrium (LTE) assumption whereas the opposite phenomenon is seen with the effect of rotation. The effect of various non-dimensional parameters on the convection onset and on transport of heat is also investigated. The results of Rayleigh-Bard-Taylor convection using the LTE assumption are obtained as limiting cases of the present study for infinite values of the ratio of thermal conductivities and the interphase heat transfer coefficient. 2021 Elsevier Ltd -
Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect
Stability analysis of free convection in a liquid-saturated sparsely-packed porous medium with local-thermal-non-equilibrium (LTNE) effect is presented. For the vertical boundaries freefree, adiabatic and rigidrigid, adiabatic are considered while for horizontal boundaries it is the stress-free, isothermal and rigidrigid, isothermal boundary combinations we consider. From the linear theory, it is apparent that there is advanced onset of convection in a shallow enclosure followed by that in square and tall enclosures. Asymptotic analysis of the thermal Rayleigh number for small and large values of the inter-phase heat transfer coefficient is reported. Results of DarcyBard convection (DBC) and RayleighBard convection can be obtained as limiting cases of the study. LTNE effect is prominent in the case of BrinkmanBard convection compared to that in DBC. Using a multi-scale method and by performing a non-linear stability analysis the GinzburgLandau equation is derived from the five-mode Lorenz modal. Heat transport is estimated at the lower plate of the channel. The effect of the Brinkman number, the porous parameter and the inter-phase heat transfer coefficient is to favour delayed onset of convection and thereby enhanced heat transport while the porosity-modified ratio of thermal conductivities shows the opposite effect. 2020, Springer Nature B.V. -
Study of chaos in the Darcy-Bard convection problem with Robin boundary condition on the upper surface
Possibility of chaos is studied in Darcy-Bard convection using the Dirichlet and the Robin boundary condition at the lower and upper boundaries, respectively. Comparison is made with the results of Dirichlet (classical-Darcy-Bard convection, CDBC) and Neumann boundary condition (Barletta-Darcy-Bard convection, BDBC). It is found that the cell size at onset is bigger in the case of BDBC compared to the generalized-Darcy-Bard convection (GDBC) and much bigger compared to CDBC. The critical-Darcy-Rayleigh number of BDBC is found to be the least and that of CDBC is the largest. Nonlinear-stability-analysis is performed leading to the scaled-generalized-Vadasz-Lorenz model (SGVLM). In deriving this model, help is sought from a local-nonlinear-stability-analysis that yields the form of the convective-mode. The SGVLM is shown to be dissipative and conservative, with its bounded solution trapped within an ellipsoid. Onset of chaos and its characteristics are studied using the Hopf-Rayleigh-number, the Lorenz-butterfly-diagram, and the plot of the amplitude of the convective-mode vs the control-parameter, R, which is the eigenvalue. Chaos sets in earlier in CDBC and much later in BDBC when compared to that in GDBC. Beyond the onset of chaos is seen a sequence of chaotic and periodic motions, with the latter sometimes being present for an extended period. 2024 Author(s). -
Rheostatic effect of a magnetic field on the onset of chaotic and periodic motions in a five-dimensional magnetoconvective Lorenz system
This paper deals with a weakly nonlinear study of two-dimensional RayleighBard magnetoconvection using a simplified five-dimensional Lorenz model. The governing equations of the system are nondimensionalized and formulated in terms of the stream function and the scalar magnetic potential. A five-modal Fourier truncation scheme is employed and the resulting equations are scaled to obtain a five-dimensional autonomous dynamical system. The Hopf-Rayleigh number, signifying Hopf bifurcation, is numerically evaluated from the analysis of weakly nonlinear stability. Chaotic and periodic motions are depicted by plotting bifurcation diagrams, largest Lyapunov exponent (LLE) diagrams and three-dimensional projections of the phase-space. For a fixed set of parameter values, increasing the strength of the applied magnetic field is found to increase the Hopf-Rayleigh number, thereby delaying the destabilization of the system's equilibrium points. It is shown that while low magnetic field strengths favor the onset of chaotic motion directly from the steady state, stronger magnetic field strengths favor the onset of periodic convection from the steady state prior to the appearance of chaotic motion. We observe here that the applied magnetic field regulates the onset of chaotic and periodic motions in the system and therefore, has a rheostatic control over chaotic and periodic behaviors. 2025 Elsevier Ltd -
Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a CubicQuintic GinzburgLandau Equation Using the Center Manifold Theorem
The differential geometric method of the center manifold theorem is applied to the magnetic-Lorenz model of ferrofluid convection in an electrically non-conducting ferrofluid. The analytically intractable tri-modal nonlinear autonomous system (magnetic-Lorenz model) is reduced to an analytically tractable uni-modal cubicquintic GinzburgLandau equation. The inadequacy of the cubic GinzburgLandau equation and the need for the cubicquintic one is shown in the paper. The heat transport is quantified using the solution of the cubicquintic equation and the effect of ferrofluid parameters on it is demonstrated. The stable and unstable regions in the conductive regime and the conductive-convective regime is depicted using a bifurcation diagram. The noticeable discrepancy between the results of the two models is highlighted and the quintic non-linearity effects are delineated. 2021, Foundation for Scientific Research and Technological Innovation. -
Study of Natural Convection with Local Thermal Non Equilibrium Effects in Nanoliquid-Saturated Low Porosity Enclosures
Natural convection of nanoliquid in densely packed vertical porous enclosure is studied by subjecting the vertical walls to constant heat flux under local thermal non-equilibrium (LTNE) assumptions. Water, copper nanoparticles and porous material made of aluminum foam, glass balls and sand are considered for the study. The governing equations are modelled using single-phase model. Thermophysical properties of nanoliquid and nanoliquid-saturated porous medium are calculated using phenomenological laws and mixture theory. An analytical expression for velocity and temperature profiles of nanoliquid (base liquid+nanoparticles) and solid (porous medium) phases has been obtained. Weighted average Nusselt number is expressed as a function of aspect ratio, volume fraction, and properties concerning LTNE effects. LTNE effect is shown to be a heat transfer enhancing mechanism. The presence of nanoparticles is to enhance the heat transfer in water. Local thermal equilibrium results are obtained as a limiting case of the present study and so obtained results are compared with previously published paper in the literature. 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited. -
Effect of Non-inertial Acceleration on BrinkmanBard Convection in Water-Copper Nanoliquid-Saturated Porous Enclosures
In the present paper we have considered rotating porous tall, square and shallow enclosures heated from below. Linear and non-linear analyses are made using a minimal representation by Fourier trigonometric series. The study is done for realistic boundary condition. Thermophysical properties of water-copper nanoliquid as a function of properties of water as base liquid, copper as nanoparticle and 30% glass fiber reinforced polycarbonate as porous medium are obtained from either phenomenological laws or mixture theory. Non-existence of oscillatory convection is discussed. The range for the existence of unicellular convection is mentioned. The effects of Brinkman number (?), porous parameter (?2), aspect ratio (A) and volume fraction (?) in the presence of rotation on the onset of convection and heat transfer are studied and illustrated graphically. The analytically intractable Lorenz model is derived and transformed into the tractable GinzburgLandau equation using the multiscales method. The definition of Ozoe heat transfer parameter is introduced to discuss the rate of heat transfer enhancement or reduction. It is observed that Ta, ? and ?2 have stabilizing effect on the system and thereby leading to diminished heat transfer whereas A and ? have destabilizing effect on the system and thereby leading to increased heat transfer. Among the three enclosures considered in the study enhanced heat transfer takes place in tall enclosure followed by square and shallow enclosures respectively. It is further observed that presence of nanoparticles advances the onset of convection and enhances the heat transfer. The results of the paper are compared with previous existing results in the absence of rotation and the good agreement is found between them. 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited. -
Study of BrinkmanBard nanofluid convection with idealistic and realistic boundary conditions and by considering the effects of shape of nanoparticles
This study deals with linear and weakly non-linear stability analyses of BrinkmanBard convection in nanoliquid-saturated porous enclosures. Water with a dilute concentration of molybdenum disulfide nanoparticles with 0.06 volume fraction and 30% glass fiber-reinforced polycarbonate as a porous medium with porosity 0.88 are considered to be a working medium. The analytical solution is obtained in the present study for idealistic and realistic boundary conditions, and their results are compared. An analytically intractable Lorenz model with quadratic nonlinearities is reduced to a tractable GinzburgLandau amplitude equation with cubic nonlinearity using the multiscale method. Nanoparticles with different shapesare considered in the study, and their effects on the onset and heat transfer are discussed in great detail graphically in the presence of other parameters arising in the problem. 2021 Wiley Periodicals LLC -
Study of chaos in RayleighBard convection of a micropolar fluid
The paper considers the micropolar fluid (MPF) in a RayleighBard situation and investigates regular and periodic convection, and chaos in the fluid for a wide range of values of the scaled Rayleigh number. The fourth-order scaled Lorenz model that governs weakly non-linear convection is an energy-conserving model whose bounded solution remains within the finiteness of a three-ellipsoid. All the characteristics of the classical Lorenz model are seen in the generalized one. The scaling of the equations is done in such a way that the classical Lorenz model can be obtained as a limiting case of the generalized Lorenz model. The scaled versions of the critical Rayleigh number and the HopfRayleigh number are quantified to determine the onset-of-regular-convection and chaos. Chaotic and periodic regimes appear alternately as the scaled Rayleigh number, r, increases. It is well known from existing literature that the effect of micron-sized particles in the Newtonian fluid is to delay the onset-of-regular-convection. In the paper, it has been found that the suspended particles delay the onset of chaos and the appearance of periodic motion when compared to that in the case of a Newtonian fluid. 2025 Elsevier Ltd -
Linear and weakly nonlinear stability analyses of Darcy Bard convection with feedback control
In this paper, the effect of feedback control on the criterion for the onset of DarcyBard convection in a horizontal Boussinesq Newtonian fluid is studied theoretically. The bounding isothermal lower and upper surfaces are considered to be rigid. The single term Galerkin method and the Maclaurin series expansion are combined with the Newton-Raphson method of three variables to perform a linear stability analysis in order to determine eigen value. To make a weakly nonlinear stability analysis of the system, a Vadasz Lorenz model is constructed. The models various properties are discovered to be identical to those of the standard Lorenz model. The exhibits both dissipative and conservative characteristics and the bounded nature of its solution is demonstrated by the trapping region, which takes the form of an ellipsoid. The Hopf-Rayleigh number determined from the autonomous dynamical system predicts the onset of chaos. The influence of the controller gain parameter and the Biot number on the onset of convection has been analyzed. Results from the study reveal that the controller gain parameter stabilizes the system and further delays the onset of chaos. Overall, the study establishes that an increase in the Biot number promotes long-term periodic motion over chaotic behavior, while an increase in the controller gain parameter enlarges the trapping region, thereby contributing to improved system stability. The Author(s) 2025. -
Rheostatic effect of a magnetic field on the onset of chaotic and periodic motions in a five-dimensional magnetoconvective Lorenz system
This paper deals with a weakly nonlinear study of two-dimensional RayleighBard magnetoconvection using a simplified five-dimensional Lorenz model. The governing equations of the system are nondimensionalized and formulated in terms of the stream function and the scalar magnetic potential. A five-modal Fourier truncation scheme is employed and the resulting equations are scaled to obtain a five-dimensional autonomous dynamical system. The Hopf-Rayleigh number, signifying Hopf bifurcation, is numerically evaluated from the analysis of weakly nonlinear stability. Chaotic and periodic motions are depicted by plotting bifurcation diagrams, largest Lyapunov exponent (LLE) diagrams and three-dimensional projections of the phase-space. For a fixed set of parameter values, increasing the strength of the applied magnetic field is found to increase the Hopf-Rayleigh number, thereby delaying the destabilization of the system's equilibrium points. It is shown that while low magnetic field strengths favor the onset of chaotic motion directly from the steady state, stronger magnetic field strengths favor the onset of periodic convection from the steady state prior to the appearance of chaotic motion. We observe here that the applied magnetic field regulates the onset of chaotic and periodic motions in the system and therefore, has a rheostatic control over chaotic and periodic behaviors. 2025 Elsevier Ltd -
Sentiment Analysis on Educational Tweets: A Case of National Education Policy 2020
Due to COVID-19 pandemic lockdowns, the transition from traditional class-room-based approaches, there has been rise in online education. There is a growing need to adopt the best global academic and innovative practices and implement the National Education Policy-2020 (NEP) in Indian education. This study uses a dataset, NEPEduset, created by gathering tweets about education. An attempt has been made in this study to examine the tweets by preprocessing, generating labels or sentiments using standard tools and libraries in Python language, applying and comparing various machine learning (ML) algorithms. ML approaches are powerful and used in various applications ranging from sentiment analysis, text analysis, natural language processing (NLP), image processing, object detection. ML methods are widely used in sentiment analysis tasks and text annotations. This work uses Text-Blob, Valence Aware Dictionary for Sentiment Reasoning (VADER), and a Customized method, SentiNEP to analyze the sentiment score of tweets' text. SentiNEP method is shown is produce better results for various experiments conducted for the dataset, NEPEduset. Various supervised ML models have been applied for text classification of user sentiment. Word2Vec feature extraction technique has been applied to build and evaluate the models. Performance metrics such as precision, accuracy, F1 score and recall have been used to evaluate the ML models. The results reveal that the support vector machine and random forest classifiers achieve higher accuracy with Word2Vec. The performance results have been compared with VADER, TextBlob and SentiNEP. It has been found that the SentiNEP method produces better results. 2023 IEEE. -
BERT-Enhanced Bi-LSTM with weighted cross-entropy for multilingual sentiment classification
With the increasing volume of multilingual user-generated content across social media platforms, effective sentiment analysis (SA) becomes crucial, especially for low-resource languages. However, traditional models relying on context-independent embeddings, such as Word2Vec, GloVe, and fastText, struggle to handle the complexity of multilingual sentiment classification. To address this, we propose an Automatic Multilingual Sentiment Detection (AMSD) framework that leverages the contextual capabilities of BERT for feature extraction and a Bidirectional Long Short-Term Memory (Bi-LSTM) network for classification. Our method, termed Elite Opposition Cross-Entropy Weighted Bi-LSTM (EOCEWBi-LSTM), integrates elite opposition-based learning to optimize hyperparameters and enhance classification accuracy. A weighted cross-entropy loss function further refines the model's sensitivity to class imbalance, thereby improving its performance. The model is trained and evaluated on the NEP_EDUSET corpus, comprising 45,434 tweets in English, Hindi, and Tamil. Experimental results demonstrate notable improvements in precision, recall, F1-score, and accuracy, highlighting the effectiveness of EOCEWBi-LSTM in multilingual sentiment analysis, especially across both high-resource and low-resource languages. The experimental results show that the proposed EOCEWBi-LSTM achieves a high F1-score ratio of 93.83% and an accuracy ratio of 93.83% compared to other existing methods. EOCEWBi-LSTM provides an effective solution for multilingual sentiment analysis, especially for languages with limited resources. 2025 The Author(s). -
Privacy Optimization in Sensors Based Networks With Industrial Processes Management
The Internet of Things (IoT) also known as IoT has the potential that is required to revolutionize industries, this has been discussed in this research article. Advancements in technology have made devices affordable, efficient and reliable. Different sectors have already started to incorporate these devices into their operations to boost productivity, to minimize failure and downtime. They also use it to optimize resource utilization which is also an important factor. However, the use of these devices also has some security challenges which need to be handled. This research paper proposes a security model specifically designed for process management in the industries. The goal of this model is to find the vulnerabilities, to minimize the risks and threats. Also ensuring integrity, confidentiality and availability of processes is a part of the goal. This paper gives evidence from its implementation and trial apart from its explanation. During the implementation phase, the sensitive data achieved a 100% encryption rate, for protection. Also, integrity checks were conducted on 99.8% of data to guarantee data integrity. 2023 IEEE.