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Study of heat transfer in a rotating weakly electrically conducting Newtonian fluid: Primary and Kpers-Lortz regimes
In this paper, we study the primary and secondary (Kpers-Lortz) instabilities of rotating RayleighBard convection for a weakly electrically conducting Newtonian fluid with idealistic boundaries. The critical Rayleigh number is obtained for each instability. Fourth-order and ninth-order Lorenz model are derived using the truncated Fourier-Galerkin expansion and the onset of primary and secondary instabilities is studied. Using a non-linear analysis, we derive the expression for the Nusselt number for both primary and secondary instabilities. The analysis reveals that the heat transfer in the case of primary instability is an over-prediction when compared with that of the secondary instability. An increase in the strength of the magnetic field is to delay the onset of primary and secondary instabilities and decrease the heat transfer. These insights advance the understanding of magnetohydrodynamic stability in rotating convective systems and have implications for geophysical and astrophysical fluid dynamics. 2025 Elsevier Masson SAS -
Study of hybrid nanofluid flow in a stationary cone-disk system with temperature-dependent fluid properties
Cone-disk systems find frequent use such as conical diffusers, medical devices, various rheometric, and viscosimetry applications. In this study, we investigate the three-dimensional flow of a water-based Ag-MgO hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties. How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynoldss linearized model for variable viscosity and Chiams model for variable thermal conductivity. The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids, incorporating the experimental data. This model is developed as a coupled system of convective-diffusion equations, encompassing the conservation of momentum and the conservation of thermal energy, in conjunction with an incompressibility condition. A self-similar model is developed by the Lie-group scaling transformations, and the subsequent self-similar equations are then solved numerically. The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed. Additionally, the Nusselt number for the disk surface is calculated. It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system, while the thermal conductivity parameter has the opposite effect. The Author(s) 2024. -
Study of Influence of Combustion on DarcyBard Convection with Inherent Local Thermal Non-equilibrium Between Phases
This work deals with a DarcyBard convection problem in the presence of combustion and with local thermal non-equilibrium between the fluid and the solid phases. The effects of combustion and local thermal non-equilibrium on the onset of convection is studied in the linear and nonlinear regimes. Unlike all reported local thermal non-equilibrium problems reported so far, the present problem has a unique situation of having thermal non-equilibrium not only in the perturbed state but also in the basic state. Further, we observe that local thermal non-equilibrium does not, under any circumstance, lead to local thermal equilibrium except in an approximate sense when the combustion is quite weak. The effect of combustion is to advance the onset of convection compared to that in its absence. The effect of local thermal non-equilibrium is to reinforce the effect of combustion. In the presence of both these effects, sub-critical instability exists. The results are obtained numerically and have implication in practical porous medium convection problems. 2022, The Author(s), under exclusive licence to Springer Nature B.V. -
Study of internal heat source generated natural convection with sinusoidal and non-sinusoidal time-periodic vertical oscillations
This study explores the effect of gravity modulation on natural convection induced by a uniform internal heat source within a fluid-saturated porous medium, a topic of growing relevance in advanced thermal management applications. Four distinct gravity waveforms, square, sinusoidal, triangular, and sawtooth, are examined under three boundary condition combinations: Rigid-Adiabatic-Rigid-Isothermal (RARI), Rigid-Adiabatic-Free-Isothermal (RAFI), and Free-Adiabatic-Free-Isothermal (FAFI). A novel analytical framework is developed by integrating a Maclaurin series expansion with a minimal FourierGalerkin approach to derive a generalized Lorenz model. Linear stability analysis, via a modified Venezian method, to determine the critical internal Rayleigh number and its correction due to modulation. A weakly nonlinear analysis based on the GinzburgLandau equation also provides closed-form expressions for the mean Nusselt number, capturing heat transfer characteristics. The findings demonstrate that square wave modulation most effectively enhances heat transport, followed by sinusoidal, triangular, and sawtooth forms. The influence of key physical parameters reveals that increasing porous parameter (?2) and Brinkman number (?) suppress heat transfer, as do higher Prandtl numbers (Pr) and modulation frequencies (?). FAFI yields the highest heat transfer among the boundary types, while RARI performs the least. The novelty of this work lies in the combined analytical treatment of diverse waveform modulations while considering a uniform internal heat source and boundary condition for natural convection. 2025 The Author(s) -
Study of Kpers?Lortz Instability in a Weakly Electrically Conducting Couple-Stress Fluid
The study aims to investigate the Kpers?Lortz instability in rotating RayleighBard convection of a weakly electrically conducting couple-stress fluid. A novel aspect of this study is the incorporation of weakly electrically conducting couple-stress fluid in a rotating RayleighBard setup to analyze Kpers?Lortz instability and examine heat transfer in both primary and secondary regimes. The main goal is to understand how the combined effects of the couple-stress, rotation, and magnetic field alter stability thresholds and impact the heat transfer. KpersLortz instability (KLI) means the roll systems obtained during the regular convection get deformed and form an angle with each other, making the system unstable. The critical Rayleigh number for regular convection is obtained using linear stability analysis. A ninth-order Lorenz model is obtained using truncated Fourier expansions to study secondary instability. A weak magnetic field (Hartmann number) and couple-stress parameter hinders the onset-of-regular convection. We also obtain the critical values at which the KLI manifests. The critical values are found at a marginal steady state. The Hartmann number and couple-stress parameters hinder the onset-of-secondary instability. Further, the Nusselt number expression is derived, and it is observed that an increase in the couple-stress parameter and Hartmann number diminishes the heat transfer. Additionally, the Nusselt number is obtained for primary and secondary regimes, showing the impact of the parameters on the efficiency of heat transfer in each regime. To validate the results on secondary instability, the study compares its findings with existing literature in the absence of a weak magnetic field and couple-stress effects. A reasonably good agreement is observed, confirming the reliability of the results. 2025 Wiley Periodicals LLC. -
Study of linear and non-linear analyses of rayleigh-benard chandrasekhar convection in micropolar fluid with saturated porous medium
Thermal instability of Chandrasekhar convection in a micropolar fluid, saturated porous layer is being investigated in this study. The model is confined between two horizon- tal plates of infinite length and separated by a fixed distance. A uniform temperature gradient is provided at the lower plate, while the upper plate is cooled. The study is analysed for both linear as well as non-linear cases to understand the stability, transfer of heat and mass within the model. The study is carried out in extending the model for Rayleigh-Benard and double diffusive convection with external constraints such as in-ternal heat, concentration source, gravity modulation, temperature modulation, coupled cross diffusion and throughflow. The outcome of the study is discussed in detail and presented pictorially through graphs. Linear and Non-linear Analyses of Double Diffusive Chandrasekhar Convection with Heat and Concentration Source in Micropolar Fluid with Saturated Porous Media under Gravity Modulation. A thermosolutal convective study is carried out in the presence of externally imposed magnetic field and gravity modulation together with heat and concentration source in a micropolar fluid. This problem is analysed for both linear and non-linear cases by as- suming the strength of heat and concentration source same. The expression for critical thermal Rayleigh number and correction thermal Rayleigh number are obtained using regular perturbation method to understand the stability of problem. The transfer of heat and mass transport is investigated by deriving the eighth order Lorentz equation. It is found that internal Rayleigh number and Darcy number speeds up the onset of instabil-ity while the coupling parameter and Chandrasekhar number has a reverse effect. Also, the transfer of mass is more compared to the transfer of heat. Linear and Non-linear Analyses of Double Diffusive Chandrasekhar Convection Coupled with Cross-diffusion in Micropolar Fluid over Saturated Porous Medium The problem aims to find the effects of coupled cross-diffusion in a micropolar fluid over a porous medium, subjected to double-diffusive-Chandrasekhar convection. The usual stability analysis has been employed to determine the critical thermal Rayleigh number. Non-linear analysis is carried out by deriving the Lorentz equations using trun- cated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood number respectively. Analysis related to the effect of various parameter are plotted and the result for the same are interpreted. As Dufour parameter increases, the diffusion of heat and solute takes place which increases the temperature difference and thereby delays the onset of convection by making the system stable. It is observed from the results that Dufour parameter and Soret parameter have opposite influence on the stability of the problem. Linear and Non-linear Analyses of Throughflow Effect on the Onset of Rayleigh-Benard-Chandrasekhar Convection in Micropolar Fluid with Porous Medium. The Rayleigh-Benard convection over a porous medium saturated with micropolar fluid is simulated via externally imposed magnetic effect. The stability of the system is ex- amined using linear analysis by the method of normal mode. The rate of heat and mass transport within the system is examined by deriving sixth order Lorentz equation using non-linear analysis. It is observed that by regulating the throughflow effect, the con- vection of the system can be controlled. Also, the pro-gravity and anti-gravity cases has a stabilizing effect on the system. From mathematical calculation, it can be seen that heat transfer rate is same for both pro-gravity and anti-gravity cases, because of the symmetric nature of the boundaries considered. Linear and Non-linear Analyses on the Effect of Time Periodic Boundary Temper- ature and Internal Heat Source in a Micropolar Fluid on the Onset of Rayleigh- Benard-Chandrasekhar Convection with Porous Medium The impact of temperature modulation at the boundaries over a surface containing voids that is soaked in micropolar fluid is investigated to understand the thermal instability of the convection exposed to magnetic effect and internal heating of the system. A small amplitude of perturbation is given to the system to analyse the thermal instability by performing a linear study through the method of regular perturbation, which yields Rayleigh number for unmodulated and modulated system. Three cases of study is car-ried out to inspect the vibrating temperature field at the boundaries, namely symmetric case where the temperature is modulated in-phase, asymmetric case where the temper-ature is modulated out-phase and the case where only the bottom wall temperature is modulated. The non-linear analysis is employed to find the heat in the system, using Lorentz model. The outcome of the study conveys that sub critical motion occurs dur- ing in-phase modulation while the out-phase modulation leads to a more stable system. Moreover, internal Rayleigh number hastens the onset of convection. -
Study of linear and non-linear analyses of Rayleigh-Benard-Chandrasekhar convecion in micropolar fluid with saturated porous medium
Thermal instability of Chandrasekhar convection in a micropolar fluid, saturated porous layer is being investigated in this study. The model is confined between two horizontal plates of infinite length and separated by a fixed distance. A uniform temperature gradient is provided at the lower plate, while the upper plate is cooled. The study is analysed for both linear as well as non-linear cases to understand the stability, transfer of heat and mass within the model. The study is carried out in extending the model for Rayleigh-Benard and double diffusive convection with external constraints such as in- ´
ternal heat, concentration source, gravity modulation, temperature modulation, coupled cross diffusion and throughflow. The outcome of the study is discussed in detail and presented pictorially through graphs. -
Study of Low-Mass Stars and Brown Dwarfs In Star Forming Regions of Diverse Environments
The formation and evolution of low-mass stars and brown dwarfs is an intricate process orchestrated by the environmental conditions in which they form. As a natural byproduct of this process, circumstellar disks are formed, whose dynamic relationship with the environment plays a pivotal role in determining the fate of the star and the timescale for planet formation. While low-mass stars are a dominant product of the star formation process, brown dwarfs occupy a unique position, bridging the gap between newlinelow-mass stars and planets. In this thesis, we have examined the low-mass stars and brown dwarfs in young clusters located at different distances with diverse UV radiation felds and stellar densities to decode the role of environment in shaping the IMF, its inand#64258;uence on disk evolution and to understand the formation of brown dwarfs. We have targeted three young star forming regions for the newlinestudy namely and#963; Orionis, twin clusters IC 1848-East and West, and IC 1396 using deep multi-wavelength photometry as well as near-IR spectroscopy with 4m and 10m class facilities. For the and#963; Orionis cluster we used deep CFHT-WIRCAM near-IR data and the novel water-band photometry technique along with Gaia DR3 to identify the candidate low-mass members. Spectroscopic follow-up observations conducted with IRTF-SpeX validated the selection of the candidates by this technique with a 100% effcacy. We then compiled a comprehensive membership catalog for a mass range and#8764;19-0.004 Mand#8857;. The form of the stellar-substellar IMF was found to be consistent with other nearby star forming regions suggesting a lack of signifcant environmental inand#64258;uence. Further, we analysed the evolutionary class of the members based on the mid-IR slope of the SED to study their disk properties. We estimated the disk fraction of the low-mass sources to be consistent with other star form ing regions considering the age of the cluster. This showed that in this region, external photoevaporation does not play a major role in the inner disk evolution. -
Study of magnetoconvection with maxwell cattaneo law
This thesis deals with the study of Rayleigh-Bard-convection in a Newtonian fluid and micropolar fluid by replacing the classical Fourier law by non-classical Maxwell-Cattaneo heat flux law. The effects of second sound, non-uniform basic temperature gradients, suctioninjection-combination, temperature modulation and gravity modulation in newlinepresence of external constraints like magnetic field and rotation are studied. newlineThe problems investigated in this thesis throw light on externally controlled convection in Newtonian and micropolar fluids in the presence of Maxwell-Cattaneo law. The problems investigated in this thesis deal newlinewith practical problems with very large heat fluxes and/or short time duration. With this motivation, we investigate in this thesis five problems and their summary is given below. (i) Effects of Coriolis force and non-uniform basic temperature gradients on the onset of Rayleigh-Bard-Chandrasekhar newlineconvection with Maxwell-Cattaneo law The effect of non-uniform temperature gradient on RayleighBard-Chandrasekhar convection in a rotating Newtonian fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalues is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset is discussed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones. It is shown that the system having magnetic field will delay in the onset newlineof instability. In general, it is observed that step function and inverted parabolic temperature profile are the most destabilizing and stabilizing profiles. -
Study of magnetoconvection with maxwell cattaneo law /
This thesis deals with the study of Rayleigh-Bénard-convection in a Newtonian fluid and micropolar fluid by replacing the classical Fourier law by non-classical Maxwell-Cattaneo heat flux law. The effects of second sound, non-uniform basic temperature gradients, suctioninjection-combination, temperature modulation and gravity modulation in
presence of external constraints like magnetic field and rotation are studied. The problems investigated in this thesis throw light on externally controlled convection in Newtonian and micropolar fluids in the presence of Maxwell-Cattaneo law. The problems investigated in this thesis deal with practical problems with very large heat fluxes and/or short time duration. With this motivation, we investigate in this thesis five problems and their summary is given below. (i) Effects of Coriolis force and non-uniform basic temperature gradients on the onset of Rayleigh-Bénard-Chandrasekhar convection with Maxwell-Cattaneo law The effect of non-uniform temperature gradient on RayleighBénard-Chandrasekhar convection in a rotating Newtonian fluid with
Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalues is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and fiveix non-linear temperature profiles are considered and their comparative influence on onset is discussed. It is found that the results are noteworthy
at short times and the critical eigenvalues are less than the classical ones. It is shown that the system having magnetic field will delay in the onset of instability. In general, it is observed that step function and inverted parabolic temperature profile are the most destabilizing and stabilizing profiles. The range of values of the parameters of the problem for which oscillatory convection in the case of free-free isothermal boundary exists is also discussed. (ii) The effect of temperature modulation on the onset of RayleighBénard-Chandrasekhar convection using Maxwell-Cattaneo law The effect of imposed time-periodic boundary temperature (ITBT, also called temperature modulation) and magnetic field at the onset of Rayleigh-Bénard convection is investigated by making a linear analysis. The classical Fourier heat law is replaced by the non-classical MaxwellCattaneo law. The venezian approach is adopted in arriving at the critical Rayleigh number and wave number for small amplitude of ITBT. Three
cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in-phase, (b) asymmetric, corresponding to out-of-phase modulation and (c) only the lower wall is modulated. The temperature modulation is shown to give rise to sub-critical motion. The shift in the critical Rayleigh number is calculated
as a function of frequency and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures. It is shown that the system is more stable when the boundary temperatures are modulated out of phase.x
(iii) The effect of gravity modulation on the onset of RayleighBénard-Chandrasekhar convection using Maxwell-Cattaneo law The effect of gravity modulation and magnetic field at the onset of Rayleigh-Bénard-Chandrasekhar convection is investigated by making a regular perturbation technique. The stability of the horizontal fluid layer heated from below is examined by assuming time-periodic body acceleration called g-jitter, which normally occurs in satellites and in vehicles connected with microgravity simulation studies. The venezian
approach is adopted in arriving at the critical Rayleigh number and wave number for small amplitude of gravity modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. It is observed that gravity modulation leads to delayed convection. (iv) The effect of suction-injection-combination (SIC) on the onset of Rayleigh-Bénard-Chandrasekhar convection in a micropolar fluid with Maxwell-Cattaneo law The effect of suction-injection-combination (SIC) on the onset of Rayleigh-Bénard-Chandrasekhar convection in a micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic on the spinvanishing boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters on the onset of convection has been analyzed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC beingxi pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. The problem suggests an elegant method of external control of internal convection. (v) The effect of non-uniform temperature gradients on RayleighBénard-Chandrasekhar convection in a micropolar fluid with
Maxwell-Cattaneo law The effect of non-uniform temperature gradient on RayleighBénard-Chandrasekhar convection in a micropolar fluid with MaxwellCattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters on the onset of convection has been
analyzed. Six different non-uniform temperature profiles are considered their comparative influence on onset is discussed. It is observed that the micropolar fluid layer heated from below is more stable compared to the classical Newtonian fluid layer. -
Study of micro and small enterprises' readiness in implementing industry 4.0: A study in marathwada district of maharashtra, india
Industry 4.0 aims tp transform the development of global value chains and the development of a digital revolution, with intelligent machines capable of communicating via wireless connections and a connection thought system, resulting in autonomous decision-making. Although large sized firms are adopting Industry 4.0, the small and micro enterprises are facing great difficulties in adopting them. This study aims to identify the areas in which Enterprises need to focus for improving their level of readiness and develop strategies and plans to adopt Industry 4.0 technologies successfully. 219 samples were collected using snowball sampling from Marathwada District in Maharashtra, India. factor analysis was conducted using SPSS and different factors acting as barriers to implementation of Industry 4.0 technologies were identified. 2023 by IGI Global. All rights reserved. -
Study of mineral and nutritional composition of some seaweeds found along the coast of Gulf of Mannar, India
The presence of Algae on the Earth is ubiquitous. The industry that widely uses algae is food industry, where the algae are used as a food supplement and also as an addition to the nutrient rich food. This study emphasizes on the mineral and nutritional composition of the selected fourteen algal species which are abundantly found along the coast of the Gulf of Mannar. The selected species of algae belong to different algal families such as Chlorophyta, Phaeophyta and Rhodophyta. The amount of minerals such as Ca, Zn, Fe, K, Mg, Mn, and Cu were estimated by employing the method of acid digestion followed by atomic absorption spectroscopy. We estimated the nutritional content based on the assessment of total protein, carbohydrate, phenol, ash and moisture contents of the algal species. The results based on the analysis of the mineral content in the algal seaweeds depicted that the seaweeds comprised of high amount of the macro minerals and trace minerals. Estimation of nutritional composition revealed that these algal species are rich in protein and carbohydrate. The ash contents were found to be very high in Jania rubens (86.66%), Padina boergesenii (85%) and Valoniopsis pachynema (84%). Based on the present study we infer that the algal seaweeds contained high amount of the nutritional compounds, which might pave the way for a higher standard of nutritional supply to the humans in the future. Jose & Xavier (2020). This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited (https://creativecommons.org/licenses/by/4.0/). -
Study of multilayer flow of a bi-viscous Bingham fluid sandwiched between hybrid nanofluid in a vertical slab with nonlinear Boussinesq approximation
Bi-viscosity Bingham plastic fluids are used to understand the rheological characteristics of pigment-oil suspensions, polymeric gels, emulsions, heavy oil, etc. In many industrial and engineering problems involving high-temperature situation, a linear density-temperature variation is inadequate to describe the convective heat transport. Therefore, the characteristics of the nonlinear convective flow of a bi-viscous Bingham fluid (BVBF) through three layers in a vertical slab are studied. The two outer layers of the oil-based hybrid nanofluid and the intermediate layer of BVBF are considered. The thermal buoyancy force is governed by the nonlinear Boussinesq approximation. Continuity of heat flux, velocity, shear stress, and temperature are imposed on the interfaces. The governing equations are derived from the Navier-Stokes equation, conservation of energy, and conservation of mass for three layers. The nonlinear multi-point (four-point) boundary value problem is solved using the differential transform method (DTM). Converging DTM solutions are obtained, and they are validated. The entropy equation and Bejan number were also derived and analyzed. It is established that the nonlinear density-temperature variation leads to a significant improvement in the magnitude of the velocity and temperature profiles due to the increased buoyancy force, and as a result, the drag force on the walls gets reduced. The drag force on the slab gets reduced by decreasing the volume fraction of nanoparticles. Furthermore, nonlinear convection and mixed convection give rise to an advanced rate of heat transport on the walls and thereby to an enhanced heat transport situation. 2022 Author(s). -
Study of multilayer flow of non-Newtonian fluid sandwiched between nanofluids
This theoretical investigation examines the nonlinear convective heat transport and multilayer flow of a non-Newtonian fluid within a vertical slab, incorporating viscous heating effects. The middle layer of the slab contains a third-grade fluid, while the outer layers are filled with a water-based Ag-MgO hybrid nanoliquid. Continuity in temperature, heat flux, velocity, and shear stress is maintained at the interfaces of the fluid layers. The thermal buoyancy force is modeled using the nonlinear Boussinesq approximation. The governing system comprises conservation equations for mass, momentum (Navier-Stokes), and energy for each of the three layers. These differential equations are non-dimensionalized, and the resulting dimensionless four-point nonlinear boundary value problem is transformed into a two-point boundary value problem before being solved numerically. For limiting cases, analytical and semi-analytical solutions are computed and used as benchmark results to validate the numerical method employed. Entropy generation analysis indicates that higher third-grade fluid parameters reduce the magnitude of velocity and temperature fields, as well as entropy production across all regions. The third-grade fluid parameter shows a decreasing influence on velocity and temperature fields throughout the system. The continuity of interfacial conditions induces a dragging effect; despite the absence of third-grade fluid parameters in regions I and III, their influence is apparent in these regions. The Bejan number slightly decreases at the walls with increasing third-grade fluid parameters, exhibiting a dual effect in the third-grade fluid layer. Near the walls, the Bejan number decreases as the nanoparticle volume fraction increases. Findings of this work may have applications in polymer industries and processes involving high temperatures. 2024 -
Study of multilayer flow of non-Newtonian fluid sandwiched between nanofluids
This theoretical investigation examines the nonlinear convective heat transport and multilayer flow of a non-Newtonian fluid within a vertical slab, incorporating viscous heating effects. The middle layer of the slab contains a third-grade fluid, while the outer layers are filled with a water-based Ag-MgO hybrid nanoliquid. Continuity in temperature, heat flux, velocity, and shear stress is maintained at the interfaces of the fluid layers. The thermal buoyancy force is modeled using the nonlinear Boussinesq approximation. The governing system comprises conservation equations for mass, momentum (Navier-Stokes), and energy for each of the three layers. These differential equations are non-dimensionalized, and the resulting dimensionless four-point nonlinear boundary value problem is transformed into a two-point boundary value problem before being solved numerically. For limiting cases, analytical and semi-analytical solutions are computed and used as benchmark results to validate the numerical method employed. Entropy generation analysis indicates that higher third-grade fluid parameters reduce the magnitude of velocity and temperature fields, as well as entropy production across all regions. The third-grade fluid parameter shows a decreasing influence on velocity and temperature fields throughout the system. The continuity of interfacial conditions induces a dragging effect; despite the absence of third-grade fluid parameters in regions I and III, their influence is apparent in these regions. The Bejan number slightly decreases at the walls with increasing third-grade fluid parameters, exhibiting a dual effect in the third-grade fluid layer. Near the walls, the Bejan number decreases as the nanoparticle volume fraction increases. Findings of this work may have applications in polymer industries and processes involving high temperatures. 2024 -
Study of multilayer flow of two immiscible nanofluids in a duct with viscous dissipation
Numerical simulations for the mixed convective multilayer flow of two different immiscible nanofluids in a duct with viscous heating effects were performed in this study. The left and right faces of the duct are maintained to be isothermal, while other side faces are insulated. The mathematical governing system for each layer consists of an incompressibility condition equation, the Navier-Stokes momentum equation, and the conservation of energy equation. At the interface of the immiscible layer, the continuity of velocity, shear stress, temperature, and heat flux are considered. The dimensionless equations governing each layer were numerically integrated using the finite difference method and the Southwell-over-relaxation method. A mesh independence test is conducted. Furthermore, a parametric study is performed to analyze how the different nanoparticle volume fractions and viscous heating affect the transport characteristics of engine oil-copper and mineral oil-silver nanofluids. The study also examined the effects of various types of nanoparticles and base fluids. The results demonstrated that heat transport could be efficiently controlled by considering the viscous heating aspect. Moreover, the effects of different nanoparticles on heat transport were found to be more significant than those of base fluids. Finally, a point-wise comparison of our numerical results demonstrates a good agreement with existing studies in the literature. 2023 Author(s). -
Study of nanofluid flow and heat transfer in a stationary cone-disk system
Rheometric, viscosimetric, bio-medical, and several other pharmaceutical machineries utilize the structural advantages provided by the geometry of a stationary conical diffuser. The problem of the Buongiorno nanofluid flow in the conical gap of a stationary cone-disk system for isothermal boundaries is studied. The governing system, comprising the incompressibility condition, NavierStokes equation, energy conservation equation, and conservation of Nanoparticle Volume Fraction (NVF) equation, is analyzed. The Lie-group theory has been used to derive a self-similar model. Solutions of the self-similar equations were computed numerically, and the expressions for the Nusselt number and Sherwood number are obtained. The parametric investigation reveals that the heat and mass transfer rate subside significantly when pre-swirl is introduced to the flow. Furthermore, the nanofluid slip mechanisms enhance the effective temperature of the system. 2023 Elsevier Ltd -
Study of nanofluid flow in a stationary cone-disk system with temperature-dependent viscosity and thermal conductivity
The substantial temperature gradient experienced by systems operating at relatively high temperatures significantly impacts the transport characteristics of fluids. Hence, considering temperature-dependent fluid properties is critical for obtaining realistic prediction of fluid behavior and optimizing system performance. The current study focuses on the flow of nanofluids in a stationary cone-disk system (SCDS), taking into account temperature-dependent thermal conductivity and viscosity. The influence of Brownian motion, thermophoresis, and Rosseland radiative flux on the heat transport features are also examined. The Reynolds model for viscosity and Chiam's model for thermal conductivity are employed. The Navier-Stokes equation, the energy equation, the incompressibility condition, and the continuity equation for nanoparticles constitute the governing system. The Lie-group transformations lead the self-similar ordinary differential equations, which are then solved numerically. Multi-variate non-linear regression models for the rate of heat and mass transfers on the disk surface were developed. Our study reveals a notable decrease in the rate of heat and mass transfer when pre-swirl exists in the flow. The significant influence of nanofluid slip mechanisms on the effective temperature and nanofluid volume fraction (NVF) within the system is highlighted. Furthermore, the variable viscosity property enhances the temperature and NVF of the SCDS. 2024 Author(s). -
Study of Nanolayered Structure of Commercially Available Carbon Materials and Soot
Developments in the modern world periodically call for the discovery or invention of new and exotic materials. In the present situation, to develop unique and novel materials, which move beyond the barriers of the physical limits of the amount of micro- miniaturization possible as well as the current technology and take advantage of the opportunities not yet imagined, is not at all a need but a necessity. The advent of Nano technology of carbon allotropes is a giant leap towards this goal. The starting of the era of carbon nanomaterials traces back to 1985 when the fullerenes with a foot ball structure were accidently discovered. From then on, the field of carbon nanotechnology was in the constant limelight on account of the amazing properties displayed by the various allotropes of carbon. These properties are dependent mainly on the type of hybridization present in the nanostructures, which categorizes them to amorphous or crystalline. Also, there exist some structures which are the combination of these two and are termed as nanocrystalline or turbostratic structures. The discovery of graphene, which has a turbostratic structure and is the thinnest material known and the strongest ever measured, with outstanding properties such as highest room temperature electrical conductivity; high mechanical robustness etc was a ground breaking one. These remarkable properties open up a wide range of potential applications ranging from clean energy to nano-electronics to bio-medical devices. Thus, it is a necessity to explore and characterize various effective sources of these nanomaterials. The present study is an attempt to investigate such efficient, easily available and cost-effective precursors. Soot, also known as black carbon, is a fine-grained solid residue that results from incomplete combustion of hydrocarbons and is a widely used precursor for the production of carbon nanomaterials. Carbon soot is a major component of smoke from the combustion of carbon-rich organic fuels and hydrocarbons and hence has a vast number of sources. In the study presented here soot obtained from the thermal decomposition of commercially available kerosene, diesel oil, paraffin wax and lubricant oil is investigated. Nanostructure of the commercially available carbon black is also studied. Various techniques such as Micro Raman spectroscopy, Fourier Transform Infrared Spectroscopy (FT-IR), X-ray diffraction (XRD), High Resolution Scanning Electron Microscopy (HR-SEM), Electron dispersive spectroscopy (EDS) and elemental analysis are employed for the structural and morphological characterization of the samples. Raman scattering is used as a probe to study the disorder in the carbon skeleton materials. The intensity ratio of the D and G modes occurring in the spectra is proportional to the number of rings at the edge of the grain and also indicates the quality of the sample. FT-IR spectroscopy is used to characterize qualitatively the functional groups of carbon materials. XRD is the most common analytical technique used for determining the structure of ordered and disordered carbons from the positions of the diffraction peaks at 2?? angle. The structural parameters like the size of the ordered grains along c and a axis (Lc and La), the average spacing of the crystallographic (002) planes (d002) can be determined through Scherrer equations. SEM micrographs give the surface morphology of the nanomaterials present and the EDS analysis gives the abundance of the microscopic constituents. Elemental composition of the samples can be derived from the elemental analysis using CHNS (Carbon Hydrogen Nitrogen Sulphur) analyser. The present study shows that all the samples investigated obeys the Tuinstra-Koening relation and posses a nanocrystalline structure. The ratio of the defect and graphite bands is found to be very low, especially in the case of diesel soot which has a value very much lower than those reported in the earlier studies, indicating high quality and a low amount of disorder in the samples. HR-SEM micrographs clearly indicate that the carbon nanostructured present in the samples are in the form of non-uniform nanospheres with diameter varying between 26-100 nm. The characteristic diffraction peak of graphene corresponding to (100) diffraction is observed in the x-ray diffraction profiles of all the samples. The interlayer spacing determined in all the samples lies very close to that of graphite. The H/C atomic ratio from the CHNS analysis is found to be very low and confirms the nanocrystalline structure of the materials. The graphite band position in the IR spectra indicates that the nanospheres formed are to be composed more of crystalline graphitic carbon. From the EDS analysis it is evident that all the samples have very high carbon content and are free from impurities and thus concludes that the materials and methods used in the present study for the synthesis of carbon nanospheres possessing a nanocrystalline structure are efficient and cost effective and are good precursors for graphene. -
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.