The current numerical exploration is aimed to study the Homotopy analysis on hydromagnetic hybrid nanofluid transient stream considering non-linear radiative heat flux and variable heat source with a special emphasis on improvement in heat exchange efficiency at the proximity of the spinning sphere's stagnation domain. The relevant transformations of similarity are applied to convert the flow representing partial differential equations (PDEs) to describe the flow phenomena into nonlinear coupled ordinary differential equations. The semi-analytical approach solves the resultant dimensionless Boundary Value Problem (BVP). Convective heat transfer coefficient optimisation is explored using Response Surface Methodology (RSM). The full quadratic regression model is used for the sensitivity analysis. The flow characteristics for the nanofluids with water as the base liquid and silver and alumina as metals, are presented in tabular and graphical form. In a limited sense, the calculated findings are confirmed by previously published literature, and it is discovered that there are strong correlations. The significant results observed that for both assisting and hindering flows, the presence of a variable heat source and thermal radiation greatly raises the temperature of the boundary layer. The rate of heat transfer has a maximum sensitivity of 1.084790 towards thermal radiation and the heat transmission rate has a lower sensitivity value of 0.078210 towards internal variable heat source. The significant impacts of numerous physical quantities are scrutinized and discussed meticulously in terms of friction factor and heat transfer coefficient.

The current numerical investigation aims to study buoyancy-driven convection of hybrid nanofluids in an annular enclosure formed by two vertical concentric cylinders. In this analysis, hybrid nanofluid containing water and Ag-MgO nanoparticles has been taken as the working medium in the annular domain. The outer wall of the annulus is maintained at lower temperature and adiabatic condition at the horizontal walls of the annulus has been considered. However, along the inner wall, two different thermal conditions are imposed. For Case-I, a linear temperature profile has been considered, and for Case-II, a uniform temperature has been considered. For both the linear and uniform heating, the impact of Rayleigh number, nanoparticle concentration, and different proportions of nanoparticles on fluid flow and thermal transport characteristics in the vertical annulus has been addressed. The numerical simulations are performed for a vast range of parameters to examine fluid flow and thermal transport characteristics in the annular enclosure. The results are represented graphically through flow and thermal contours, and local and average Nusselt numbers. It is noticed that the presence of nanoparticles greatly helps in enhancing the heat removal rate in the annulus. In addition, several numerical computations have been carried out to identify the optimum thermal boundary condition to achieve enhanced heat transport rate.

This article focuses on the onset of dissolution-driven convection in an inclined porous layer and explores the influence of several important control parameters, including the inclination angle, Damköhler number, and Rayleigh number. Our investigation reveals that the boundaries of linear instability and nonlinear stability do not align, indicating that different behaviors occur in these regions of parameter space. As the inclination angle increases, the subcritical instability region expands, indicating a wider range of conditions where subcritical instability can occur. Moreover, transverse rolls demonstrate greater stability when compared to longitudinal rolls, highlighting the significant impact of convection pattern orientation on stability. Furthermore, both the Damköhler number and inclination angle have stabilizing effects on the system, contributing to increased stability. Moreover, the subcritical region between longitudinal and transverse rolls appears to expand.

The flow through porous medium accounts for numerous applications in various fields namely, agriculture, geothermal sciences, and engineering. Furthermore, dissolution-driven convection in porous media has grabbed great attention in recent years due to its practical applications in long-term geological storage of carbon dioxide, in the production of mineral deposits, and other industrial applications. In this regard, the current numerical analysis focuses on addressing the thermal instability of dissolution-driven convective phenomena of a power-law fluid through a porous horizontal domain with a first-order chemical reaction. For linear stability analysis, the method of normal modes has been employed to solve governing dimensionless equations which give rise to an eigenvalue problem. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for the onset of convection. The impact of Damköhler number, Péclet number, and power-law index on the onset of convection has been investigated. The role of these critical parameters is found to be highly significant in stabilizing the system. An increase in the power-law index causes stabilization or destabilization in the system, depending on the Péclet number. An enhancement in the magnitude of Damköhler number makes the system stable for all values of the Péclet number. Also, Damköhler and critical Rayleigh number are inter-related, that is, an increment in Damköhler number results in the enhancement of critical Rayleigh numbers, which in turn leads to stabilization of the system. The critical wave number is observed to have a remarkable influence on Damköhler number as well as power-law index.

This paper reports numerical investigation of buoyant convection of nanofluid in a tilted parallelogrammic porous enclosure. The upper and lower portions of the geometry are preserved at thermally insulated condition; left and right surfaces are linearly heated and uniformly cooled, respectively. The momentum equations are modeled by utilizing Darcy’s law and thermal processes are considered using transient energy equation. The partial differential equations governing the physical processes are numerically solved by FDM-based ADI and SLOR techniques. In this analysis, we have used an appropriate coordinate transformations to transform the model equations from the parallelogram domain to rectangular-shaped computational domain. The flow and thermal distributions are illustrated through streamlines and isotherms, while the thermal transport rates are measured using the Nusselt number. Numerical computations predict the influences of sidewall inclination angle and nonuniform thermal condition on the flow and thermal distributions and heat transport rates for wide parametric ranges chosen in the present study.

Purpose: One of the major challenges in the design of thermal equipment is to minimize the entropy production and enhance the thermal dissipation rate for improving energy efficiency of the devices. In several industrial applications, the structure of thermal device is cylindrical shape. In this regard, this paper aims to explore the impact of isothermal cylindrical solid block on nanofluid (Ag – H2O) convective flow and entropy generation in a cylindrical annular chamber subjected to different thermal conditions. Furthermore, the present study also addresses the structural impact of cylindrical solid block placed at the center of annular domain. Design/methodology/approach: The alternating direction implicit and successive over relaxation techniques are used in the current investigation to solve the coupled partial differential equations. Furthermore, estimation of average Nusselt number and total entropy generation involves integration and is achieved by Simpson and Trapezoidal’s rules, respectively. Mesh independence checks have been carried out to ensure the accuracy of numerical results. Findings: Computations have been performed to analyze the simultaneous multiple influences, such as different thermal conditions, size and aspect ratio of the hot obstacle, Rayleigh number and nanoparticle shape on buoyancy-driven nanoliquid movement, heat dissipation, irreversibility distribution, cup-mixing temperature and performance evaluation criteria in an annular chamber. The computational results reveal that the nanoparticle shape and obstacle size produce conducive situation for increasing system’s thermal efficiency. Furthermore, utilization of nonspherical shaped nanoparticles enhances the heat transfer rate with minimum entropy generation in the enclosure. Also, greater performance evaluation criteria has been noticed for larger obstacle for both uniform and nonuniform heating. Research limitations/implications: The current numerical investigation can be extended to further explore the thermal performance with different positions of solid obstacle, inclination angles, by applying Lorentz force, internal heat generation and so on numerically or experimentally. Originality/value: A pioneering numerical investigation on the structural influence of hot solid block on the convective nanofluid flow, energy transport and entropy production in an annular space has been analyzed. The results in the present study are novel, related to various modern industrial applications. These results could be used as a firsthand information for the design engineers to obtain highly efficient thermal systems.

Purpose: Natural convection in finite enclosures is a common phenomenon in various thermal applications. To provide the thermal design guidelines, this study aims to numerically explore the potential of using internal baffles and nanofluids to either enhance or suppress heat transport in a vertical annulus. Furthermore, the annular-shaped enclosure is filled with aqueous-silver nanofluid and the effects of five distinct nanoparticle shapes are examined. In addition, the influence of baffle design parameters, including baffle position, thickness and length, is thoroughly analyzed. Design/methodology/approach: The finite difference method is used in conjunction with the alternating direction implicit and successive line over relaxation techniques to solve nonlinear and coupled partial differential equations. The single phase model is used for nanofluid which is considered as a homogeneous fluid with improved thermal properties. The independence tests are carried out for assessing the sufficiency of grid size and time step for obtaining results accurately. Findings: The baffle dimension parameters and nanoparticle shape exhibit significant impact on the convective flow and heat transfer characteristics, leading to the following results: sphere- and blade-shaped nanoparticles demonstrate around 30% enhancement in the heat transport capability compared with platelet-shaped nanoparticles, which exhibit the least. When considering the baffle design parameter, either a decrease in the baffle length and thickness or an increase in baffle height leads to an improvement in heat transport rate. Consequently, a threefold increase in baffle height yields a 40% improvement in thermal performance. Originality/value: Understanding the impact of nanoparticle shapes and baffle design parameters on flow and thermal behavior will enable engineers to provide valuable insight on thermal management and overall system efficiency. Therefore, the current work focuses on exploring buoyant nanofluid flow and thermal mechanism in a baffled annular-shaped enclosure. Specifically, an internal baffle that exhibits conductive heat transfer through it is considered, and the impact of baffle dimensions (thickness, length and position) on the fluid flow behavior and thermal characteristics is investigated. In addition, the current study also addresses the influence of five distinct nanoparticle shapes (e.g. spherical, cylindrical, platelet, blade and brick) on the flow and thermal behavior in the baffled annular geometry. In addition to deepening the understanding of nanofluid behavior in a baffled vertical annulus, the current study contributes to the ongoing advancements in thermal applications by providing certain guidelines to design application-specific enclosures.

In various industrial applications, the main objective is to enhance thermal efficiency by minimizing the generation of entropy. Specifically, achieving optimal thermal efficiency in a tilted cylindrical chamber poses significant challenges due to the combined effects of tangential and normal gravity components. Our study focuses on the flow dynamics, thermal transport, and entropy generation of Fe3O4/H2O nanoliquid within a cylindrical annular enclosure by incorporating the synergistic effects of magnetic force, geometric inclination angle, and thickness of the porous region. The Brinkman–Forchheimer-extended Darcy model for ferrofluid motion and the one-equation model for heat transfer are applied in the porous region, while the conventional Navier–Stokes and energy equations are used in the fluid-only region. A series of computations is performed for various key parameters, such as Hartmann number (0 ≤ Ha ≤ 60), Darcy number (10−5 ≤ Da ≤ 10−1), porous layer thickness (0:1 ≤ e ≤ 0:9), and angle of inclination (−60∘ ≤ c ≤ 60∘). Our results reveal that the heat transport rate is enhanced by 48.6% with an increase in the Darcy number from 10−5 to 10−1. Moreover, the flow circulation and heat transport can be optimized by tilting the enclosure anticlockwise. It has been found that 91.8% of flow strength can be enhanced by rotating the enclosure from −60∘ to 60∘. Finally, this study suggests that the inclination angle of 30∘ and a porous layer thickness of 0.3 emerge as the ideal configuration to obtain optimal performance, particularly for lower Hartmann and higher Darcy numbers. Our findings will provide insight into optimizing thermal processes in nanoliquid-filled enclosures subjected to magnetic force.

This study deals with a numerical investigation of conjugate heat transfer phenomena in a porous enclosure subjected to magnetic field with internal heat generation/absorption. The physical domain of the numerical model encompasses a vertical annulus with a thick inner cylinder wall, where the porous annular region is saturated with an aqueous-MWCNT nanofluid. In this model, the momentum equation includes the non-Darcy viscous terms and additional body term to accurately represent the influence of porous media and magnetic fields on the flow behavior. To estimate conjugate heat transfer phenomena, the energy conservation equations for the solid wall and the fluid-saturated porous region are solved simultaneously. The finite difference technique is used to solve the non-dimensionalized governing equations, and validated against existing studies. Using the proposed model, a series of numerical calculations is performed for various parameters including Hartmann number (Ha=0∼50), Darcy number (Da=10-5∼10-1), thermal conductivity ratio (Kr=0.1∼10), dimensionless solid wall thickness (ε=0.1∼0.5), nanoparticle concentration (ϕ=0∼0.05), and dimensionless internal heat generation/absorption rate (Q=-10∼10). The numerical results reveal that a significant improvement in thermal transport can be achieved by increasing either Da or Kr: An increment in Da from 10-5 to 10-1, for example, results in 95.6% increase in the flow circulation rate. Either a decrease in Q or an increase in ϕ also contributes to enhancing the heat dissipation rate. For instance, there is a 16.6% reduction in heat dissipation rate for internal heat generation (Q=10) case compared to internal heat absorption (Q=-10) case. On the other hand, an increase in either Ha or ε results in a suppression in flow and heat transport. Among the considered range of parameters, greater heat dissipation could be obtained for Da = 10-1, Kr = 10, ε=0.1, and Ha <10. These findings can expand our understanding of natural circulation and heat transfer within the fluid-filled enclosures and serve as building block for efficient thermal design guidelines in diverse applications.

Fractional-based fluid transport modeling provides a deeper and more comprehensive understanding of the thermophysical properties of small-scale fluids and polymer solutions. Moreover, the fractional-order fluid dynamics framework finds applications in various fields, including renewable energy systems, thermal energy storage, and oil storage tanks. Inspired by these developments, the current study addresses the computational challenges inherent in modeling nanofluid dynamics within a square enclosure by introducing a fractional-order approach to enhance the simulation of buoyant flow and heat transport. Our model integrates the linear interpolation (L1 approach) and finite difference approximation for temporal and spatial derivatives by utilizing the Caputo time-fractional derivative instead of the conventional time derivative. This integration facilitates the use of the Backward Difference Alternating Direction Implicit (BD-ADI) method, which was specifically chosen to reduce the computational burden associated with the non-local characteristics of fractional models. Our results show that by altering the fractional order, significant improvements in heat transfer efficiency are achieved compared to classical models. For instance, compared to the integer order, a lower fractional-order parameter of γ=0.80 with a 4% nanoparticle volume fraction at a Rayleigh number of 103 increases the heat transfer rate by 15.77%. However, at a Rayleigh number of 106, the enhancement reduces to 4.15%, indicating that fractional adjustments’ influence diminishes at higher thermal buoyancy levels. This behavior of the fractional-order nanofluid model, influenced by thermal buoyancy force, has been investigated by using a Multiple Linear Regression(MLR) analysis with 258 numerical samples. Besides, MLR analysis further identifies the nanoparticle volume fraction as a critical factor, influencing the heat transfer rate by 10.48% at lower fractional-order settings.

The current numerical investigation deals with natural convection in a nanofluid-saturated porous cylindrical annulus subjected to partial heating and cooling of side walls by adopting Brinkman-extended Darcy Model to govern the fluid flow in porous media. By choosing five different locations and four lengths of thermal source–sink pairs, the impact of discrete heating–cooling on fluid flow, thermal transport rates and thermal mixing in a porous annular enclosure has been addressed. From the vast range of numerical simulations, the results provide information on the proper size and location of source–sink combinations to dissipate maximum thermal transport along with better thermal mixing in the enclosure. The importance of porosity, nanoparticle concentration, Darcy and Rayleigh numbers on overall thermal dissipation rate has also been discussed. The results showed that identifying an optimum source–sink location along with an appropriate choice of other control parameters can lead to higher thermal transport enhancement and thermal mixing.

The role of heat and mass transfer as well as entropy generation in cooling/heating processes is indispensable since it plays a crucial role in a variety of industrial applications. Impressed by these applications, the current chapter scrutinizes the entropy generation along with thermal and solutal dissipation rates resulting from MHD double-diffusive convective phenomenon in a nanoliquid-filled annular enclosure. Along the vertical surfaces of the annulus, the uniform temperature and concentration conditions are specified, while the upper and lower boundaries are maintained as insulated and impermeable. The effects influencing the fluid movement, temperature, concentration, and entropy production by different parameters, namely, the buoyancy ratio (-5 ≤ N ≤ 5), Lewis number (0.5 ≤ Le ≤ 5), Hartmann number (0 ≤ Ha ≤ 50), and nanoparticle volume fraction (0 ≤ ≤ 0.05), are examined in detail. Variations in heat and mass dissipation rates, entropy production, and Bejan number are graphically illustrated and are discussed with physical interpretation. Through the vast range of computational study, it has been found that the irreversibility in the system could be controlled by the proper choice of parametric values.

In majority of industrial and engineering applications, enhanced heat transfer with minimum entropy production is the major concern. With several theoretical and experimental works, it has been found that replacing the traditional heat transfer liquids with nanoliquid is one of the reliable ways to enhance the thermal transport with minimum loss of system energy. In this regard, the current article deals with the convective nanoliquid flow and the associated thermal dissipation as well as entropy generation rates in a porous annular enclosure saturated nanoliquid. The vertical surface of interior and exterior cylinders is maintained with sinusoidal thermal conditions with different phase deviations, while the horizontal boundaries are thermally insulated. The governing physical equations are solved by implementing finite difference method (FDM). The variation in buoyant nanoliquid flow and the corresponding heat transport rates along with local and global entropy production rates are systematically examined. For the numerical simulations, a vast range of parameters such as the Rayleigh (103 ≤ Ra ≤ 105) and Darcy (10–6 ≤ Da ≤ 10–2) numbers, phase deviation (0 ≤ γ ≤ π), and nanoparticle volume fraction (0 ≤ ϕ ≤ 0.05) are considered in this analysis. The contributions of heat transfer entropy and fluid friction entropy to global entropy production in the geometry are determined through the Bejan number. The numerical results reveal the impact of various parameters on control of convective flow, heat transfer, and entropy generation rates. Further, the results are in excellent agreement with standard benchmark simulations. The predicted results could provide some vital information in choosing the proper choice of parameters to enhance the system efficiency.

Purpose: This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport. Design/methodology/approach: The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated. Findings: Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model. Research limitations/implications: The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects. Practical implications: The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design. Originality/value: A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

The current numerical investigation deals with the conjugate (conduction–convection) magnetohydrodynamic (MHD) incompressible flow and thermal dissipation processes of Multi-wall carbon nanotube - silver (MWCNT - Ag) water hybrid Newtonian nanoliquid filled in an annular enclosure. The inner cylinder having finite thickness is subjected to uniform/non-uniform thermal profiles whereas the exterior cylinder is kept at low temperature. However, the horizontal surfaces are retained adiabatic. An in-house FORTRAN code has been developed to solve the two dimensional, axisymmetric and unsteady governing equations by employing time-splitting technique. Detailed numerical simulations have been carried out for control parameters such as Rayleigh number, thermal conductivity ratio, wall thickness, Hartmann number, nanoparticle concentration and for a clear visualization of the impact of various range of these parameters, the obtained numerical results are represented by the streamlines, isotherms and plot of average Nusselt number values. From detailed numerical computations, greater heat transport rate is achieved with minimum wall thickness and maximum thermal conductivity ratio irrespective of thermal boundary condition. The results also reveal that hybrid nanoliquid with equal proportion of MWCNT and silver (Ag) nanoparticles dispersed in the water helps in dissipating maximum amount of thermal energy from the solid–fluid interface of annulus. In addition, uniform heating condition helps in extracting greater amount of heat dissipation compared to linear heating.

The current article deals with the computational study of buoyant convection and heat dissipation processes of hybrid nanoliquid saturated in an inclined porous annulus. The fluid flow movement in the porous annular region is modeled using Darcy-Brinkman-Forchheimer model. The vertical boundaries of the cylinder are subjected to uniform but different heating profiles and horizontal surfaces are maintained adiabatic. In the current investigation, for the conservation laws which govern the considered physical process, numerical simulations have been performed using the time-splitting ADI (Alternating Direction Implicit) and line over-relaxation methods. Computations have been performed for broad range of physical and geometric parameters, such as Hartmann number (0≤Ha≤50), geometric inclination angle (-6°≤γ≤6°), Darcy number (10-5≤Da≤10-1), aspect ratio (0.5≤Ar≤2) and internal heat generation (0≤Q≤20) to address their impacts on hybrid nanofluid movement and associated heat dissipation rate in the annulus. In addition, heat transfer rate has also been estimated by considering the impact of concentration of each nanoparticle present in the hybrid nanofluid pair. The outcome of numerical computations reveal that an increment in Darcy number enhances the average Nusselt number. Additionally, it has been noticed that the geometric tilt angle of 30° results in dissipating maximum amount of thermal energy in the system. Through this investigation, it is also noticed that shallow annular enclosure exhibits greater amount of heat transport compared to other aspect ratios. Also, significant impact of magnetic field on fluid flow and thermal transport rate has been noticed from the detailed numerical simulations. Further, an enhancement in internal heat generation deteriorates the heat transfer rate and this reduction becomes more steep as the internal heat generation increases.

The present computational investigation explores the fluid and thermal characteristics along with entropy generation due to buoyancy-driven magnetohydrodynamic (MHD) convective flow of aqueous hybrid nanoliquid filled in a nonuniformly heated porous cylindrical chamber. The fluid motion in the enclosure is modeled by Brinkman — extended Darcy model. The modeled equations are resolved by finite difference approach. The computations are conducted for Rayleigh number (103–105), Hartmann number (0–50), Darcy number (10−5–10−1), different nanoparticle shapes and nanoparticle volume fraction (Ag/MgO: 0–0.05) to understand the characteristic of flow, thermal and irreversibility distribution. With vast numerical simulations, the outcomes reveal that though the buoyancy force is greater, the fluidity cannot be enhanced unless the permeability and magnetic field strength are optimally maintained. As Ra,Ha and Da is varied respectively from 103 to 105, 50 to 0 and 10−5 to 10−1, the fluidity has been enhanced by 99.39%,83.26% and 99.79%. Among all considered parametric combinations, it has been noticed that the choice of Ha=0,Ra=105,Da=10−1 with proper ratio of nanoparticles enhance the system efficiency. However, minimal entropy generation can be achieved with greater Hartmann and lower Darcy numbers. Furthermore, it has been found that blade shaped nanoparticles lead to increase the performance of thermal system.

The physical structure in several industrial applications which includes cooling of electronic equipment, heat exchangers, nuclear reactors, and solar collectors, could aptly represent the cylindrical annular porous geometry. The prior knowledge of buoyant flow and thermal transport rates in this geometry provides the vital information to the design engineers. In this article, we analyze the convective nanoliquid flow and associated thermal dissipation as well as entropy generation rates in an inclined annular enclosure filled with nanoliquid saturated porous medium. The vertical surfaces of inner and outer cylinders are maintained at uniform, but different temperatures and horizontal boundaries are kept insulated. The momentum equations are modeled utilizing the Darcy law, the coupled partial differential equations are numerically solved adopting the time splitting and line over relaxation techniques. For the numerical simulations, a vast range of parameters such as the Darcy Rayleigh number (10 ≤ RaD ≤ 103), annulus inclination angle (0° ≤ γ ≤ 60°), aspect ratio (0.5 ≤ Ar ≤ 2) and nanoparticle volume fraction (0 ≤ ϕ ≤ 0.05) are considered. The contributions of heat transfer and fluid friction entropies to global entropy production in the geometry are determined through the Bejan number. The numerical results reveal that the convective flow, heat transfer and entropy generation rates could be controlled with the aid of cavity inclination angle. It is found that the shallow annular enclosure gives better thermal performance with minimum entropy generation regardless of RaD, γ and ϕ. Further, the results are in excellent agreement with standard benchmark simulations. The predicted results could provide some vital information to enhance the system efficiency.

Many of the engineering/industrial applications involving the energy transport undergoes entropy generation which is unavoidable and this leads to degradation of system efficiency. Several researchers working in this field are exploring new ways to minimize the entropy generation so that the efficiency of the system could be enhanced. Motivated by these applications, the current article scrutinizes the rate of entropy generation along with thermal and solutal transport resulting from double-diffusive convective phenomenon in a nanoliquid-filled annular enclosure. Along vertical surfaces of the annulus, the uniform temperature and concentration conditions are specified, while the upper and lower boundaries are maintained as insulated and impermeable. The set of non-linear coupled governing equations in vorticity-stream function form supported by related initial and boundary conditions are computed numerically using time-splitting technique. The influence of various controlling parameters namely the buoyancy ratio (- 5 ≤ N≤ 5), Lewis number (0.5 ≤ Le≤ 2), aspect ratio (0.5 ≤ Ar≤ 2) and nanoparticle volume fraction (0 ≤ ϕ≤ 0.05) on fluid movement, temperature, concentration and entropy production are scrutinized and variation in thermal and solutal dissipation rates, entropy production and Bejan number are graphically illustrated and are discussed with physical interpretation. Through the vast range of computational experiments, it has been found that the quantity of generated entropy in an enclosure is greater during aided flow compared to that of opposing case. Further, it has also been found that higher thermal and solutal performance rates with minimal loss of system energy (entropy generation) could be achieved with a shallow annulus.

This investigation is devoted to analyze the buoyancy-driven flow behavior and associated thermal dissipation rate in a nanofluid-filled annular region with five different single source-sink and three different dual source-sink arrangements along the vertical surfaces. The remaining region on the vertical boundaries and horizontal surfaces are kept adiabatic. Numerical simulations have been performed by employing the finite difference method. To analyze the impacts of different nanofluids, nanoparticle volume fraction, Rayleigh number, size, and arrangement of sources and sinks, the results are graphically represented through streamline and isotherm contours, thermal profiles, average Nusselt number, and cup-mixing temperature. The results showed that identifying an optimum location and length of source-sink with a proper selection of other control parameters can lead to enhanced thermal transport and thermal mixing in the enclosure. In particular, middle-middle thermally active location and placing source-sink separately on the vertical walls lead to the production of maximum heat transport compared to other single and dual source-sink arrangements, respectively. Also, among the two nanofluids considered in the current investigation, larger enhancement in thermal transport has been achieved for Cu-water nanofluid. The calculated enhancement ratio of the heat dissipation rate enhances with an increment in nanoparticle concentration.

In the present work, the convective flow and thermal pattern, associated heat transport rates of buoyant convection in an annular geometry is theoretically analyzed. The inner cylindrical wall has finite thickness and is kept at high temperature, while the outer cylindrical wall is held at low temperature. The vorticity-stream function form of model equations are solved using FDM based on ADI and SLOR techniques. The numerical simulations for various parameters are presented. In particular, this analysis focused on the effects of conjugate heat transport characteristics.

The vertical, open-ended double-passage annular space between three vertical concentric co-axial cylinders is an important geometry representing significant number of industrial applications. For a design engineer, the knowledge of fully developed mixed convection in this geometry is very essential. Hence, in this paper, it is proposed to numerically as well as analytically investigate the fully developed mixed convective flow in the vertical annuli having two annular passages with open upper and lower boundaries by taking viscous dissipation into consideration. The prime objective of the analysis is to bring out the influences of the location of middle cylinder, known as baffle, and viscous dissipation on the fluid flow and temperature profiles as well as the associated thermal transport rates. By neglecting the viscous dissipation influences, exact solutions are determined, while the finite difference-based numerical solutions are achieved in the presence of viscous dissipation. Further, excellent agreement is obtained between the analytical and numerical solutions under limiting conditions. The roles of viscous dissipation and baffle location are meticulously brought out through the flow pattern, temperature profiles and heat transport rates.

In this paper, the impacts of the location of a thermal source on buoyant convection of nanofluids in an annular region are analyzed numerically through the finite volume technique. Five different thermal source positions along the inner cylinder of the annulus have been analyzed. The prime objective is to identify the optimal position of the source to maximize or minimize the thermal transport at different values of Ra and diverse volume fractions of the nanoparticle ranging from 0 to 10%. The location of the thermal source has a profound impact on the flow and temperature patterns as well as thermal transfer from the discrete source to the nanofluid. Further, the volume fraction of nanoparticles also controls the heat transport in the annular geometry.

A sealed annular geometry containing nanoliquids with differently heated boundaries aptly describes the geometrical structure of many important cooling applications. The present study reports the numerical investigation on the effect of axially varying temperature in the form of sinusoidal thermal profiles along the side walls of an annular enclosure containing different hybrid nanoliquids with insulated horizontal boundaries. An implicit FDM based approach is adopted to solve the transient and steady-state model equations and numerical simulations are presented to describe the qualitative flow behavior as well as the quantitative thermal transport rates. The prime objective of the analysis is to enhance the buoyant flow circulation strength as well as the associated thermal dissipation rates and is achieved by identifying a suitable combination of nanoparticle along with a proper choice of geometrical parameters. Numerical predictions revealed the buoyant motion and thermal dissipation rate could be effectively controlled by a proper selection of phase deviation. Further, the appropriate combination of nanoparticles is another crucial parameter in enhancing the thermal transport in the geometry.

A vertical annular configuration with differently heated cylindrical surfaces and horizontal adiabatic boundaries is systematically studied in view to their industrial applications. In this paper, we investigate the effects of conjugate buoyant heat transport in water based nanofluids with different nanoparticles such as alumina, titania or copper, and is filled in the enclosed annular gap. The annulus space is formed by a thick inner cylinder having a uniform high temperature, an exterior cylindrical tube with a constant lower temperature, and thermally insulated upper and lower surfaces. By investigating heat transport for broad spectrum of Rayleigh number, solid wall thickness, thermal conductivity ratio and nanoparticle volume fraction, we found that the influence of wall thickness on thermal dissipation rate along wall and interface greatly depends on conductivity ratio and vice-versa. In particular, we uncover that the choice of nanoparticle in a nanofluid and its concentration are key factors in enhancing the thermal transport along the interface. Specially, copper based nanofluids produces higher heat transport among other nanoparticles, and for the range of nanoparticle concentration chosen in this analysis, enhanced thermal dissipation along the interface has been detected as nanoparticle volume fraction is increased. Our results are applicable to choose nanofluids along with other critical parameters for the desired heat transport.

This paper reports the influence of non-uniform thermal conditions on buoyancy-driven convection of water based nanofluids in a cylindrical annulus. Annular geometry is formed by two upright co-axial cylinders. In this analysis, two different non-uniform temperature profiles are applied at bottom boundary, while the side boundaries are kept at lower temperature and top boundary is taken as thermally insulated. For the first case, the bottom boundary is sinusoidally heated, while linear thermal profile is applied in the second case. The annular gap is filled with water based nanofluids with copper nanoparticle. Using ADI based finite difference technique, the model equations are solved for vast range of parametric values. Numerical simulation results reveal the bi-cellular flow pattern for both non-uniform thermal conditions at all range of Rayleigh numbers. Further, the heat transport rates are highly sensitive to non-uniform conditions supplied at the bottom wall. The results of this analysis could be utilized for applications involving non-uniform thermal conditions in an annular geometry.