Nanofluid Saturated Porous Medium Research Articles

Mixed convection heat transfer in a partial porous layered split lid-driven wavy wall cavity with Cu–H2O nanofluid

This numerical study investigates mixed convection heat transfer in a two-dimensional irregularly-shaped enclosure with a nanofluid-saturated porous medium. The enclosure has wavy vertical walls, a centered triangular block, and a lid split into two regions moving in opposite directions. Transport equations are solved using the finite element method under varied Darcy (10−5 to 10−1), Reynolds (50 to 200), Richardson (0.1 to 10), amplitude (0 to 0.2), and nanoparticle volume fraction (0 to 0.1) numbers. Results demonstrate the combined effects of forced convection from lid motion and natural convection from temperature differences significantly enhance heat transfer. The wavy walls induce secondary flows and periodic disruption of thermal boundary layers. Increasing Darcy number enables deeper penetration into the porous block. Copper nanoparticles incrementally improve conductive heat transfer. Richardson number effects are more prominent at higher Reynolds numbers as buoyancy forces influence vertical convection. This study provides novel insights into synergistically utilizing wavy geometries, nanofluids, porous media, and active pumping for optimizing heat transfer in irregular enclosures for electronics cooling and thermal management.

Effect of gravity settling on the onset of thermal convection in a nanofluid-saturated porous medium layer

The onset of convection in a horizontal porous medium layer saturated with a nanofluid and heated from below is investigated via linear stability analysis and numerical simulation. The Darcy–Buongiorno model is used to describe the convective transport behaviour of the nanofluid and the settling effect of nanoparticles due to gravity is considered in addition to thermophoresis and Brownian diffusion. The linear stability analysis shows that the gravity settling is a substantial stabilizing mechanism restraining the destabilizing factors such as thermal buoyancy and thermophoresis. The stability threshold is determined by the relative strength of thermophoresis to gravity settling. It is found that the system is destabilized when the thermophoretic mobility prevails. As the nanoparticle size increases, the gravity settling effect is promoted and makes the system more stable. In particular, the onset of instability is dominated by the oscillatory mode once the nanoparticle concentration is in a stably stratified profile across the porous layer. When the Rayleigh–Darcy number $Ra_D$ exceeds the critical value, the spectrum of the growth rates of the unstable modes rises with increasing $Ra_D$ and $Rn$ (i.e. the concentration Rayleigh number), and eventually the unstable modes in the high-wavenumber region exhibit the same instability. The evolution of the convection is further examined by numerical simulation. The results verify the stability characteristics predicted by linear stability analysis. Moreover, the pattern of fingering convection of the nanofluid concentration is observed once the nanofluid concentration is unstably stratified and the density difference across the porous layer is large enough.

Unsteady Boundary Layer Heat and Mass Transfer Flow of Nanofluid Over Porous Stretching Sheet with Non-Uniform Heat Generation/Absorption and Double Stratification

The influence of thermal radiation and stratification process on unsteady MHD flow over stretching sheet embedded in “nanofluid saturated porous medium with non-uniform heat source/sink was analyzed numerically in the present analysis. Proper similarity transformations reduce the nonlinear partial differential equations into ordinary differential equations and are solved numerically by using Galerkin Finite element method. Impact of different parameters, such as, magnetic parameter (0.1–1.0), buoyancy ratio parameter (0.1–4.5), radiation parameter (0.5–1.7), Rayleigh number (0.1–0.7), thermophoresis parameter (0.4–1.5), thermal stratification parameter (0.01–1.0), Brownian motion parameter (1.0–2.0), solutal stratification parameter (0.01–1.0), unsteadiness parameter (0.1–0.4), space–dependent (-0.5–0.4) and temperature dependent (-0.5–0.2) heat source/sink parameters on velocity, temperature and concentration profiles is calculated and are illustrated graphically. Skin-friction coefficient, Nusselt and Sherwood number are calculated and the results are shown in tabular form. It is found that the thermal stratification parameter deteriorates the temperature of the fluid. The concentration of the fluid diminishes with rising values of solutal stratification parameter. The thermal boundary layer thickness elevates” with higher values of Brownian motion and thermophoresis parameters.

Effect of Three Types of Magnetic-Field Modulation and Different Shapes of Nanoparticles on the Instability of Nanofluid (Al2O3 + H2O) Saturated Porous Medium with Internal Heating

In this article the authors investigate the effect of three different types of magnetic-field modulation namely triangular-wave form, sine-wave form, and square-wave form on the instability of nanofluid (Al2O3 + H2O) saturated porous medium with internal heating. Linear stability analysis is done analytically using the normal mode approach, whereas nonlinear stability analysis is done by using the truncated Fourier series method. We obtained that the internal heating parameter destabilizes the system, whereas Darcy number and magnetic Chandrasekhar number stabilizes the system. The impact of three different shapes (Sphere/Bricks/Cylinder) of nanoparticles over instability is also analyzed, and it is found that the system is most stable for sphericalshaped nanoparticles while least stable for cylindrical-shaped nanoparticles. Mass/heat transfer in the system is analyzed by two different approaches, Mathematica NDSolve and Runge-Kutta-Fehlberg method (RKF-45), and it is found that the rate of mass/heat transfer is exactly the same in both cases. The internal heating and magnetic Chandrasekhar number play a crucial role in the heat/mass transfer in the system. Moreover, it is also noticed that heat and mass transfer start earliest in the case of triangle-waveforms as compared to other types of magnetic-field modulations.

Natural convection due to lateral uniform heat flux in a slender porous cavity saturated with nanofluid: Departure from LTE state

The present article deals with the influence of the local thermal nonequilibrium (LTNE) state on natural convection in an enclosure filled with nanofluid-saturated porous medium. The flow is induced due to the maintenance of constant heat flux on the vertical walls and insulation of horizontal walls. The Darcy model has been adopted to describe the flow governing equations. These equations are solved numerically by using the alternate direction implicit method and analytically by applying parallel flow assumptions valid for large aspect ratios. Boundary layer analysis is performed to report the boundary layer thickness ( δ x ∼ 2 1 / 2 ( k nf / k f ) 1 / 10 ( R a T ) − 1 / 5 ) as well as the heat transfer rate of nanofluid ( N u nf ∼ ( k nf / k f ) − 1 / 5 R a T 2 / 5 ) . The combined effect of LTNE state parameters (interface heat transfer coefficient (H), porosity scaled thermal conductivity ratio (γ)) and volume fraction of nanoparticle ( ϕ ) is addressed on the flow dynamics and heat transfer mechanism. Rigorous analysis, indicates that the average heat transfer rate of nanofluid and solid porous matrix are increasing function of H and γ, however, the role of γ is accelerated for a relatively high value of H. For increasing the value of γ from 1 to 10, the enhancement in the heat transfer rate of nanofluid is reported to be up to 27% at 10% volume fraction of nanoparticles. The average Nusselt number of nanofluid, as well as solid phase, are reduced when the value of ϕ is increased under the LTNE circumstances. Furthermore, the flow structure is controlled by unicellular structure with rotating anticlockwise direction in the entire study. For the very small value of H the temperature distribution in the solid porous matrix is mainly by conduction mode and distribution is linear, however, for a relatively high value of H the distribution in the same is controlled by both conduction as well as convection, and it will be more pronounced for the higher value of γ.

Internal Heat Modulation on Darcy Convection in a Porous Media Saturated by Nanofluid

In this paper we investigate the effect of internal heat modulation over a nanofluid saturated porous medium. We consider a small variation in time dependant heat source and vary sinusoidally with slow time. An energy equation will be altered by adding time dependant internal heat source. This internal heat source has its time dependent and independent parts. Time dependent part shows that the internal heat modulation over a porous media and defines controls on heat/mass transfer in the layer. We have performed a nonlinear stability analysis to investigate heat/mass transfer in the system. The nonlinear system of partial differential equations are transformed into nonlinear ordinary differential equations under similarity transforms up to the second term. This system has different system parameters and they have been investigated on heat and mass transfer graphically. The dual nature, stabilize or destabilize is due to the significant effect of internal heating modulation of the system. Further, the effect of internal heating is to destabilize the system, as a consequence heat/mass transfer enhances. It is found that internal heating modulation can be used effectively to regulate heat/mass transfer in the system.

The Cheng-Minkowycz problem for quadratic convective and radiative heat transfer in a nanofluid saturated porous medium: A revised model

The characteristics of heat transport in a porous medium saturated by a nanoliquid subject to non-linear variations of density-temperature relation and a novel quadratic thermal radiation are studied. For the first time, the well-known Cheng-Minkowycz problem was revisited by nonlinear convection and radiation. The governing equations, based on Darcy's law and Buongiorno's model, are simplified using boundary layer theory, which is further solved by the finite element method. The parameterization of the problem is used to describe the characteristics of the Boussinesq quadratic approximation, Brownian diffusion, quadratic radiation, thermophoretic diffusion, and no-mass flux conditions on the rheological and heat transport features. Our results demonstrate that the rate of heat transport (Nusselt number) is reduced due to thermophoretic diffusion, and the rate of reduction increases with increasing Lewis number values. The Nusselt number is improved due to increasing the values of the Brownian motion parameter at the rate of 0.00616835 and 0.00113362 for the cases of linear thermal radiation and quadratic thermal radiation, respectively. The improvement/reduction rate of the Nusselt number is higher for the case of quadratic thermal convection than for linear thermal convection. Furthermore, the heat transfer rate is achieved for the convection parameter, temperature ratio, and radiation parameter.

Multiple solutions and their stability for a Ti-alloy nanofluid saturated Darcy porous medium: Flow separation and reversal

In this article, the authors provided the stability analysis for Darcy porous medium saturated by a Ti-alloy nanofluid in the presence of tilted magnetic field, Joule heating, heat generation, and velocity slip effects. The Tiwari-Das model is implemented and the relevant similarity transformations are identified for mathematical modeling of the proposed fluid flow problem. The set of resultant ODEs has been solved using the shooting method in conjunction with the RK-4th order scheme. The existence of dual solutions is observed along with their critical values for the present setup at and after the bifurcation point but for a limited range of certain fixed parameters. Through the eigenvalue approach, it is shown that the first solutions are stable, but not the second solutions. The streamlines are depicted to understand the flow patterns in addition to the identification of flow separation point and flow reversal. The important findings are as follows: (a) the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and the inclined magnetic parameter in the presence of suction, (b) the Ti-alloy nanofluids velocity rises but the temperature decays with rising values of the Ti-alloy nanoparticle volume fraction, and (c) the value of smallest eigenvalues is growing with the growing values of magnetic parameter. Finally, this type of research may be extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines, and high-performance automatic parts) and medicine.

LINEAR CONVECTIVE STABILITY IN AN INCLINED CHANNEL FILLED WITH A NANOFLUID-SATURATED POROUS MEDIUM

In this study, convective stability of nanofluid flow in an inclined porous channel is being numerically investigated. The effects of Brownian motion and thermophoresis are accounted for in the nanofluid model. In addition, the flow in the porous region governs Brinkman's equation. A normal mode analysis is used to get the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation approach. The influence of various governing parameters, the critical Rayleigh number, and associated wavenumber are graphically displayed.

ENHANCEMENT OF DUPUIT-DARCY THERMAL CONVECTION OF SWCNT-WATER NON-NEWTONIAN NANOFLUID SATURATED POROUS MEDIUM

The focus of this manuscript is to investigate numerically the free convection of a single-wall carbon nanotube-water non-Newtonian nanofluid saturating an inclined square porous medium, where the Dupuit-Darcy model is used for modeling the fluid flow inside the cavity along with the Carreau-Yasuda model for describing the apparent viscosity of the nanofluid. The top and bottom walls of the enclosure are kept adiabatic, whereas the others are differentially heated. The governing parameters for the problem are the Rayleigh number, nanotubes volume fraction, inertial effect parameter, the Carreau-Yasuda non-Newtonian parameters as well as the inclination angle of the cavity. The finite difference method is used to resolve the governing partial differential equations of the problem. The obtained results are presented through graphs, streamlines, isotherms, and apparent viscosity contours. In addition, a scale analysis is presented to show the maximum heat transfer enhancement recorded. As a matter of fact, the obtained momentum equation enables the analysis of the Newtonian and non-Newtonian behavior of the nanofluid along with the Darcy and the departure from Darcy situation. The findings show that the increase of the single-wall carbone nanotube (SWCNT) percentage significantly enhances the heat transfer even with the increase of the fluid viscosity. Furthermore, the increase of inertial effect parameter inhibits the flow inside the cavity and causes a decrease in the convection rate. In actual fact the power-law index parameter of the Carreau-Yasuda model has a significant effect on the fluid flow strength as well as the convection rate inside the enclosure, i.e., the more the shear thinning the fluid, the better is the rate of convection. The inclination angle of -30° presents better angle for maximum convection rate. An enhancement of 8% in convection rate is recorded for the case of the Newtonian behavior, while for the shear-thinning situation the enhancement reaches eight times of that recorded of Newtonian condition.

THERMAL INSTABILITY OF BLOOD-COPPER CASSON NANOFLUID SATURATED POROUS MEDIUM UNDER LTNE, ROTATION, AND THROUGH-FLOW

Because of the antibacterial characteristics of copper, the thermal instability of blood-copper (B-Cu) nanoliquid plays a crucial role in the field of medical science, specifically in the cardiovascular system. In this article, the convective instability of B-Cu nanoliquid filled in a porous medium is investigated using a Casson model. A thermal nonequilibrium condition is taken for the nanoliquid and porous matrix. The Brinkman model is used because of the high porosity of the material. The influence of rotation and through-flow (both positive and negative) over the instability has also been examined. The amount of through-flow and rate of rotation are respectively governed by Peclet number and Taylor number. A comparison between the impacts of through-flow and rate of rotation is done, and it is found that through-flow is more effective than the rate of rotation to delay the onset of convection. Both steady and unsteady weakly nonlinear analyses are performed to understand the heat transport in the system. It is concluded that the Casson nanofluid parameter has both stabilizing and destabilizing impact depending upon the rate of rotation and therefore the current work can be possibly utilized in both places where heat removal and heat conservation is required. One more important thing is observed: the effect of local thermal nonequilibrium (LTNE) can also be regulated using the Casson nanofluid parameter.

Buoyancy-induced convective flow and heat transfer over obstacles embedded inside a Cu–water nanofluid-saturated porous cavity

In this article, a comprehensive study of convective flow over the obstacles (i.e., heaters and freezer) inside the cavity filled with Cu–water nanofluid-saturated porous medium is made. The flow is induced due to heated vertical walls and a cooled top wall, as well as partial attachment of obstacles with the bottom wall. A non-Darcy model that includes Darcy and Brinkman terms has been adopted. The coupled governing equations are solved numerically by the finite element method using the penalty approach. The influence of different controlling parameters, Rayleigh number (Ra), nanoparticle volume fraction (), Darcy number (Da), Prandtl number (Pr), aspect ratio (Ar ), and porosity (ε) on the dynamics of flow and heat transfer rate have been addressed. The flow dynamics as well as heat transfer rate have been analyzed with help of streamfunction and temperature contours. Results show that the flow structure (i.e. streamlines) is controlled by nipple shape bicellular structure and the velocity profile includes the point of inflection. The variation of the Nusselt number as a function of the volume fraction of the nanoparticle is almost linear. In contrast to pure fluid, at 10% volume fraction of nanoparticle, the enhancement in heat transfer rate is found up to 30%.

Thermal behavior of a conical antenna cooled with nanofluid saturated porous media: effects of the cavity’s inclination and aspect ratio

Purpose The aim of this work is to determine the average surface temperature of a conical antenna. Its cooling is ensured by means of a nanofluid-saturated porous structure. The volume fraction of the H2O–Cu nanofluid ranges between 0% (pure water) and 5%, whereas the ratio between the thermal conductivity of the used porous materials and that of water (fluid base) varies in the wide 4–41.2 range. The antenna is contained in a coaxial conical closed cavity with a variable distance between the cones, leading to an aspect ratio varying between 0.2 and 0.6. The axis of the assembly is also inclined with respect to the gravity field by an angle varying between 0° (a vertical axis with top of the cone oriented upwards) and 180° (a vertical axis with top of the cone oriented downwards). Design/methodology/approach Simulations have been done by means of the volume control method based on the SIMPLE algorithm. Findings Results of the numerical approach show that the cavity’s aspect ratio and inclination with respect to the gravity field significantly affect the thermal behavior of the active cone. Otherwise, the work confirms that the Maxwell and Brinkman models used to determine the nanofluid’s effective thermal conductivity and viscosity, respectively, are adapted to the considered assembly. Originality/value A new correlation is proposed, allowing the determination of the average surface temperature of the active cone and its correct thermal sizing. This correlation could be used in various engineering fields, including electronics, examined in the present study.

Heat transfer enhancement in a nanofluid saturated porous medium with cross diffusion and nonequilibrium: A regression approach

The work has been made to analyze the influence of local thermal nonequilibrium through a stretching surface in a laminar transient flow of nanofluid with the inclusion of cross diffusion. Brownian motion and thermophoresis are taken into account for the modeling of nanofluid. To describe the departure from thermal equilibrium, three temperature model has been assumed. The governing transport equations are transformed using similarity analysis and they are evaluated by Runge–Kutta–Fehlberg with shooting technique. The present results are compared with the previously published reports and they met agreement. The obtained numeric values of the boundary layer flow characteristics such as velocity, thermal, and mass transfer among the phases are illustrated graphically for different combinations of the interphase parameters. In addition, the regression study on heat and mass transfer with prominent parameters has been made to provide a highly accurate rendition and can be accessibly used in engineering problems.

Experimental study on the influence of a conical cavity’s inclination angle and aspect ratio on thermal behavior of a cone cooled with nanofluid saturated porous media

ABSTRACT An experimental setup has been developed to measure the thermal state of a conical antenna cooled by means of porous media saturated with water-based copper nanofluid. Thermal conductivity of the used porous materials varies between 4 and 41.2 times that of the water which constitutes the base fluid of the nanofluid whose volume fraction ranges from 0% (pure water) to 5%. The antenna is placed in the center of a coaxial concentric cavity of the same shape. Aspect ratio of the enclosure varies between 0.2 and 0.6. Its base is inclined with respect to the horizontal plane with an angle ranging between 0° and 180° corresponding to a horizontal circular base with the top of the cone oriented upwards and downwards, respectively. Measurements validate the calculations obtained in a recent numerical approach based on the finite volume method. They confirm that the Maxwell and Brinkman models remain valid for the ranges of the Rayleigh number considered here and Water based-Copper nanofluid volume fraction (0–5%). This work also confirms the effectiveness of porous materials saturated with nanofluids to ensure the thermoregulation of electronic equipment dissipating a large amount of thermal power.

MHD effects on natural convection in a U-shaped enclosure filled with nanofluid-saturated porous media with two baffles

The present work examines numerically the heat transfer and the buoyancy-driven flow within a U–shaped baffled enclosure filled with a nanofluid-saturated porous medium in the presence of an inclined magnetic field using a finite element scheme. The enclosure bottom wall is heated sinusoidally while the two baffles and the inner walls are maintained at a constant cold temperature. The rest walls of the enclosure are kept adiabatic. The parameters under investigation are Hartmann number (Ha), volume fraction (φ), Darcy number (Da), Rayleigh number (Ra), nanoparticles aspect ratio (AR), and the angle of applied magnetic field (γ). The results are crucial and illustrate that increasing the values of Ra, Da and the nanoparticles volume fraction enhances the heat transfer while the Hartmann number inversely affects the heat transfer augmentation. Moreover, the average Nusselt number (Nuave) increases by increasing the enclosure aspect ratio. For the geometry under consideration and for a better heat transfer rate, it is recommended to choose an AR = 0.6 at Ha = 0 with a 0.1 vol fraction.

Effect of Local Thermal Nonequilibrium on the Stability of the Flow in a Vertical Channel Filled With Nanofluid Saturated Porous Medium

Abstract The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal nonequilibrium state of the fluid, particle, and solid–matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy–Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle, and solid–matrix phases separately, for the temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal nonequilibrium parameters. It is noticed that the influence of local thermal nonequilibrium (LTNE) parameters on convective instability is significant.

Thermovibrational instability in a nanofluid porous medium

Thermovibrational convection in a water based metallic (Cu-water and Ag-water) or metallic oxide (Al2O3-water and TiO2-water) nanofluid saturated porous medium is addressed incorporating the Brinkman boundary correction. The nanofluid behaves more like a fluid rather than a conventional solid–fluid mixture and is studied through Khanafer–Vafai–Lightstone (KVL) model. A linear stability analysis is carried out through the Floquet theory to find the instability thresholds for convection onset in terms of critical Rayleigh number and critical wavenumber. The results corresponding to synchronous as well as subharmonic modes are obtained for the Darcy and Brinkman regimes. A rise in particle concentration is found to cause stabilizing response in general. However, it leaves an opposite effect in the Brinkman regime when the medium is filled with metallic nanofluid and is heated from above. Under this situation, the use of oblate-spheroidal particles in achieving optimal convective heat transfer enhancement is highlighted.

Effect of partial wall motion on MHD mixed convection heat transfer undergoing in a porous cavity filled with Cu–water nanofluid with a centrally mounted heat source

The Magneto-hydrodynamics (MHD) convective heat transfer process in a partially driven cavity (PDC) containing a centrally mounted heat source is focused in the present study. The cavity is filled with Cu–water nanofluid saturated porous medium. Heated cavity fluid is cooled through the upper half of the two sidewalls. These cold sidewalls are allowed to move in upward direction at the same velocity. The horizontal walls and lower part of the sidewalls are insulated. The cavity subjected to an externally imposed uniform magnetic field. The flow structures and mixed convection heat transfer characteristics are analyzed numerically utilizing developed CFD code adopting FVM and SIMPLE algorithm. The thermo-fluid phenomena are analyzed under a range of governing parameters like Richardson number (Ri), Hartmann number (Ha), concentrations of nanoparticles (ϕ). The results reflect that the heat transfer characteristics of the PDC are greatly influenced by all of the above parameters. Heat transfer is enhanced significantly at the higher Ri and higher volume fraction.

Bioconvection in a Convectional Nanofluid Flow Containing Gyrotactic Microorganisms over an Isothermal Vertical Cone Embedded in a Porous Surface with Chemical Reactive Species

In this examination, a mathematical model is developed for Darcy free convection with reference to an isothermal vertical cone along with fixed apex half angle, pointing downward in a nanofluid-saturated porous medium. The aim of this methodology is to offer another sort of primary fluid containing nanoparticles and gyrotactic microorganism’s consistence of permeable medium, chemical reaction alongside convective boundary circumstance. The model presents design rules for improvement of imperative fabrication of fertilizer and polymer substance. The present model includes the gyrotactic microorganisms alongside nanoparticles, and cone is dependent on concentration of nanoparticles as well as density of motile microorganisms. Two important impacts Brownian motion as well as thermophoresis are also included in the present model for nanofluids. Reduced system of nonlinear differential equations is derived from governing partial differential of the present flow by using usual transformations along with Oberbeck–Boussinesq approximation. After that, this reduced system is solved numerically with the use of fifth-order Runge–Kutta method in conjunction with the shooting technique. Relevant outcomes are exhibited graphically and talked about quantitatively as for variety in the flow controlling parameters related to the present analysis. Mainly, the observations are bioconvection parameters will in general improve the concentration of the rescaled density of microorganisms and nanoparticles volume fraction and dimensionless motile microorganisms reduce with strong chemical reactions.