Solid Volume Fraction Of Nanoparticles Research Articles

Entropy generation analysis of unsteady MHD nanofluid flow in a porous pipe

This article presents a numerical investigation into the entropy production of nanofluids flowing through a porous medium in a permeable conduit, focusing on water-based solutions containing Titanium Carbide (TiC) and Silicon Carbide (SiC) nanoparticles. These nanoparticles are selected for their heat transfer properties. The flow system's governing equations are developed and solved using the Runge-Kutta-Fehlberg method. The study examines the influence of key nondimensional parameters, including the solid volume fraction of nanoparticles, radiation parameters, and Reynolds number, on temperature, velocity profiles, and entropy generation. The results show that Silicon Carbide-water nanofluids perform efficiently in terms of heat transfer and entropy minimization. Additionally, Silicon Carbide exhibits low skin friction at the pipe wall, with this effect increasing as the solid volume percentage of nanoparticles rises. The study also indicates that irreversibility due to heat transfer becomes more significant near the pipe wall as the solid volume fraction decreases and increases with higher radiation parameters and Reynolds number. These findings are presented graphically and in tabular form to illustrate the physical significance of the problem.

Influence of space conjugate temperature varying non-uniform heat sink/source on hydromagnetic slip water-EG (50:50) nanofluid

Significant cooling is an essential requirement in the field of aeronautical and bio-medical engineering, nuclear reactor system, solar collectors, and in development of electronic chips etc. Involving rotating conical geometries. In view of this, flow and heat transfer over conical geometries subject to different constraints of motion are highly needed. Implementation of magnetic field subject to flow pattern controls the fluid motion thereby imparting better cooling. Consideration of nanofluid instead of regular fluid yields prominent cooling of the associated surface. Such relevance has motivated the authors to work on magnetohydrodynamics and heat transfer investigation of water-EG (50:50) mixture based Al2O3 and Fe3O4 past heated and rotating down-pointing upright cone subject to impact of space and temperature varying non-uniform heat source or sink. Numerical solution of dimensionless governing equations is accomplished by implementing Runge-Kutta method. The findings indicate that swirl and axial velocities peter out with rise in magnetic parameter while both exhibit opposite impact in response to slip parameter. Temperature profiles upgrade due to amplification of space and temperature dependent parameters. Skin friction and heat transportation upsurge with growth of solid volume fraction of nanoparticle.

Thermal management and power generation characteristics in a bifurcating channel by using a piezo-embedded inclined elastic fin assembly during turbulent forced convection of ternary nanofluid

Numerous engineering systems use piezoelectric energy harvesters (PE-EHs), which have several benefits including low cost, simplicity, better power density, and ease of installation. They can be used in different applications for energy harvesting and different external sources such as wind and vortex induced vibrations due to fluid–structure interaction can be utilized. This study uses a unique elastic fin PE/EH assembly for power generation, thermal management, and flow control in a bifurcating channel. Performance of the system is improved by using ternary nanofluid in the channel cooling system. Galerkin weighted residual FEM with ALE is used as the solution method. The convective heat transfer performance and power generation by the EH device are investigated in relation to the varying following parameters: Reynolds number (Re between 10000 and 30000), PE-EH inclination (γ between 0 and 60), fin horizontal location (xf between −H and H), and nanoparticle loading in the base fluid (ϕ between 0 and 0.03). The vortex size and distribution near the junction are significantly influenced by the fin inclination and horizontal location of the fin assembly within the bifurcating channel. When varying other parameters of interest, using nanofluid at the highest loading results in significant deflection of the fin assembly and power generation within the PE-EH. Enhancement factors (EFs) for power generation becomes 15.6 and 39.8 when cases of lowest and highest Re are compared with pure fluid and nanofluid while they are 2.93 and 3.38 for thermal performance improvements. Fin inclination of γ=30 is found as the optimum inclination for achieving the highest power from the assembly. Higher inclination of elastic fin/PE-EH assembly results in cooling performance deterioration while average Nu reduces by a factor of 2.94 by varying inclination from γ=30 to γ=60 with nanofluid. For power generation, effects of using nanofluid with varying inclination is significant and EF becomes 252 from γ=0 to γ=30. There are opposing tendencies for the device’s power generation and cooling performance enhancement when the fin’s horizontal placement is changed. EF for average Nu is 7.25 for varying fin location. As the loading of nanoparticle inside the base fluid increases, the average Nu and generated power exhibit non-linear rising characteristics. Polynomial type correlations are provided for the average Nu and power from the device by varying elastic fin assembly inclination and nanoparticle solid volume fraction. Potential of using hybrid nanofluid in PE-EH embedded thermo-fluid system is shown. The design, development, and optimization of self-sufficient power production systems that may be used to various thermo-fluid systems, such as electronic cooling and thermal control in a range of heat transfer devices, may benefit from the findings.

Melting and heat management of phase change material using smart ternary-hybrid coolant

This research investigates the effectiveness of using a smart ternary-hybrid nanofluid to enhance the melting rate and convective behavior of electrically conducting tin (Sn) in a rectangular enclosure under the influence of a uniform magnetic field. The enclosure has adiabatic vertical walls with hot and cold temperatures on the bottom and top walls. The finite element method (FEM) is used to solve the governing equations with appropriate boundary conditions using Galerkin's weighted residual approach. The study focuses on applying tin as the phase change material (PCM), with the highest temperature of 508 K, the lowest temperature of 503 K, and the melting interface temperature of 505 K. To enhance the heat transfer performance, tin-based ternary (graphene (G), silicon carbide (SiC), and nickel (Ni)) hybrid smart coolant is applied into the system. To investigate the mechanism of the melting and convective thermal transfer process, the results of the present study are reported with time for various values of the magnetic field (Ha) and solid concentration of ternary hybrid nanoparticle (ϕ). This study represents the streamlines, isothermal lines, melting interface, melting fraction, and heat transfer for the above-mentioned parameters. The results show that increasing the magnetic field reduces the rate of thermal transport by 38.96 % at t = 4000s. However, at a particular time of 2500s, increasing the solid volume fraction of nanoparticles enhances the melting fraction by approximately 8.34 %. Two regression equations are derived for the Nusselt number and melting fraction, with multiple response variables. This article improves understanding of natural convective heat transport during phase change processes for various coolants in different engineering applications.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Dual solutions of Darcy-Forchheimer radiative-convective magneto-nanofluid flow over an exponentially stretching/shrinking surface: Stability and entropy generation analysis

A numerical investigation was conducted to examine the existence of dual solutions over exponentially stretching or shrinking permeable surfaces. The study aimed to analyze the impact of thermal and second-order velocity slip on magnetohydrodynamic (MHD) mixed convective radiative nanofluid flow within a Darcy-Forchheimer porous medium while considering heat generation. Two distinct types of nanofluids, namely Cu-water and TiO 2/water, were employed in the investigation. To address the nonlinear partial differential equations (PDEs), similarity transformations were utilized to transform them into a system of ordinary differential equations (ODEs). The resulting coupled higher-order nonlinear ODEs were then solved using a MATLAB-based boundary value algorithm known as bvp4c. Two distinct solutions are observed within a restricted range of the stretching/shrinking parameter ξ ( ξ > ξ c ) and suction parameter S ( S > S c ), terminating respectively at ξ = ξ c or S = S c . The critical values are identified as ξ c = − 1.1952 ( Cu − water ) , − 0.9304 ( Ti O 2 − water ) and S c = 1.6437 ( Cu − water ) , 1.8900 ( Ti O 2 − water ) , maintaining the fixed values of the remaining physical parameters. Notably, the critical value for Cu-water is lower than that of TiO 2-water. Moreover, in both solution branches, the range of skin-friction coefficient and local Nusselt number for Cu-water surpasses that of TiO 2-water. An evaluation of the temporal stability of these solutions reveals that only the first solution remains stable. This is supported by the positivity of the smallest eigenvalues ( γ 1 > 0 ), indicating stability. Conversely, for the second solution, the smallest eigenvalues ( γ 1 < 0 ) are negative, signifying its instability. Also, Cu-water nanofluid exhibits higher fluid velocity and lower fluid temperature than TiO 2-water nanofluid for stable solutions and the opposite behavior for unstable solution branches. Significantly, within the initial solution branch, there is an escalation in velocity profiles attributed to the magnetic parameter, Grashof number, porous parameter, and first- and second-order velocity slip parameter. Conversely, a decrease is observed for the Forchheimer number, while the opposite holds true for the second solution branch. For both solution branches, the temperature profiles experience a reduction due to thermal slip and stretching/shrinking parameters, whereas enhancements are noted for thermal radiation and heat generation parameters. Furthermore, an increase in the suction parameter leads to elevated skin friction coefficient and local Nusselt number in the first stable solution, thereby promptly improving heat transfer efficiency. Moreover, improvements in entropy generation arise from factors such as thermal radiation, magnetic field, and nanoparticle solid volume fraction, presenting opportunities to optimize heat transmission in cooling and heating systems.

THERMAL MANAGEMENT OF LITHIUM-ION BATTERY PACKS BY USING CORRUGATED CHANNELS WITH NANO-ENHANCED COOLING

In this study, a cooling system using corrugated cooling channels and Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;-Cu/water hybrid nanofluid is offered as the battery thermal management system (BTMS) for prismatic Li-ion batteries. A computational model built based on the finite element approach uses hybrid nanofluid at solid volume fractions ranging from 0 to 2&amp;#37; at various Reynolds numbers. The cold plates are corrugated and have a variety of square grooves positioned between prismatic Li-ion battery cells. The maximum temperature decreases as the volume fraction of solid nanoparticles and the number of corrugated cooling channels increases. When cases of using lowest and highest number of cooling channels are compared, maximum temperature reduction is found as 3.07 K when using water and 1.86 K when using Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;-Cu/water hybrid nanofluid (at the largest solid volume fraction). The number of square grooves in the cooling channels does not have any significant impact on the temperature drop when using nanofluid at the highest solid volume fraction.

Effect of External Flow Mode on Nanofluid Mixed Convective Cooling Inside a Multi-Vented Cavity

The purpose of this paper is to study numerically laminar mixed convection in a multiple vented cavity. This enclosure is continuously heated by constant temperature from the bottom wall, while the other boundaries are presumably thermally insulated. The imposed water-Al2O3 nanofluid flow is injected or sucked. The Influences of various control parameters, e.g.: Reynolds number Re, from 200 to 5000, the solid volume fraction of nanoparticles, , from 0to 7 %, and external flow mode (injection or suction) on the thermal patterns, the flow and the heat transfer within the enclosure are studied. Numerical results revealed that the presence of nanoparticles contributes to enhancement in the heat exchange and increase in the mean temperature within a cavity. Also, it was found that the heat performance and Applying the suction mode enhances the efficiency of cooling compared to the injection mode.

Mixed convective flow of nanofluid across exponential surface: A numerical assessment of the impact of Darcy-Forchheimer and nanoparticle aggregation

Improving heat transmission is a modern difficulty faced in a multitude of areas, incorporating but not limited to electronics, heat exchangers, biochemical reactors, and other similar areas. In their capacity as cutting-edge heat transfer fluids, nanofluids have the promise of becoming a useful instrument in the pursuit of greater energy transfer efficiency. So, the focus of this work is on how it is possible to enhance heat transmission by using nanofluids. Using a stretched exponentially accelerating surface, this analysis investigates the effect that nanoparticle aggregation with thermal radiation has on the nanofluid of mixed convective stagnation point flow through Darcy-Forchheimer porous surfaces. The aggregation of nanoparticles may be assessed using modified Krieger-Dougherty and Maxwell-Bruggeman models. By using the right similarity transformations, the controlling equations of this problem were turned into a numerical model that can be unraveled. Mathematica was used to resolve the issue numerically by using the shooting with Runge-Kutta (RK-IV) procedure. nanoparticles with base fluid under aggregation effect boost heat transfer performance. A diversity of parameter estimates, including the mixed convection, mass suction, solid volume fraction of nanoparticles, thermal radiation, and stretching, were used to provide solutions for heat transfer and lower skin friction coefficients, as well as velocity and temperature curves. In addition to the findings, there were graphs and tables with explanations. The increase in heat transfer rates was 6.7021% when the suction parameters were set between 2.0 to 2.5 with =0.01. When the amount of nanoparticles volume fraction went from 0% to 1% by volume, the ineptitude of heat transfer went by an average of 4.249%. Aggregation models are often favored over non-aggregation models due to their ability to provide more accurate velocity and skin fraction profiles. Because of their superior precision, they are often used in situations where accuracy is paramount.

Thermal analysis for hydromagnetic flow of Darcy-Forchheimer hybrid nanofluid with velocity and temperature slip effects: Scrutinization of stability and dual solutions

This article explores heat transfer characteristics of magnetohydrodynamics water-base silver (Ag) and iron oxide (Fe3O4) hybrid nanomaterials flow in a Darcy-Forchheimer porous medium induced by a stretching/shrinking surface with impacts of heat sink/source. Moreover, thermal radiation effects and the slip boundary conditions are also incorporated in the given problem. Governing partial differential equations (PDEs) are first altered into the ordinary differential equations (ODEs) using suitable similarity transformations. These achieved ODEs are solved by the well-known shooting technique in Maple software to get the required numerical solutions for the variation in different physical parameters. Here, the numerical findings show duality in solutions in case of stretching/shrinking parameter over different ranges of the comprised distinguished parameters. In this regard, the stability analysis is done and the first solution is found stable and physically acceptable, while the second one unstable and physically infeasible. Besides, the skin friction increases for the case of shrinking but it decreases for case of stretching parameter due to the greater impacts of the mass transfer parameter while the heat transfer phenomenon upsurges for the case of shrinking parameter. Moreover, the skin friction, and the heat transfer rise with variation of the suction parameters when the quantity of solid nanoparticles volume fraction is increased.

Numerical studies on the effects of melting heat transfer over quadratic radiative-magnetic hybrid nanofluid flow toward a porous shrinkable surface influenced by second-order slip velocity: Stability analysis and entropy generation

ABSTRACT The exclusive behavior of hybrid nanofluid flow and heat transmission properties through a porous medium toward a porous shrinking surface along with the external magnetic field, melting heat transfer, and second-order slip is investigated in this study. Moreover, the effects of a porous medium and quadratic thermal radiation are also incorporated. Molybdenum disulfide () and silicon dioxide () are hybridized as a very dilute homogenous mixture in the base fluid water (). Nonlinear partial differential equations with specified boundary constraints are transformed into a set of nonlinear ordinary differential equations using similarities transformation before being solved numerically with the help of default solver by bvp4c technique in MATLAB programming. This work is distinctive because it presents a novel hybrid nanofluid mathematical model with multiple (lower and upper) solution branches for the shrinking case within the defined ranges of the physical parameters. The temporal stability analysis shows that only one solution is stable as time evolves. The results are shown as velocity and temperature curves, skin friction coefficient, and local Nusselt number in the form of tabulated data and graphical structures. The heat for quadratic thermal radiation and melting heat transfer parameters contribute to the progress of thermal enhancement. Furthermore, by combining silicon oxide with a volume percentage of molybdenum disulfide, the flow is retarded, and heat transfer is enhanced. Entropy formation is considerably enhanced by quadratic thermal radiation and nanoparticle solid volume fraction parameters. In engineering, hybrid nanofluid has many uses, including in cosmetics, fabrics, paper plastics, automobiles, soaps, food packaging, food colorants, homes, cancer treatment, pharmaceuticals, ceramics, and paints.

Effects of Brownian Motions and Fractal Structure of Nanoparticles on Natural Convection

The study simulated heat transfer in alumina-water nanofluid in a natural convection flow and Rayleigh-Benard configuration considering the Brownian motions and fractal structure of the nanofluids. The simulations were based on a two-dimensional, Eulerian-Eulerian method. Many simulations have been performed to examine the effect of aspect ratio, heat flux, and para-meters related to the structure of the nanoclusters including size, fractal dimension, and volume fraction on the natural convective heat transfer coefficient. The comparison between the simulation results and the experimental data of heat transfer coefficient indicates a good agreement. The simulation results indicated that the enhancement of aspect ratio, heat flux, and fractal dimension increases the heat transfer coefficient. On the other hand, the reduction of nanoclusters and nanoparticle size decreased this coefficient. Moreover, the simulation results showed that in high heat transfer fluxes, the heat transfer coefficient first increases by increasing the nanoparticles solid volume fraction and then decreases. However, heat transfer coefficient decreased steadily with the increase in the nanoparticles solid volume fraction in low heat transfer fluxes. The results suggested that using the nanoparticles Brownian motion mechanism along with their fractal structure can be well-applied in natural-convection heat transfer modelling of nanofluids.

Adding tungsten oxide-MWCNTs-silica ternary nanopowders to water-ethylene glycol hybrid base fluid to investigate the rheological behavior of a created nanocolloid

Nanofluid rheology and heat transfer were lately the subjects of several research and investigations. In this paper, an experimental investigation was used to investigate the influence of temperature and volume fraction of nanoparticles on dynamic viscosity (µnf) of WO3-Multi-Walled Carbon Nanotubes (MWCNT)-SiO2/ water-EG ternary hybrid nanofluids. The impacts of these factors were also evaluated on mono nanofluids. The nanofluids were made using a two-step process at solid volume fractions of nanoparticles (SVF) of 0.2 to 0.6% and temperatures ranging from T = 20 to 60 °C. The zeta-potential test was used to measure the stability of nanofluids. According to the obtained results, the nanofluids have high qualities. A Brookfield viscometer was used to measure the µnf. All volume fractions of nanoparticles show that µnf decreases with temperature rise. At all temperatures, the µnf increases as the SVF increase, regardless of temperature. The results showed that in ternary nanofluids the highest amount of viscosity is related to the SVF = 0.6% and the T = 20 °C, which shows a value of 79.7% increase compared to the base fluid at the same temperature. Also, among mono nanofluids, the highest amounts of viscosity were observed for MWCNT at all temperatures and volume fractions. Finally, a mathematical model for calculating the µnf is established. The results of the proposed models were well correlated with laboratory data. The results of the established model show an acceptable correlation with experimental data.

Soret-Dufour Effects on The Waterbased Hybrid Nanofluid Flow with Nanoparticles of Alumina and Copper

The two-dimensional mathematical model ofwater-based hybrid nanofluid, where the nanoparticles of the model are alumina (Al2O3) and copper (Cu) is analyzed in this article. It describes the heat and mass transfer which are induced by concentration and temperature differences, respectively. The current mathematical model extended the works by implementing both directions of moving sheet in the boundary conditions: stretching and shrinking, and use the exponential variations of the sheet velocity, temperature, and concentration of the hybrid nanofluid at the sheet. The final numerical solutions can be obtained by implementing Matlab bvp4c, which involves the step of choosing the most reliable solution in an actual fluid situation. This selection technique on numerical solutions is known as stability analysis and only needs to apply when more than one numerical solution appears in the Matlab bvp4c program. Finally, the controlling parameters such as nanoparticle solid volume fraction, suction, shrinking/stretching, Soret and Dufour cause an increment or decrement in the flow, heat and mass transfer in the hybrid nanofluid. For the stable solution, fluid velocity becomes slower whereas temperature and concentration of the fluid increase when the percentage of Cu, as well as Al2O3, rises into the water. Moreover, in case of local Nusselt number and local Sherwood number it is proved that Soret effect is the opposite phenomenon of Dufour effect.

Electrothermal transport of water conveying copper, silver and alumina nanoparticles through a vertical wavy microchannel

This study emphasizes the significance of optimizing heat transmission, energy conversion, and thermal management in electronic devices, renewable energy systems, and emerging technologies like thermoelectric devices and energy storage systems. The aim is to enhance heat transfer efficiency for improved performance and lifespan of electronic equipment. The research utilizes a mathematical flow analysis to study a water-based ternary nanofluid’s flow and thermal characteristics in a vertical microfluidic channel driven by peristalsis and electroosmosis. The ternary-hybrid nanofluid (THNF), comprising copper, silver, and alumina nanoparticles dissolved in water, is examined considering induced magnetic fields. The study delves into fluid flow, heat absorption, and mixed convection, using Debye–Hückel, lubrication, and long wavelength approximations. Results show that THNF exhibits superior heat transmission compared to pure water. Increasing solid volume fraction of nanoparticles decreases THNF’s temperature. Induced magnetic fields impact the system. This research could influence thermal pipe heat sinks and bioengineered medical devices design.

Chemically reactive water-based carbon nanotubes flow saturated in Darcy-Forchheimer porous media coupled with entropy generation

This investigation described the features of magnetized water-based carbon nanotubes in slip flow saturated through Darcy-Forchheimer porous space. Cattaneo and Christov heat diffusion relation is used for the modeling of energy equation. Chemical reaction and heat generation influences are accounted. The entropy generation (EG) volumetric rate relation is modeled. The Fehlberg numerical scheme is implemented for the construction of the solutions. The results revealed that the EG is augmented in the presence of magnetic field and porosity parameter but decays against solid volume fraction of nanoparticles for both SWCNTs (single-wall carbon nanotubes) and MWCNTs (multi-wall carbon nanotubes).

A scientific report on Stokes' second problem for a transient nanofluid model with a heated boundary in the presence of a magnetic field

Stoke's second problem is a well-known classical boundary layer (BL) issue involving the time-dependent shear flow of viscous fluid about a flat porous plate in the magnetic field. This study has several applications, including chemical engineering, nanotechnology, heat conduction issues, and biological and medical sciences. A theoretical heat transfer (HT) analysis analyzes Stoke's second problem for an MHD time-dependent nanofluid flow through a porous plate. It produces a sinusoidal oscillation that is perpendicular to the flat plate. Copper (Cu) nanoparticles are suspended in water or ethylene glycol (EG), a base fluid. Modeling the fluid flow uses dimensional PDEs, which are then altered into dimensionless forms by adding the proper parameters. With no slip, the resulting non-dimensional PDEs are handled analytically by the Laplace transform approach (LTA). It is demonstrated that EG-Cu nanofluid has greater skin friction and higher HT rate than water-Cu nanofluid. Furthermore, skin friction is reduced by magnetic and porosity parameters, whereas the nanoparticle solid volume fraction and porosity parameters improve HT.

Natural Convection in Trapezoidal Cavity containing Hybrid Nanofluid

In this paper, a numerical study of natural convection in a trapezoidal cavity with left heated wall, right cold wall and filled with Cu – Al2 O3 and water hybrid nanofluid. The remaining walls of the cavity are kept at adiabatic. An enhancement in heat transfer is observed with the increase of three different parameters. Based upon the numerical predictions, the effect of Rayleigh number, inclination of the slopping wall, solid volume fraction of nanoparticles on flow and patterns as well tested. We found that acute slopping wall, high Rayleigh number and Cu – Al2 O3 nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle, effective thermal conductivity and viscosity as well as Rayleigh number.

Impact of Navier’s slip and MHD on laminar boundary layer flow with heat transfer for non-Newtonian nanofluid over a porous media

The current studies analytically summarize the impact of magnetohydrodynamic and thermal radiation on the non-Newtonian continuous uniform motion of viscid non-compressible nanofluid across a penetrable stretching/shrinking sheet, even though accomplish Navier's first and second order slips along mass transpiration. Blood-bearing silver and copper nanomaterials have distinct flow and heat transfer properties when exposed to heat. Silver (Ag) as well as copper (Cu) nanoparticles are assumed to be present in blood as the non-Newtonian liquid; this fluid serves as the base. We anticipate that the current study will be useful in fields including food, petrochemical products, and medicines, as well as blood circulation, and highly beneficial for patients who are dealing with blood clotting in the uterus, which may result in infertility or cancer, to evaluate the blood flow in the tube. Employing the similarity conversion technique, the ruling partial differential equations are modified into a couple of non-linear ordinary differential equations. Then the transformed ordinary differential equations are analytically solved with the Laplace transformation and expressed in terms of an incomplete gamma function. The current analytical results are compared to previous studies. It is addressed how several physical features such as magnetic field M, Navier’s first and second order slip, permeability, Prandtl number Pr, and radiation parameter affect non-dimensional velocity as well as temperature patterns through graphs. The results obtained reveal that there is an enhancement in the rate of heat transfer with the rise in nanoparticle volume fraction and radiation. The temperature distribution is also influenced by the presence of Prandtl numbers, radiation, solid volume fraction, permeability, and slip conditions. This shows that the solid volume fraction of nanoparticles can be used to control the behaviour of heat transfer and nanofluid flows.

Multiple solutions of Hiemenz flow of CNTs hybrid base [formula omitted] nanofluid and heat transfer over stretching/shrinking surface: Stability analysis

The purpose of the current article is to numerically and theoretically examine the flow of two-dimensional (2D) steady Hiemenz with the transfer of heat of carbon nanotubes (CNTs) hybrid base C2H6O2+H2O (Ethylene glycol + water) nanofluid across a linear shrinking/stretching surface. The equations of Navier–Stokes have been converted into equations of self-similar applying suitable transformations of similarity variables, and then numerically resolved using the three-stage Labatto-three-A formula. In addition, an endeavor is made to extend the behavior of asymptotic of the solution to massive stretching. The comparison between the found asymptotic solutions and previously reported numerical results is rather impressive. Observations indicate that equations of self-similar display double solutions within the restricted shrinking parameter range. There exists one solution for every case of stretching. In the first solution, the impacts of nanoparticle solid volume fraction and shrinking parameters on velocity and thermal fields exhibit an increasing trend. Consequently, the linear analysis of temporal stability has been performed to establish the most fundamentally viable option. The smallest eigenvalue sign determines whether a solution is unstable or stable for the purposes of stability analysis. The analysis of stability demonstrates that the first solution describing the primary flow is stable.