Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation

The heat transfer phenomena and oscillatory flow of an electrically conducting viscous nanofluid (NF) in a channel with porous walls and saturated porous media exposed to the thermal radiation are studied. The nanoparticles (NPs) Fe₃O₄ and Al₂O₃ are taken with water as base fluid along with nonuniform temperature and velocity slip at the wall of channel (y′ = 0). The basic laws of momentum and energy conservation are converted into the dimensionless system of the partial differential equations (PDEs) using similarity variables. Closed‐form solutions of these coupled PDEs are constructed for all values of time by taking the oscillatory pressure gradient. The physical insight of involved parameters on the fluid velocity, temperature profile, heat transfer rate, and surface friction is studied and analyzed graphically. It is noted from this study that the fluid velocity shows a decreasing behavior with the volume fraction of NPs. Furthermore, the amplitude of the oscillatory motion in case of skin friction decreases for a large magnetic field.     

Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field

ABSTRACT

In this work, the effect of a variable spatial magnetic field on ferro-nanofluid flow and heat transfer in a double-sided lid-driven enclosure with a sinusoidal hot wall is investigated. The working fluid is a mixture of iron oxide (Fe₃O₄) nanoparticles and water and is referred to as a ferro-nanofluid. The control volume-based finite element method (CVFEM) is used to solve the governing equations in the stream function–vorticity formulation. In deriving the governing equations for this investigation, the effect of both ferro-hydrodynamics and magneto-hydrodynamics is taken into account. The numerical calculations are performed for different governing parameters namely; the Reynolds number, nanoparticle volume fraction, magnetic number (arising from Ferrohydrodynamics (FHD) consideration), and the Hartmann number (arising from Magnetohydrodynamics (MHD) consideration). The results show that an enhancement in heat transfer has a direct relationship with the Reynolds number and the Hartmann number, but it has an inverse relationship with the magnetic number. Also, it can be concluded that the Nusselt number increases with the increase of the nanoparticle volume fraction, magnetic number, and the Reynolds number while the opposite trend is observed for the Hartmann number.     

Heat transfer in dusty fluid with suspended hybrid nanoparticles over a melting surface

The melting effect with the magnetic field performs a significant role in various manufacturing and industrial applications, such as welding, casting, magma-solidification, nuclear engineering, and so forth. The present study focuses on the impact of the melting effect and magnetic field with inhomogeneous heat origination and sink. The formulation of the mathematical model is done by considering fluid with hybrid nanoparticles and dust particles in two different phases. We have considered Fe₂SO₄ and Cu as nanoparticles dispersed in the base fluid water along with suspended dust particles. The set of partial differential equations is reduced by using apt similarity variables and boundary conditions to obtain ordinary differential equations. The numerical solution is approximated using MATLAB-bvp4c adopting the shooting technique. The impact of numerous pertinent physical parameters on the velocity and thermal profiles is plotted and deliberated. Furthermore, the rate of heat flow and friction factor is also tabulated and visualized through the graphs. Streamlines are also drawn to know the behavior of the fluid flow. The rise in values of M_E quickly increases the velocity of the fluid motion but declines the thermal gradient and thickness of its related boundary layer. Also, inclining values of Pr enhance the thermal profile due to the impact of melting.     

Hybrid nanofluid flow over a stretched cylinder with the impact of homogeneous–heterogeneous reactions and Cattaneo–Christov heat flux: Series solution and numerical simulation

The Catteno–Christov heat flux plays a dynamic role in flow of heat enhancement in various manufacturing, industrial, and engineering applications. This present work focuses on the influence of Catteno–Christov heat flux model on Darcy–Forchheimer flow of a hybrid nanofluid placed in a porous medium. The formulation of the mathematical model is done by considering a fluid with two different nanoparticles Al₂O₃ and Cu dispersed in the water as the base fluid. The set of partial differntial equations is reduced by using similarity variables and boundary conditions to obtain ordinary differntial equations. The coupled nonlinear governing differential equations are solved using Runge–Kutta fourth–fifth order (RKF-45). The impact of numerous dimensionless parameters on the velocity, thermal, and concentration profiles are plotted and studied. Furthermore, the coefficient of skin friction for the relevant parameters are analysed through graphs. Result reveals that, increase in the porosity parameter declines the velocity gradient and shoots up the thermal and concentration gradients. Inclination in magnetic parameter declines velocity and concentration profiles due to the Lorentz force. Enhancement in the thermal relaxation parameter declines the thermal profile. Inclination in homogeneous-heterogeneous reaction parameters declines the mass transfer rate. Also, the well-known differential transform method is used for the validity of RKF-45 method and an impressive agreement is noticed between the results of RKF-45 and DTM.     

Effects of Newtonian heating and thermal radiation on micropolar ferrofluid flow past a stretching surface: Spectral quasi‐linearization method

This study article addressesthe flow and heat transfer characteristics of a magnetite Fe₃O₄ micropolar ferrofluid flow past a stretching sheet. For practical interest, thermal radiation, Newtonian heating, and a heat source or sink are considered in this investigation. A useful Tiwari‐Das nanofluid model is considered to analyze the microstructure and inertial characteristics of the water‐based nanofluids containing iron oxide. The dimensionless nonlinear ordinary differential equations are solved by employing suitable similarity variables. The resulting nonlinear system is solved by the spectral quasi‐linearization method. The effects of different nondimensional parameters on various profiles are shown graphically and explored in detail. It is found that the micropolar ferrofluid exhibits a higher energy distribution than that of a classical micropolar fluid. Compared to the classical micropolar liquid, local skin‐friction is more significant for the micropolar magnetite ferrofluid. In the presence of Newtonian heating, the thermal behavior of the micropolar nanofluid is remarkably better than that of the classical micropolar fluid.     

Numerical investigation of nonuniform transverse magnetic field effects on the flow and heat transfer of magnetic nanofluid in a sintered porous channel

In this paper, fluid flow and convective heat transfer of a ferrofluid (water and 4 vol% Fe₃O₄) in sintered Aluminum porous channel, which is subjected to a nonuniform transverse magnetic field have been studied. The numerical simulations supposed an ordinary cubic and staggered arrangement organized by uniformly sized particles with a small contact area for the porous media and constant heat flux at the surface of the microchannel. A wire, in which the electric current passes creates a nonuniform magnetic field, which is perpendicular to the flow direction. To do this simulation, the control volume technique and the two‐phase mixture model have been employed. The results show that the obtained local heat transfer coefficient on the channel surface increased with increasing mass flow rate and decreased slightly along the axial direction. Moreover, exerting the above‐mentioned magnetic field increases the Nusselt number that enhances the heat transfer rate while it has no effect on the pressure drop along the channel.     

Catalytic transfer hydrogenation of furfural to furfuryl alcohol over Fe3O4 modified Ru/Carbon nanotubes catalysts

In this study, magnetic Fe₃O₄ modified Ru/Carbon nanotubes (CNTs) catalysts were used to achieve the catalytic transfer hydrogenation of furfural (FF) to furfuryl alcohol (FFA), with alcohols as the solvent and hydrogen donors. According to the result of the catalyst characterization, Fe₃O₄ promoted the formation of Ru⁰ species. The effects of Fe₃O₄ loading and different hydrogen donors on the catalytic transfer hydrogenation of FF were tested, and the reaction parameters and catalyst stability were also analyzed. It is found that Fe₃O₄ effectively enhanced the activity of Ru/CNTs in catalytic transfer hydrogenation of FF, the catalytic activity was optimized at the Fe₃O₄ loading of 5 wt%, and the optimal hydrogen donor was i-propanol. Moreover, the Ru–Fe₃O₄/CNTs could be easily collected for further use and possessed excellent stability. The mechanism of the catalytic transfer hydrogenation of FF using Ru–Fe₃O₄/CNTs was discussed, and the corresponding catalyst activity groups included metal Ru sites and RuO_x-Fe₃O₄ Lewis acid sites, which account for the excellent catalytic activity of transfer hydrogenation.     

The analogy of nanoparticle shapes on the theory of convective heat transfer of Au–Fe3O4 Casson hybrid nanofluid

In recent times, Au nanoparticles have been commonly used for delivering the drug especially in the case of hypothermia of tumors, but low absorption of IR light does not solve destruction of tumor cells. However, nanoparticles such as Fe₃O₄ coated with Au could be used to deliver the drug to a specific spot due to applied external magnetic field. Due to these applications, boundary layer approximation is invoked to simplify the mathematical model. This paper presents the nanoparticle shape analysis and heat transfer features of the Au–Fe₃O₄–blood hybrid nanofluid flowing past a stretching surface on a magnetohydrodynamic medium. Numerical solutions of nonlinear differential equations are obtained by RKF-45 method with the help of shooting technique. The behavior of emerging parameters is described graphically for velocity and temperature profiles. It is found that the blade-shaped Au and Fe₃O₄ nanoparticles have better thermal conductance than brick, sphere, cylinder, needle, and platelet shapes. It is also observed that the Lorentz force generated due to magnetic field helps in controlling the flow and enhance the thermal conductivity of hybrid nanofluid.     

Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme

Key developments in the field of nanotechnology have drawn the attention of many scholars toward the interaction of nanoparticles due to their capturing applications in solar energy systems and thermal engineering. Larger consumption of energy posed a challenge for thermal science, so thermal engineering is trying to solve this issue by increasing the thermal conductivity of the fluid. The thermal conductivity of conventional fluid is increased by incorporating the nanoparticles in the base fluid. Keeping this in mind, the present research project addresses the utilization of nanoparticles in a steady three-dimensional rotating flow of magnetohydrodynamic water-based hybrid fluid over an extending sheet. Nanoparticles of aluminum oxide (Al₂O₃) and silver (Ag) are being used with water (H₂O) as base fluid. The velocity of nanoparticles is being captured under the influence of an inclined magnetic field and the transport of heat is scrutinized through thermal radiation. The physical model generates partial differential equations and then transported into an equivalent set of a nonlinear ordinary differential equations. The purpose of numerical computation is made by the Lobatto IIIA method, which is a type of Matlab scheme bvp4c and based on the finite difference method. Geometry of velocity profile is explained with different parameters in presence and absence of magnetic field and energy of hybrid nanofluid is explained under the influence of the inclined and perpendicular magnetic field. Gradual increment in ϑ both f and g profiles because strengthen the magnetic field results lower velocity. An increment in nanoparticle concentration of Al₂O₃ and Ag gives a larger magnitude of velocity. The rotation parameter shows the rotation of nanoparticles; due to these rotations both linear and angular components of velocity increase in the presence and absence of a magnetic effect.     

Influence of nanofluids on parallel flow square microchannel heat exchanger performance

The effects of using various types of nanofluids and Reynolds numbers on heat transfer and fluid flow characteristics in a square shaped microchannel heat exchanger (MCHE) is numerically investigated in this study. The performance of an aluminum MCHE with four different types of nanofluids (aluminum oxide (Al₂O₃), silicon dioxide (SiO₂), silver (Ag), and titanium dioxide (TiO₂)), with three different nanoparticle volume fractions of 2%, 5% and 10% using water as base fluid is comprehensively analyzed. The three-dimensional steady, laminar developing flow and conjugate heat transfer governing equations of a balanced MCHE are solved using the finite volume method. The MCHE performance is evaluated in terms of temperature profile, heat transfer rate, heat transfer coefficient, pressure drop, wall shear stress pumping power, effectiveness, and overall performance index. The results reveal that nanofluids can enhance the thermal properties and performance of the heat exchanger while having a slight increase in pressure drop. It was also found that increasing the Reynolds number causes the pumping power to increase and the effectiveness to decrease.     

Mixed convection hybrid nanofluids flow of MWCNTs–Al2O3/engine oil over a spinning cone with variable viscosity and thermal conductivity

This work analyzed the effects of variable viscosity and thermal conductivity, with mixed convection, thermal radiation and viscous dissipation effects, on multiwalled carbon nanotubes (MWCNTs)–aluminum oxide (Al₂O₃)/engine oil hybrid nanofluid flow due to a vertically inverted spinning cone embedded in a porous medium. Using suitable similarity transformation, the boundary layer fluid flow governing equations are transformed into dimensionless systems of coupled nonlinear ordinary differential equations. Then, the solutions are obtained numerically employing the spectral relaxation method. The influences of involved parameters are examined, and the results are presented with graphs and tables. The obtained results disclose that both the tangential and azimuthal skin friction coefficients increase with increasing values of temperature-dependent viscosity and mixed convection parameters. The local heat transfer rate reduces with increasing values of the Eckert number and variable thermal conductivity parameter, whereas it enhances with greater values of the thermal radiation parameter. Generally, hybrid nanofluids of (MWCNTs–Al₂O₃)/engine oil show better flow distributions with good stability of thermal properties than MWCNTs/engine oil and Al₂O₃/engine oil mono-nanofluids.     

Heat and mass transfer characteristics of radiative hybrid nanofluid flow over a stretching sheet with chemical reaction

Unsteady magnetohydrodynamic heat and mass transfer analysis of hybrid nanoliquid flow over a stretching surface with chemical reaction, suction, slip effects, and thermal radiation is analyzed in this study. A combination of alumina (Al₂O₃) and titanium oxide (TiO₂) nanoparticles are taken as hybrid nanoparticles and water is considered as the basefluid. Using the similarity transformation method, the governing equations are changed into a system of ordinary differential equations. These equations together with boundary conditions are numerically evaluated by using the Finite element method. The influence of various pertinent parameters on the profiles of fluids concentration, temperature, and velocity is calculated and the outcomes are plotted through graphs. The values of nondimensional rates of heat transfer, mass transfer, and velocity are also analyzed and the results are depicted in tables. Temperature sketches of hybrid nanoliquid intensified in both the steady and unsteady cases as the volume fraction of both nanoparticles rises.     

Nonlinear thermal radiation on MHD tangential hyperbolic hybrid nanofluid over a stretching wedge with convective boundary condition

In this study, two distinct nanoparticles: aluminum oxide (Al₂O₃) and copper (Cu) are chosen as nanomaterials to examine the effects of nonlinear electrically conducting magnetohydrodynamic radiation on the flow of tangential hyperbolic hybrid nanofluid across a nonlinearly stretched sheet with convective boundary conditions. The equations that regulate fluid flow are represented as partial differential equations. These equations are reduced to their equivalent ordinary differential equations, which are solved using the homotopy analysis approach with the help of similarity variables. The effect of essential physical factors on fluid velocity, temperature, skin friction coefficient, and local Nusselt number is investigated and discussed. Results ascertain that the heat transfer rate of Cu/H₂O nanofluid becomes high when equated to Cu–Al₂O₃/H₂O nanofluid. Furthermore, the temperature distribution enhances with the rise in solid volume fraction while it diminishes with improved magnetic field for both nanofluid and hybrid nanofluid.     

Hydrothermal Behavior of a Ferrofluid in a Corrugated Channel in the Presence of a Magnetic Field

In this paper, results of applying a non‐uniform magnetic field on a dilute ferrofluid (water and 3% vol. Fe₃O₄) flow in a corrugated channel under a constant heat flux boundary condition have been reported. The thermal behavior of the flow is investigated numerically using a two‐phase mixture model and control volume technique. It is concluded that using a magnetic field with a negative gradient on a nanofluid flow in corrugated channels can be proposed as a suitable method to achieve higher heat transfer performance and augment the heat transfer coefficient and also reduces the wall temperature. This method can lead to the design of more compact heat exchangers. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 80–92, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21060     

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al₂O₃), are suspended in the base fluid H₂O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge‐Kutta‐Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu‐Al₂O₃/water hybrid nanofluids. There is an increase in hybrid nanofluid velocity profile with mounting values of $\lambda$, and the Cu‐water nanofluid converges to the boundary more quickly than the hybrid nanofluid due to the occurrence of variable viscosity. The results concluded that the Nusselt number of the viscous fluid is lower than that of the nanofluid and hence the hybrid nanofluid (ie, heat transfer rate: normal fluid < nanofluid < hybrid nanofluid). The outcomes of present investigations are in close agreement with the viscous fluid as a particular case.     

Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet

We consider the steady state, viscous, incompressible two-dimensional magneto hydrodynamic flow of an electrically conducting power law fluid over a vertical stretching sheet. The stretching of the surface velocity and the prescribed surface temperature are assumed to vary linearly with the distance from the slit. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation. The transformed boundary layer equations are solved numerically by Keller-Box method for several sets of values of the parameters governing the flow and heat transfer. The flow and heat transfer characteristics are analysed and discussed for different values of the parameters. We observe that the local skin friction coefficient and the local Nusselt number decrease as the magnetic parameter Mn increase for fixed value of the buoyancy parameter λ. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Radiative CNT-based hybrid magneto-nanoliquid flow over an extending curved surface with slippage and convective heating

This study concentrates on the hydrothermal prominence of a mixed convective flow of a hybrid nanoliquid over a convectively heated extending curved surface under the influence of a uniform transverse magnetic field. Two types of carbon nanotubes (CNTs), namely single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), and magnetite nanoparticles are dispersed in the host liquid (water) to simulate the hybrid nanoliquid flow model. First- and second-order velocity slip conditions and nonlinear radiative heat flux are incorporated in this model. First, the system of governing partial differential equations is changed into nonlinear ordinary differential equations through the utilization of appropriate transformations and computed numerically via MATLAB built-in function bvp4c based on the three-stage Lobatto IIIA technique. The consequences of physical and geometrical parameters pertinent to this analysis on the dimensionless physical quantities of interest are deliberated using requisite graphs and tables. Our simulation communicates that the first-order velocity slip parameter decreases the velocity profile, whereas the second-order velocity slip parameter is found to be augmented. The suspension of CNTs in the magnetite nanoliquid improves the local surface drag force but diminishes the local heat flux. Moreover, it is examined that SWCNTs have greater impacts than MWCNTs.     

Performance analysis of hybrid/single nanofluids on augmentation of heat transport in lid-driven undulated cavity

This numerical study reveals the heat transfer performance of hybrid/single nanofluids inside a lid-driven sinusoidal trapezoidal-shaped enclosure. The right and left inclined surfaces of the trapezium have been considered as insulated, whereas the bottom sinusoidal wavy and the flat top surfaces of the enclosure as hot and cold, respectively. The governing partial differential equations of fluid's velocity and temperature have been resolved by applying the finite element method. The implications of Prandtl number (4.2-6.2), Richardson number (0.1-10.0), undulation number (0-3), nanoparticles volume fraction (0%-3%), and nanofluid/base fluid (water, water–copper (Cu), water–Cu–carbon nanotube, water–Cu–copper oxide (CuO), water–Cu–TiO₂, and water–Cu–Al₂O₃) on the velocity and temperature profiles have been studied. Simulated findings have been represented by means of streamlines, isothermal lines, and average Nusselt number of above-mentioned hybrid nanofluids for varying the governing parameters. The comparison of heat transfer rates using hybrid nanofluids and pure water has been also shown. The heat transfer rate is increased about 15% for varying Richardson number from 0.1 to 10.0. Blending of two nanoparticles suspension in base fluid has a higher heat transfer rate—approximately 5% than a mononanoparticle. Moreover, a higher average Nusselt number is obtained by 14.7% using the wavy surface than the flat surface of the enclosure. Thus, this study showed that applying hybrid nanofluid may be beneficial to obtain expected thermal performance.     

Heat transfer and nanofluid flow characteristics through a circular tube fitted with helical tape inserts

Numerical investigations are performed using finite volume method to study laminar convective heat transfer and nanofluids flows through a circular tube fitted with helical tape insert. The wall of tube was subjected to a uniform heat flux boundary condition. The continuity, momentum and energy equations are discretized and the SIMPLE algorithm scheme is applied to link the pressure and velocity fields inside the domain for plain tube. Four different twist ratios of 1.95–4.89, two different types of nanoparticles, Al₂O₃ and SiO₂ with different nanoparticle shapes of spherical, cylindrical and platelets, and 0.5–2.0% volume fraction in base fluid (water) and nanoparticle diameter in the range of 20–50 nm were used to identify their effect on the heat transfer and fluid flow characteristics through a circular tube fitted with helical tape insert geometries. The results indicate that the four types of nanofluid achieved higher Nusselt number than pure water. Nanofluid with Al₂O₃ particle achieved the highest Nusselt number. For all the cases studied, the Nusselt number increased with the increase of Reynolds number and with the decrease of twist ratio of helical tape insert.