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The combined effects of diffusion-thermo and radiative absorption on free convective hydromagnetic heat-generating chemically reactive flow of Cu-water nanofluid past an instantaneously accelerated unlimited vertical plate nested in a porous medium are investigated. A comparative analysis is executed for both isothermal and ramped conditions. The set of transformed domain equations has been obtained using a closed form of the Laplace transform method with the help of the Heaviside step function. Graphical and tabular explanations are provided for the physical characteristics of several flow parameters affecting the problem. Graphs are generated using MATLAB computing software. Findings of the problem manifest that the diffusion-thermo parameter and the radiation absorption parameter intensify the velocity and fluid temperature in the entire fluid area. This augmentation is most prominent for copper nanoparticles. Concentration, temperature, and velocity profiles in the case of ramped conditions are less than in isothermal conditions. Furthermore, the ramped parameter amplifies the heat transfer rate while reversing the mass transfer rate. It is also established that the volume concentration of nanoparticles enhances the heat transfer rate. The present study is of great interest in numerous fields of industry and machine-building applications. [ABSTRACT FROM AUTHOR]

The thermal radiation and convective condition principles were working on specific functions like gas turbines, electrical fuel, renewable energy, projectiles, nuclear power plants, aerospace engineering, and thermal transportation. Considering the aforementioned functions, the present analysis inspected the stagnation point hybrid nanofluids movement over the rotating sphere on the behavior of viscous dissipation and thermal radiation. Silver and Ferrous nanoparticles including the host fluid water were held into affected the flow. The presence of convective boundary conditions is incorporated within the system. Applying appropriate correspondence factors, nonlinear governing equations were transformed with ordinary differential equations. This finite element method is applied to find the mathematical solutions to the boundary conditions and simplified equations. These outcomes convey to temperature was decreased about accelerated factor, although primary velocity was found into increased. The heat transfer was magnified by thermal Biot number, and that rate of development was greater about hybrid nanosuspension. The heat transport method was reduced by the Eckert number; also that reduction rate was similarly dull on hybrid. [ABSTRACT FROM AUTHOR]

Motivated by the thermal importance of feeble electrically conducting nanofluids and their flow controls in many industrial and engineering applications, the present scrutinization intended to evidence comprehensively the main electro-magneto-hydrothermal and mass aspects of convective non-homogeneous flows of alumina-based pure water nanofluids A l 2 O 3 - H 2 O over a horizontal flat surface of an electromagnetic actuator (i.e., Riga pattern, which is embedded geometrically in a Darcy-Forchheimer porous medium. Further, the present nanofluid flow model is formulated realistically under the umbrella of the renovated two-phase Buongiorno's approach with the inclusion of Brownian motion and thermophoresis diffusive phenomena, in which the vertical component of the nanoparticles' mass flux tend to vanish at the limiting contact surface due to its impermeability trend. For streamlining the technical handling of the present nanofluid flow problem, the governing partial differential equations (PDEs) are simplified mathematically by adopting the physical approximations of the boundary layer theory and then transformed into a differential structure of ordinary differential equations (ODEs) based on several similarity changes. Methodologically, the resulting nonlinear coupled ODEs are solved numerically via a validated differential quadrature procedure. Besides, the generated graphical demonstrations show that the nanofluid temperature is enhanced significantly with the porosity factors, the nanoparticles' loading, the convective heating strength, and the thermophoresis process. However, the porosity factors and the nanoparticles' loading exhibit a slowing-down impact on the nanofluid motion. Usefully, it is revealed from the obtained GDQM - NRT datasets that the nanoparticles' loading and the porosity factors express an important improvement in the strength of the surface viscous drag forces, whereas the induced electromagnetic field shows a reverse viscous frictional impact. [ABSTRACT FROM AUTHOR]

Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanoparticles dispersed in a variety of conventional fluids can change the flow and heat transmission properties of the fluids. The mathematical technique is used in this work to investigate the MHD water-based nanofluid flow via an upright cone. The heat and mass flux pattern is used in this mathematical model to examine MHD, viscous dissipation, radiation, chemical reactions and suction/injection processes. The finite difference approach was used to find the solution to the basic governing equations. A combination of nanofluids comprising nanoparticles including aluminum oxide (Al 2 O 3 ), silver (Ag), copper (Cu) and titanium dioxide (TiO 2 ) with a volume fraction of nanoparticles (0, 0.01, 0.02, 0.03, 0.04), viscous dissipation ( ϵ = 0.4 , 0.8 ), MHD (M = 0.5, 1.0), radiation (Rd = 0.4, 1.0, 2.0), chemical reaction ( λ = 0.2 , 2.0 ) and heat source/sink ( Δ = - 3 , - 2 , 0.5 , 1 ). The mathematical findings of velocity, temperature, concentration, skin friction, heat transfer rate as well as Sherwood number distributions are analyzed diagrammatically using non-dimensional flow parameters. It has been discovered that by increasing the value of the radiation parameter, velocity and temperature profiles enhance. The production of safe, high-quality products for consumers across the world depends on vertical cone mixers, from food to medicine, household cleansers to personal hygiene products. Every vertical cone mixer type we provide was especially developed to meet the demands of industry. As the mixer warms up on the slanted surface of the cone while vertical cone mixers are being utilized, the effectiveness of the grinding may be felt. The temperature is transferred along the cone's slant surface as a consequence of the mixture being mixed quickly and repeatedly. This study describes the heat transmission in these events and their parametric properties. The heated cone's temperature is then convective to its surroundings. [ABSTRACT FROM AUTHOR]

Present research focuses on nonsimilar analysis of the flow of a non‐Newtonian Carreau nanofluid against different geometrical configurations affected by thermal radiations. The flow is induced by stretchable surface with the implementation of zero‐net mass‐flux conditions on the surface. This considered model is commonly known as Kuznetsov and Nield's proposed updated model for nanoparticles. The derived flow equations are first nondimensionalized by employing appropriate nonsimilar transformations. The transformed system is analytically tackled by employing the local nonsimilarity (LNS) approach up to the second‐truncation level in association with the numerical algorithm bvp4c. The consequences of appropriate parameters, such as the suction parameter, wedge angle parameter, Weissenberg number, Prandtl number, constant velocity parameter, temperature ratio, Brownian motion, Lewis number, thermophoresis and radiation parameters, on fluid velocity, thermal, and concentration profiles are calculated and graphed. Drag coefficient, Nusselt, and Sherwood numbers are also computed and presented in tabular form. It is observed that intensification in the suction parameter shows augmentation in the local skin friction coefficient. Enhancement in the wedge angle parameter increases both the Sherwood and Nusselt numbers. Enhancement in velocity profile of the nanofluids is noticed with the increasing estimations of suction parameter. Thermophoresis parameter enhances both thermal and concentration profiles, however increasing Lewis number leads to a decline in the concentration boundary layer. With judgment, a comparative assessment is made of the present and previous results. This research may be helpful for the researchers that are interested in studying prospective industrial and engineering nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, and many others. [ABSTRACT FROM AUTHOR]

This study examines the magnetohydrodynamic flow of hybrid silver-alumina (Ag-Al 2 O 3 )/water nanofluid within a corrugated trapezoidal cavity that contains a heat-generating rotating solid cylinder. The hybrid nanofluid flow and convective heat transfer are modelled using a single-phase approach. The governing equations for fluid flow and convective heat transfer are solved using the penalty finite element method. The finite element algorithm was validated against previously published work, and it was found to be in good agreement with the existing literature. We investigate the effects of the Ag and Al 2 O 3 nanoparticle diameters and the radius of the heat-generating solid cylinder on streamlines, isotherms and average Nusselt number. The results of this study reveal that the flow circulation regions near the rotating cylinder are enhanced with increased nanoparticle diameters and cylinder radius. Moreover, the nanofluid temperature and heat transfer rate are increased with reduced nanoparticle diameters and increased cylinder radius. [ABSTRACT FROM AUTHOR]

In this study, a theoretical analysis is performed to address the features of heat and mass transfer phenomena of two-dimensional viscous fluid flow of Oldroyd-B nanofluid over a vertical stretched sheet which contains gyrotactic microorganisms by considering the mixed convection and inclined magnetic field effects. The induced flow features have been considered by triple stratified medium. Additionally thermal radiation effect is included in the energy equation. To make the present study reasonably worthy, impact of Joule heating and heat sink/source is also considered. By applying the defined similarity transformations physical flow system is reduced to nonlinear system. Thereafter, numerical solution with desired accuracy is obtained with the help of RKF-45 method. Graphical representation is done for the flow controlling parameters involved in this analysis. Main observations of the present study are velocity distribution declined with a relaxation time and thermal stratification parameter and motile density profile is promoted by increasing bioconvection Rayleigh number and buoyancy ratio. These results are reasonable correlated with the previous findings reported in literature. Based on these scientific reports, this work is relevant to bio-inspired nanofluid-enhanced fuel cells and nanomaterials fabrication processes. [ABSTRACT FROM AUTHOR]

Modeling and computations are performed to study the ND-Co3O4/EG hybrid nanoliquid mixed convective flow past a vertical porous cylinder. The flow analysis and formulation are given accounting for slip effects and homogeneous-heterogeneous reaction impacts. The governing complex equations formed with prescribed boundary conditions are simplified into self-similar equations through the use of suitable transformations. The numerical solutions of the drag coefficient, Nusselt number, liquid velocity, liquid temperature, and the liquid concentration are explored through graphs with the setting of pertaining parameter values. From the results, it is noticed that an ND-Co3O4/EG nanofluid plays a more impressive role in the process of energy transfer than a Co3O4/EG nanofluid. Further, it is found that the heterogeneous reaction parameter decreases the concentration whereas multiple slips enhance the temperature. [ABSTRACT FROM AUTHOR]

An exploration of the unsteady MHD boundary layer flow over a moving vertical porous surface with nanofluids under the influence of a uniform transverse magnetic field and heat radiation absorption effects has been brought out. Two different kinds of water-based nanofluids comprising of Al 2 O 3 and TiO 2 are adopted into deliberation. The governing equations for the flow are solved by making use of the Laplace transform method, and the solutions are displayed in closed form. The velocity, temperature, concentration, the shear stress, the rate of heat and mass transportations near the surface has been described graphically for numerous values of the relevant parameters. The velocity and temperature enhances with increasing radiation absorption parameter. It is also observed that an increase of volume fraction of nanoparticles leads to the enhancement of the temperature on central line of the flow. Nusselt number might be tracked down to be elevated for alumina than titanium dioxide nanofluid. The present investigation originated applications in aerospace engineering as well as industrial many mechanisms. [ABSTRACT FROM AUTHOR]

The entropy production and mixed convection within a trapezoidal nanofluid-filled cavity having a localised solid cylinder is numerically examined using the finite element technique. The top horizontal surface moving at a uniform velocity is kept at a cold temperature, while the bottom horizontal surface is thermally activated. The remaining surfaces are maintained adiabatic. Water-based nanofluids ( Al 2 O 3 nanoparticles) are used in this study, and the Boussinesq approximation applies. The influence of the Reynolds number, Richardson number, nanoparticles volume fraction, dimensionless radius and location of the solid cylinder on the streamlines, isotherms and isentropic are examined. The results show that the solid cylinder's size and location are significant control parameters for optimising the heat transfer and the Bejan number inside the trapezoidal cavity. Furthermore, the maximum average Nusselt numbers are obtained for high R values, where the average Nusselt number is increased by 30% when R is raised from 0 to 0.25. [ABSTRACT FROM AUTHOR]

• Hybrid nanofluid flow and entropy generation analyses in a complex enclosure are done. • The porous enclosure embodies three circular cylinders is subject to a magnetic field. • The active hot central cylinder can move along the vertical central axis. • The finite element method (FEM) is applied to discretize the governing equations. • Changing the relative position of the hot cylinder plays a crucial role. In this numerical contribution, hybrid nanofluid flow behavior, thermal characteristics, and entropy generation analysis through a porous enclosure containing three circular cylinders with magnetic field effects were investigated using finite element approach. The cylinders are arranged in horizontal arrangement in the middle of cavity height, and the active hot central cylinder can move along the vertical central axis while other cold cylinders are considered fixed. The cylinders are enclosed by an adiabatic wavy cavity loaded with Cu-Al 2 O 3 -water. The results are discussed for the scrutinized parameters e.g., Rayleigh number (Ra), Darcy number (Da), Hartmann number (Ha), relative position of the hot cylinder (δ), and concentration in volume of nanoparticles (ϕ). It was inferred that the thermal-natural convective flow and overall heat transmission were reinforced by boosting Ra and Da , and lowering Ha. Changing the relative position of the hot cylinder has a remarkable effect on nanoliquid flow patterns, convective heat transfer and entropy generation characteristics. [Display omitted] [ABSTRACT FROM AUTHOR]

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the magnets are extremely important to create three dimensional images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present research is to the effects of thermal radiation and rotation on the unsteady MHD convective flow past an infinite vertical moving absorbent plate. The similarity transformations are employed to migrate the governing partial differential equations in a system of non-linear ordinary differential equations and elucidated computationally by making use of cubic B-splines collocation method. The consequences of physical variables on fundamental segmentations are commented through visual aids. Even if the digital estimates of frictional force, Nusselt number and Sherwood number with respect to different parameters are delivered in matrix template and exchange of views proportionally. From the results, the resultant velocity magnifies with an increasing in rotation parameter, the thermal and solutal buoyancy forces. Reversal performance is adhered with expanding in the slip parameter. An enlargement in the radiation parameter, rise in the fluid speed and temperature profiles. The concentration profiles augments with increasing in suction parameter. The rate of mass transport is influenced on strengthening in Schmidt number and slip parameter. [ABSTRACT FROM AUTHOR]

In the present study, it is explored theoretically Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) rotating flow of a viscous, incompressible electrically conducting, and optically thick radiating Jeffreys fluid over an impulsively, moving vertical plate embedded in a saturated porous medium, when the temperature of the plate has a provisionally ramped profile. The exact solutions of the governing equations for the flow domain are attained by making use of the Laplace transform method. The specified analytical solutions are also acquired for some limiting cases. The research phrases of engineering curiosity for skin friction and Nusselt number are originated for both ramped wall temperature and the isothermal plate. Sherwood number is also obtained. The numerical results of velocity, temperature, and concentration distributions are exhibited graphically whereas skin friction, Nusselt number, and also Sherwood number are mentioned in a table form. It is observed that on either cases of ramped wall temperature and isothermal plate, the resultant velocity enhances with an increase in Hall and ion slip parameters. Reversal behavior is observed with an increase in magnetic field parameter, Jeffreys fluid parameter and Prandtl number. Thermal and concentration buoyancy forces and thermal radiation tend to accelerate the resultant velocity throughout the boundary layer region. The temperature reduces with an increase in Prandtl number and reverse effect is observed with an increase in thermal radiation parameter. Mass diffusion tends to enhance to species concentration. The rotation and Jeffreys fluid parameters tend to enhance both stress components. Nusselt number enables to lessen with growing in thermal radiation parameter and is magnified on escalating in time. The Sherwood number is improved with increasing in Schmidt number at the plate and it is refused on increasing in time. [ABSTRACT FROM AUTHOR]

In the current study, magnetohydrodynamics mixed convective flow of Ag–MgO/water hybrid nanofluid in a triangular shaped partitioned cavity involving a porous layer is numerically investigated by using the finite element method. In the numerical simulation, various effects of pertinent parameters such as Richardson number (between 0.01 and 100), Hartmann number (between 0 and 60), magnetic field inclination angle (between 0 and 90), Darcy number (between 10 - 4 and 5 × 10 - 2 ), location of the vertex of triangular porous region (between 0.2 and 0.8 H) and hybrid nanoparticle solid volume fraction ( ϕ 1 between 0 and 0.01, ϕ 2 between 0 and 0.01) on the fluid flow and convective heat transfer features are examined. It was observed that a large vortex is established below the main vortex near the upper wall for the lowest value Ri number. At the highest magnetic field strength, multi-recirculation flow pattern is seen in the right bottom corner. The average heat transfer enhances with higher values of permeability of the porous medium, magnetic field inclination angle, distance of the porous layer vertex from the hot wall and solid nanoparticle volume fraction of each particles in the hybrid nanofluid. The impact is reverse for higher values of Richardson number and Hartmann number. In the current work, significant changes in the average Nusselt number are obtained by varying the location of the porous medium. The triangular shaped porous compound can be used as an excellent tool for convective heat transfer control. [ABSTRACT FROM AUTHOR]

We have explored theoretically the Hall and ion slip impacts on an unsteady laminar MHD convective rotating flow of heat generating or absorbing second grade fluid over a semi-infinite vertical moving permeable surface. The non-dimensional equations for the governing flow are solved to the most excellent possible investigative solution using perturbation methodology. The effects of parameters on velocity, temperature and concentration are demonstrated graphically and described in detail. For engineering curiosity, the shear stresses, Nusselt number and Sherwood number are obtained analytically, represented computationally in a tabular format as well as explained with respect to foremost parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and ion slip parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Rotation parameter is to diminish the skin friction, whereas it is augmented through an increase of the Hall and ion slip effects. The rate of mass transfer is increased with increasing chemical reaction parameter. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) free convective rotating flow over an exponentially accelerated inclined plate entrenched in a saturated porous medium with the effect of angle of inclination, variable temperature and concentration. The flow induced by the presence of heat source/sink and destructive reaction. The Laplace transform technique has been used to solve the governing equations. The effects of the non-dimensional parameters on the governing flow velocity, temperature and concentration are examined with graphical profiles. Also for engineering interest the shear stress, Nusselt number and Sherwood number are obtained analytically and discussed computationally with reference to foremost flow parameters. It is reported that the presence of magnetic field prevents the flow reversal. Angle of inclination sustains a retarding effect on velocity distribution. The present study has an immediate application in understanding the drag experienced at the heated and inclined surfaces in a seepage flow. [ABSTRACT FROM AUTHOR]

The main objective of this numerical investigation was to analyze the entropy generation and natural convection flow under magnetic field in a square enclosure filled with Cu–Al2O3/water hybrid nanofluid. The enclosure is equipped with a conducting hollow cylinder. The free convective flow in the enclosure is created by a horizontal temperature difference between the vertical left hot wall and the right cold wall under the Boussinesq approximation. The dimensionless equations of steady laminar natural convection flow for Newtonian and incompressible mixture are discretized using the finite volume method. The effective thermal conductivity and viscosity of the hybrid nanofluid are calculated using Corcione correlations taking into consideration the Brownian motion of nanoparticles. Numerical solutions were performed for different values of the nanoparticles volumic concentration, Hartmann number, Rayleigh number, radius ratio, and solid–fluid thermal conductivity ratio. The analyzed results show that inserting a hollow conducting cylinder plays an important role in controlling flow characteristic and heat transfer rate as well as irreversibilities within the cavity. [ABSTRACT FROM AUTHOR]

• Nano-Encapsulated Phase Change Materials (NEPCMs) are suspended in a base fluid. • Free convection heat transfer of NEPCMs is addressed in a cavity. • Fusion temperature of NEPCM particles is a key factor in heat transfer enhancement. • There is an optimum range of fusion temperature leading to maximum heat transfer. • Up to 10% heat transfer enhancement was observed by using NEPCM particles. Free convective flow and heat transfer of a suspension of Nano Encapsulated Phase Change Materials (NEPCMs) in an enclosure is studied. NEPCM particles are core-shell structured with Phase Change Material (PCM) as the core. The enclosure is a square cavity with top and bottom insulated walls and differentially-heated isothermal vertical walls. The NEPCM particles circulate under natural convection inside the cavity. The PCM cores undergo phase change from solid to liquid and absorb some of the surrounding's heat in the form of latent heat in the hot region, and release the absorbed heat in the cold region by solidification. The governing equations representing the conservation of mass, flow, and heat of NEPCM suspension are introduced in the form of partial differential equations. The governing equations are transformed into non-dimensional form and solved by the finite element method. A grid check and validation test are performed to ensure the accuracy of the results. The outcomes show that the fusion temperature of NEPCM particles is the key factor affecting the heat transfer enhancement of NEPCMs in the natural convection flow. The enhancement of heat transfer is highly dependent on the non-dimensional fusion temperature, θ f , and very good performance can be achieved in the range of ¼ < θ f < ¾. Comparing to the base fluid, a relative enhancement of about 10% can be achieved by using NEPCMs at a non-dimensional fusion temperature of ¼. [ABSTRACT FROM AUTHOR]

A computational analysis has been conducted to investigate turbulent flow and convective thermal transfer characteristics in a twodimensional horizontal rectangular section channel with a hot lower wall-mounted diamond-shaped baffle. The calculations are based on the finite volume method, by means of Commercial Computational Fluid Dynamics software FLUENT, standard k-epsilon turbulence model with QUICK numerical scheme, and the SIMPLE discretization algorithm has been applied. The fluid flow and heat transfer characteristics, i.e., dynamic pressure coefficient, stream function, mean, axial, and transverse velocities, turbulent viscosity, temperature field, skin friction coefficients, local and average Nusselt numbers, and thermal enhancement factor are presented for flow Reynolds numbers based on the aeraulic diameter of the computational domain ranging from 12,000 to 32,000 at constant surface temperature condition along the upper and lower walls. Effect of the diamond configuration of the insulated baffle is studied numerically and the data obtained from this same baffle model are also compared with that of the simple flat rectangular baffle under similar operating conditions. Over the range under investigation, the improvements are found to be around 3.962 and 29.820 times higher than the smooth air channel with no baffle for heat thermal transfer and skin friction factor, respectively. The maximum TEF is around 1.292 at the highest Reynolds number value, Re = 32,000. [ABSTRACT FROM AUTHOR]

Numerical simulation of mixed convection heat transfer in a lid-driven triangular cavity filled with power law nanofluid and with an opening was performed under the effect of an inclined magnetic field. The left vertical wall of the cavity moves in + y-direction, and the bottom wall of the cavity is partially heated. Galerkin weighted residual finite element method was used to solve the governing equations. Influence of Richardson number, Hartmann number, inclination angle, opening ratio and nanoparticle volume fraction on the fluid flow and heat transfer is examined for various power law indices. It was observed that average heat transfer deteriorates as the value of Richardson number and Hartmann number enhances. At the lowest value of Richardson number, the discrepancy between the average heat transfer corresponding to different power law indices is higher. The inclination angle of the magnetic field where the minimum of the average Nusselt number is seen depends on the fluid type. Average heat transfer number is the highest for the highest value of the opening ratio. The average Nusselt number enhances with solid particle volume fraction, and there are slight variations in the reduction in the average Nusselt number when base fluid and nanofluid are considered for various power law indices. [ABSTRACT FROM AUTHOR]

In this paper, the effect of a baffle on free convection heat transfer of a water-Fe3O4 nanofluid in a C-shaped enclosure in the presence of a magnetic field is investigated numerically. The enclosure is subjected to a constant magnetic field. The vertical wall on the left side is maintained at a constant hot temperature of Th, and the right one is kept at a constant cold temperature of Tc. The rest of the walls are insulated. The governing equations are discretized by the control volume method and solved simultaneously by the SIMPLE algorithm. The numerical results show very good agreement with other published works. The results indicate that by increasing the enclosure's aspect ratio, the Nusselt number is increased. It is also found that the volume fraction of nanoparticles can be raised in order to achieve increased cooling in the enclosure. By increasing the aspect ratio, the effect of the nanoparticles on the enhancement of the Nusselt number is more pronounced. Also, the maximum effect of the baffle on the heat transfer is seen at the bottom of the hot wall. Generally, increasing the baffle length produces increases in the Nusselt number. The maximum cooling level is occurred for AR = 0.7 and Bf = 0.2. [ABSTRACT FROM AUTHOR]

In this paper, we have presented a numerical solution to the general problem of MHD flow, heat and mass transfer of viscous incompressible nanofluid past a uniformly stretching sheet through porous media with heat generation/absorption, thermal radiation, chemical reaction, thermo-diffusion and diffusion-thermo effects. Many theoretical and experimental studies suggested that the thermal conductivity of the base fluid increases in the range of 15–40% when nanoparticles are added to the base fluid. This enhancement in the thermal conductivity of the nanofluid depend on many mechanisms of the added nanoparticles like particle agglomeration, volume fraction, Brownian motion, thermophoresis, nanoparticle size, etc. Though we have different varieties of nanofluids, we have considered Al 2 O 3 –water and TiO 2 –water based nanofluids in this problem. The transformed conservation equations for the nanofluid are solved numerically subject to the boundary conditions using an optimized, extensively validated, variational finite element method. The numerical code is validated with previous studies. The influence of important non-dimensional parameters, namely nanoparticles volume fraction ( φ ), Prandtl number ( Pr ), magnetic parameter ( M ), Soret parameter ( Sr ), Dufour parameter ( Du ), space-dependent ( A 1 ) and temperature-dependent ( B 1 ) heat source/sink parameters on the velocity, temperature and nanoparticle concentration fields as well as the skin-friction coefficient, Nusselt number and Sherwood number are examined in detail and the results are shown in graphically and in tabular form to illustrate the physical importance of the problem. [ABSTRACT FROM AUTHOR]

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This work is focused on the numerical modeling of steady laminar mixed convection flow in a lid-driven cavity with a wavy wall filled with a water–CuO nanofluid. The left and right walls of the enclosure are kept insulated while the bottom and top walls are maintained at constant temperatures with the top surface being the heated lid wall and moving at a constant speed. The governing equations for this investigation are given in terms of the stream function–vorticity formulation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by a second-order accurate finite-volume method. Various comparisons with previously published work are performed and the results are found to be in good agreement. A parametric study of the governing parameters such as the Richardson number, bottom wall geometry ratio (B/H) and the nanoparticles volume fraction is conducted and a representative set of graphical results is presented and discussed to illustrate the effects of these parameters on the flow and heat transfer characteristics. It is found that the presence of nanoparticles causes significant heat transfer augmentation for all values of Richardson numbers and bottom wall geometry ratios. [ABSTRACT FROM AUTHOR]

The coupled heat and mass transfer by mixed convection boundary layer flow of a micropolar fluid over a continuously moving isothermal vertical surface immersed in a thermally and solutally stratified medium have been investigated in the presence of chemical reaction effect. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by the Keller box method. Comparison with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the skin-friction coefficient as well as the Nusselt number and the Sherwood number is presented graphically for various parametric conditions and discussed. [ABSTRACT FROM AUTHOR]

Local thermal non-equilibrium effects on heat natural convection features in a horizontal confocal elliptical annulus with the inner cylinder covered with a nanofluid-saturated porous sleeve is investigated in this study. The steady and laminar natural convective flow is incited by the thermal buoyancy resulting from the differential heating between the inner and outer annulus' surfaces. The nanofluid phase and the solid phase of the porous sleeve are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model for the porous region were computationally solved by the finite volume technique using the standard SIMPLER algorithm. The results were analyzed according to different porous materials characteristics under LTNE condition. The standard 0.05 significance level was employed to determine the local thermal equilibrium situation in the porous sleeve. For the first time, contours of the spatial distribution of the LTNE sources within the porous sleeve region were represented. [ABSTRACT FROM AUTHOR]

This study aims to explain the impact of the presence of a solid conductive partition on the thermal-free convective motion mechanism and heat transmission process within a concentric circular annulus filled with a water-based hybrid nanoliquid containing Copper (Cu) and Alumina (Al 2 O 3) nanoparticles. The thermal natural convective flow is formed within the annulus due to the temperature difference which is externally imposed between the internal heated cylinder and the external cooled one and internally generated by the interior heat generation/absorption (IHG/A) phenomenon. The technique of finite volume is applied to discretize and approximately solve the non-dimensional conservation equations. The influence of selected factors such as the nanoparticles concentration, Rayleigh number, fluid/solid heat conductivity ratio, and the IHG/A parameter on the thermo-hydrodynamic behavior and heat exchange rate is interpreted. The findings show that, in the presence of a conductive solid partition, the combined effects of the IHG/A phenomenon and the combined nanoparticles considerably modify the flow and heat exchange behaviors within the annulus. We also employed a new correlation to predict the mean heat exchange rate in the defined input parameter range. [ABSTRACT FROM AUTHOR]

A numeric investigation is executed to understand the impact of moving-wall direction, thermal radiation, entropy generation and nanofluid volume fraction on combined convection and energy transfer of nanoliquids in a differential heated box. The top wall of the enclosed box is assumed to move either to the left or the right direction which affects the stream inside the box. The horizontal barriers are engaged to be adiabatic. The derived mathematical model is solved by the control volume technique. The results are presented graphically to know the impact of the dissimilar ways of moving wall, Richardson number, Bejan number, thermal radiation, cup mixing and average temperatures. It is concluded that the stream and the thermal distribution are intensely affected by the moving-wall direction. It is established that the thermal radiation enhances the convection energy transport inside the enclosure. [ABSTRACT FROM AUTHOR]

We investigated the Hall and ion slip effects on the MHD convective flow of elastico-viscous fluid through porous medium between two rigidly rotating parallel plates with time fluctuating sinusoidal pressure gradient in this paper. In an initially undisturbed state both the fluid and the plates are in rigid rotation with the uniform angular velocity Ω about the normal to the plates. At t > 0 the fluid is driven by a fluctuating pressure gradient parallel to the channel walls. Analytical solutions for the velocity, temperature and concentration are evaluated and discussed computationally with the help of graphical profiles. For engineering interest, we obtained skin friction, Nusselt number, Sherwood number and volumetric flow rate and discussed numerically. Elasticity and magnetic field resist the fluid motion gets thinner boundary layer. Lesser frequency of oscillating pressure gradient frightens the reverse flow. The similar variation of skin friction should be circumvented with less significant time span and strength of the magnetic field. [ABSTRACT FROM AUTHOR]

Mixed convection of carbon-nanotube/water nanofluid in a vented cavity with an inner conductive T-shaped object was examined under pulsating flow conditions under magnetic field effects with finite element method. Effects of different parameters such as Richardson number (between 0.05 and 50), Hartmann number (between 0 and 30), cavity wall inclination (between 0 ∘ and 10 ∘ ), size (between 0.1 H and 0.4 H) and orientation (between −90 ∘ and 90 ∘ ) of the T-shaped object, and amplitude (between 0.5 and 0.9) and frequency (Strouhal number between 0.25 and 5) of pulsating flow on the convective flow features were studied. It was observed that the average Nusselt number enhanced with the rise of strength of magnetic field, solid nanoparticle volume fraction, and amplitude of the pulsation, while the effect was opposite for higher values of Ri number and cavity wall inclination angle. The presence of the T-shaped object and adjusting its size and orientation had significant impact on the main flow stream from inlet to outlet and recirculations around the T-shaped object and in the vicinity of hot wall of the cavity along with the magnetic field strength. Pulsating flow resulted in heat transfer enhancement as compared to steady flow case for all configurations. However, the amount of increment was different depending on the variation of the parameters of interest. Heat transfer enhancements were 41.85% and 20.81% when the size of the T-shaped object was increased from 0.1 H to 0.4 H. The T-shaped object can be utilized in the vented cavity as an excellent tool for convective heat transfer control. As highly conductive CNT particles were used in water, significant enhancements in the average Nusselt number between 97% and 108% were obtained both in steady flow and in pulsating flow cases when magnetic field was absent or present. [ABSTRACT FROM AUTHOR]

In this study, numerical analysis of forced convective pulsating nanofluid flow over a backward-facing step with different nanoparticle shapes was performed by the finite volume method. The effects of the Strouhal number (between 0.1 and 2), solid nanoparticle volume fraction (between 0 and 0.04) and nanoparticle shapes (spherical, blade and cylindrical) on the heat transfer and fluid flow were examined with the aid of numerical simulation. It was observed that the average Nusselt number is a decreasing function of the Strouhal number for the considered range, and it enhances for higher solid particle fractions. Using nanofluids with spherical particles is advantageous in pulsating flow, whereas cylindrically-shaped particles are preferred in steady flow configurations. Average Nusselt number enhancements up to 30.24% and 27.95% are achieved with cylindrical- and spherical-shaped particles at the highest volume fraction. [ABSTRACT FROM AUTHOR]

Control Volume Finite Element Method (CVFEM) is a new approach in which all advantages of finite volume method and finite element method are combined together. In this research, CVFEM is employed to simulate the impact of radiative heat transfer on magnetohydrodynamic free convection of water based nanofluid. Fe 3 O 4 – H 2 O ferrofluid has been used and viscosity of nanofluid is variable respect to magnetic field. Roles of the radiation parameter R d , numbers of undulations N , Fe 3 O 4 –water volume fraction ϕ , Hartmann number H a and the Rayleigh number R a are depicted. Nu a v e is present as a formula according to effect of various parameters. Results prove that the inner surface temperature decreases with the augment of buoyancy forces. Nu a v e enhances with the augmentation of the thermal radiation parameter while it decreases with the augment of H a and N . [ABSTRACT FROM AUTHOR]

This paper investigate the numerical study of MHD boundary layer flow, heat and mass transfer analysis of water based nanofluids containing single and multi-walled CNTs over a vertical cone embedded in porous medium with convective boundary condition under the influence of chemical reaction and suction/injection. The similarity transformation technique is used for converting the governing non-linear partial differential equations, which represents the momentum, temperature and concentration of nanofluid, into the system of coupled ordinary differential equations. The transformed conservation equations together with boundary conditions are solved by using Finite element method. The sway of various pertinent parameters on hydrodynamic, thermal and solutal boundary layers is investigated and the results are displayed graphically. Furthermore, the values of local skin-friction coefficient, rate of temperature and concentration is also inspected for various values of non-dimensional parameters and the results are shown in tabular form. The numerical data results are compared with available data for special cases and found in good agreement. It is found that the skin-friction coefficient, Nusselt number and Sherwood number enhances with rising values of Biot number ( B1 ) in both SWCNTs-water and MWCNTs-water based nanofluids. [ABSTRACT FROM AUTHOR]

In this study, mixed convection of CuO–water nanofluid filled lid driven cavity having its upper and lower triangular domains under the influence of inclined magnetic fields is numerically investigated. The top horizontal wall of the cavity is moving with constant speed of u w with + x direction while no-slip boundary conditions are imposed on the other walls of the cavity. The top wall of the cavity is maintained at constant cold temperature of T c while the bottom wall is at hot temperature of T h and on the other walls of the cavity are assumed to be adiabatic. The governing equations are solved by using Galerkin weighted residual finite element formulation. Entropy generation is produced by using formulation and integrated with calculated velocities and temperatures. The numerical investigation is performed for a range of parameters: Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), inclination angle of magnetic field (between 0° and 90°) and solid volume fraction of the nanofluid (between 0 and 0.05). Different combinations of Hartmann numbers and inclination angles of the magnetic fields are imposed in the upper and lower triangular domains of the square cavity. It is observed that the local and averaged heat transfer deteriorates when the Richardson number, Hartmann number of the triangular domains increase. When the Hartmann number and magnetic angle of the upper triangle are increased, more deterioration of the averaged transfer is obtained when compared to lower triangular domain. Local and averaged heat transfer increase as the solid volume fraction of the nanoparticles increases and adding nanoparticles is more effective for the local enhancement of the heat transfer when the heat transfer rate is high and convection is not damped with lowering the Hartmann number. Second law analysis of the system for different combinations of flow parameters is also performed. [ABSTRACT FROM AUTHOR]

Abstract: Steady laminar mixed convection inside a lid-driven square cavity filled with water is studied numerically. The lid is due to the movement of the isothermal top and bottom walls which are maintained at T c and T h, respectively, with T h is higher than T c. A partial slip condition was imposed in these two moving walls. The vertical walls of the cavity are kept adiabatic. The appliance of the numerical analysis was USR finite difference method with upwind scheme treatments of the convective terms included in the momentum and energy equations. The studied relevant parameters were: the partial slip parameter S (0–∞); Richardson number Ri (0.01–100) and the direction of the moving walls (λ t = 1, λ b = ±1). The results have showed that there are critical values for the partial slip parameter at which the convection is declined. [Copyright &y& Elsevier]

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers. [ABSTRACT FROM AUTHOR]

[Display omitted] • Flow, heat, and mass transfer of hybrid nanofluids in a wavy chamber were addressed. • A two-phase approach, including the Brownian motion and thermophoresis forces, was introduced. • The drift flux of composite hybrid nanoparticles was computed. • The concentration distribution of composite nanoparticles was investigated. • The location of the solid block and undulation of surfaces are investigated. Mixed convection flow and heat transfer within various cavities including lid-driven walls has many engineering applications. Investigation of such a problem is important in enhancing the performance of the cooling of electric, electronic and nuclear devices and controlling the fluid flow and heat exchange of the solar thermal operations and thermal storage. The main aim of this fundamental investigation is to examine the influence of a two-phase hybrid nanofluid approach on mixed convection characteristics including the consequences of varying Richardson number, number of oscillations, nanoparticle volume fraction, and dimensionless length and dimensionless position of the solid obstacle. The migration of composite hybrid nanoparticles due to the nano-scale forces of the Brownian motion and thermophoresis was taken into account. There is an inner block near the middle of the enclosure, which contributes toward the flow, heat, and mass transfer. The top lid cover wall of the enclosure is allowed to move which induces a mixed convection flow. The impact of the migration of hybrid nanoparticles with regard to heat transfer is also conveyed in the conservation of energy. The governing equations are molded into the non-dimensional pattern and then explained using the finite element technique. The effect of various non-dimensional parameters such as the volume fraction of nanoparticles, the wave number of walls, and the Richardson number on the heat transfer and the concentration distribution of nanoparticles are examined. Various case studies for Al 2 O 3 -Cu/water hybrid nanofluids are performed. The results reveal that the temperature gradient could induce a notable concentration variation in the enclosure. The location of the solid block and undulation of surfaces are valuable in the control of the heat transfer and the concentration distribution of the composite nanoparticles. [ABSTRACT FROM AUTHOR]

Abstract This paper aims to review all the published studies about mixed convection of nanofluids in enclosures. The papers are categorized into four main classes, namely square (and rectangular), triangular, trapezoidal, and unconventional shapes, then their important information is summarized in a table. Most studies have reported a remarkable heat transfer enhancement with increasing the nanoparticle volume concentration, Reynolds number and Richardson number and the required pumping power increases by adding nanoparticles to the base fluids. Graphical abstract Unlabelled Image [ABSTRACT FROM AUTHOR]

[Display omitted] • Examined MHD non-uniform heating convective dynamics of hybrid nanofluid flow in a porous system. • Non-uniform heating boosted heat transfer by ∼722% at certain parameters. • The amplitude, frequency, and offset temperature significantly impacted heat tr ansfer. • Under multi-frequency heating, heat flow visualization made through heatlines. • Developed mathematical correlations for predicting heat transfer characteristics. In high-performance thermal systems, convective heat transport is a critical phenomenon for sustainable operation from an energy efficiency standpoint. This study examines the convective heat transport dynamics of a hybrid nanofluid (aluminum oxide-copper–water nanofluid) under spatially varying nonuniform temperature conditions within a porous thermal system in the presence of a magnetizing field. The flow domain experiences nonuniform heating (following a half-sinusoidal profile) from both sidewalls and is cooled from the top, while the lower wall remains adiabatic. The flow domain is filled with a porous substance and a hybrid nanoliquid. The non-dimensional governing equations are derived and numerically solved using a finite volume method-based solver. To accurately capture thermal behavior, available experimental data on hybrid nanofluid thermophysical properties are utilized. The study analyzes significant control variables such as half-sinusoidal heating amplitude, frequency, and offset temperature, as well as flow control variables such as Darcy number (Da), modified-Rayleigh number (Ra m), and Hartmann number (Ha). The analysis shows that non-uniform heating consistently enhances transfer by up to approximately 722% compared to uniform heating. The three temperature-controlling parameters (amplitude, frequency, and offset temperature) play a crucial role in enhanced heat transfer, and the higher their magnitudes, the higher the heat transfer. Heat flow dynamics between the heat source and the heat sink are well visualized through heat function and heatlines. Heat transfer is an increasing function of Ra m and frequency, which is opposite to the rising Da or Ha. An optimum frequency at which thermal convection is maximum is about 70 for the considered range of Ra m. Furthermore, mathematical correlations that combine control variables are developed for predicting heat transfer characteristics. [ABSTRACT FROM AUTHOR]

• The work presents impact of surface undulation on mixed MHD nano-bioconvective heat and mass transfer due to swimming of oxytactic bacteria in a porous enclosure. • Bioconvection from oxytactic organisms produces a secondary circulation on the left heated wavywall. The shape and strength of this circulation are markedly influenced by the involved flow controlling parameters n, Rb, Ha, Da, Le, Pe and Gr. • The curved surface enhances the heat transfer up to certain optimum undulations (n), whereas mass transfer increases with the increasing undulations (n). • The average value of Sh magnitude increases with undulations, bioconvection raises further the Sh value. Transport phenomena involving thermo-bioconvection have become an interesting field of research due to their novel application in various fields of engineering, bio-energy systems, fuel cells, medical science, etc. Design as well as proper control of such a system involving multiphysical transport in a complex geometry is a very difficult task. On such a system, the present study is conducted aiming to examine the magnetohydrodynamic (MHD) mixed bioconvection with oxytactic microorganisms suspended in copper-water nanofluid. The flow takes place through porous media in a top-wall-translating enclosure with a complex wavy sidewall heated uniformly. The right vertical wall is isothermally cooled; other walls are adiabatic. A magnetic field is imposed along the horizontal direction. Evolved flow physics are analyzed by modeling this complex problem involving an undulating heated wall and many coupled transport equations (due to the presence of motile bacteria or organisms) are numerically solved through a finite volume-based code. The thermo-fluid behaviors are studied extensively to explore the controllability of different involved parameters that could help the system's design and operation. The important parameters influencing the complex physics in the enclosure are the number of undulations (n), bioconvection Rayleigh number (R b), Darcy number (Da), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le), oxygen diffusion ratio (χ), Grashof number (Gr). The study reveals that the undulating curved surface enhances the heat transfer up to certain optimal magnitudes of undulations at the different operating conditions. The mass transfer rate increases with all undulations and bioconvection supports this trend. Bioconvection always favors heat transfer. In general, it is found that by adjusting the involved flow parameters and number of undulations, the local as well as global transport mechanisms, can be controlled effectively. The concept of this investigation could be found in the designing of microbial fuel cells and different nanotechnology-based bioconvection. [Display omitted]. [ABSTRACT FROM AUTHOR]