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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]

A numerical study was conducted to determine the impact of MHD on mixed convection of a Cu-water nanofluid in a horizontal channel attached to two open enclosures filled with a porous material is implemented in this paper. Uniform heat is supplied on the base of the two enclosures while the other walls are considered adiabatic. The finite element method has been utilized in this study to solve the considered equations and other numerical simulations that needed to be validated, assessed with previous papers to ensure that the model works correctly. Furthermore, this study considers a range of each of the Reynolds number (Re = 25, 50, 100, 150, 200), Richardson number (Ri = 0.1, 1, 3, 5, 8, 10) and the Hartmann number (Ha = 0, 5, 10, 15, 30, 50) at a constant volume fraction ( φ = 0.08) and porous media properties (Da = 10-2, and ε = 0.7). The results stated that the strength of the streamlines, isotherms, and the average Nusselt number (Nu avg ) increases with increasing values of the Richardson and Reynolds numbers while they decrease upon increasing the Hartmann number. The result shows that no big difference between cases 2 and 3, and the maximum enhancement in Nu avg is 9.84% in case 2 compared with case 1 at Re = 200, Ri = 1, and Ha = 0. [ABSTRACT FROM AUTHOR]

In this study, natural laminar convection of Al 2 O 3 /water nanofluid in a cavity slightly different from shaped H was investigated using the monophasic model. The various parameters of this flow were determined numerically using CFD-Fluent software using the finite-volume method by introducing Boussinesq approximation. The analysis is carried out for three values of the Rayleigh number (10 5 ; 2.3 · 10 5 and 3.072 · 10 5) and for three values of the form factor defined for this enclosure (0.2; 0.3 and 0.4). The impact of Rayleigh number, nanofluid concentration and cavity form factor on dynamic and thermal structure of the flow was analyzed. The results are shown in form of streamlines, isotherms, and profiles of velocity, temperature, and Nusselt number. Nusselt number rises with increasing Rayleigh number and nanofluid concentration and decreases with the form factor of the cavity. This study is well developed relative to those carried out before. With using Al 2 O 3 nanofluid, the heat transfer is improved because its thermal conductivity is increased compared to that of the base fluid. Finally, to predict heat transfer inside cavity, correlations for the Nusselt number were proposed for each form factor of the cavity. These correlations are rarely presented in this type of study. [ABSTRACT FROM AUTHOR]

A nanofluid flow under the influence of magnetic field with heat generation/absorption is considered in the cooling of electronic systems, nuclear reactors and physical phenomena such as geology. For the first time, in the present work, natural convection heat transfer in a two-dimensional enclosure with three types of wall shapes filled with a cu-water nanofluid in terms of the effect of Brownian motion of nanoparticles with heat generation/absorption and in the presence of a magnetic field is investigated by using the Lattice Boltzmann Method (LBM). The left vertical wall of the enclosure is examined in two modes: constant temperature heating and linear temperature heating and the cold wall of the enclosure in three different forms (a) diagonal, (b) curved and (c) smooth. The effect of parameters such as the Hartmann number, nanoparticle volume fraction, heat generation/absorption coefficient, cold wall shape and the type of wall heating on the nature of flow and heat transfer is investigated. The results of the authors' research were validated with other sources, and the accuracy of the outputs was ensured. The outcomes of research show that in all instances, increasing the strength of the magnetic field and the heat generation/absorption coefficient decrease the average Nusselt number. In addition, the effect of Hartmann number in various states is different. The highest heat transfer also occurs when the vertical wall has a constant temperature. In this case, the average Nusselt number is about 35% higher on average. The effect of the magnetic field is greater when the cold wall is smooth. By keeping all the parameters constant, the diagonal wall design increases the average Nusselt number by an average of about 30%. The effect of adding nanoparticles to the base fluid on decreasing or increasing the average Nusselt number depends on the Hartmann number and the heat generation/absorption coefficient. Using this numerical simulation, a comprehensive view on the optimal design of heat transfer from equipment can be obtained. [ABSTRACT FROM AUTHOR]

Exploiting the impact of Lorentz force and convective heating boundary on second-grade nanofluid flow alongside a Riga pattern is the main objective of the present work. Modelling of the present work is done through Grinberg term and a Lorentz force applied parallel to the wall of a Riga plate. The nanoparticles fraction on the solid surface of Riga pattern maintained a strong retardation because of zero mass flux. Theories of Cattaneo–Christov heat flux and generalized Fick's relations are employed by following the modern aspects of heat and mass transportations. In the current study, additional features of thermal radiation are also included in the energy equation in terms of linear expressions. In order to make the analysis more worthy, effect of chemical reaction is also included. By applying the suitable variables, constituted problem is converted into dimensionless form. Solution of the problem with desired accuracy is obtained by utilizing popular method called Runge–Kutta–Fehlberg. The graphical representations are used to illustrate the flow controlling parameters involved by their attractive physical consequences. Velocity distribution is observed for the increase with the second-grade parameter. Further, an improved nanoparticles temperature distribution is observed with the increase in radiation parameter and Biot number. Additionally, the distribution of the concentration of nanoparticles increases with increase in values of the thermophoretic parameter. Based on the scientific calculations obtained, it is established that the reported results may play a useful role in production processes and in the improvement of energy and thermal resources. [ABSTRACT FROM AUTHOR]

Two-dimensional forced convective steady boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving plate in a porous medium in the presence of a parallel free-stream is investigated. The governing coupled non-linear partial differential equations (PDEs) along with boundary conditions are transformed into a set of non-linear coupled ordinary differential equations (ODEs) by using appropriate transformations. The obtained non-linear ODEs with modified boundary conditions are converted into a system of first-order ODEs which are solved using the classical and efficient shooting method. Dual solutions for velocity, temperature and nanoparticle concentration distributions for Eying–Powell fluids similar to Newtonian fluid in some special flow situations are obtained, when the plate and free-stream are moving along mutually opposite directions. The stability analysis of the obtained solutions is performed and it is found that the upper branch solutions are physically stable, while lower branch solutions are unstable. The impacts of different dimensionless physical parameters on velocity, temperature and nanoparticle concentration are reported in the form of graphs and tables. An important result is obtained and it reveals that the 'dual solutions' character has been destroyed if resistance due to the porous medium is raised up to a definite level (i.e., permeability parameter K > 0.07979 ), though the range of existence of unique solution becomes larger with further increase of resistance due to porous medium. It is also observed that heat transfer rate diminishes with increasing thermophoresis parameter, Brownian diffusion parameter and Lewis number in all the cases, whereas mass transfer rate enhances with thermophoresis parameter (for dual solutions), Brownian diffusion parameter (for unique solutions) and Lewis number (for unique solutions). Further, skin-friction coefficient, i.e., the surface drag force, increases with permeability parameter, suction/injection parameter and decreases with Eyring–Powell fluid parameter. Also, increments in permeability parameter and the suction/injection parameter lead to the delay in the boundary layer separation. The critical values of velocity ratio parameter beyond which the boundary layer separation appears are − 0.5476432, − 0.5987132, − 0.704862, − 0.816944, − 0.9365732, − 0.96179102, − 1.057104, − 1.062004, − 1.09222, − 1.115824, − 1.193413, − 1.591023 and − 1.898366 for K = 0 , 0.01, 0.03, 0.05, 0.07, 0.074, 0.08, 0.082, 0.085, 0.09, 0.1, 0.15 and 0.2, respectively. [ABSTRACT FROM AUTHOR]

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

This paper investigates the natural convection inside a partially layered porous cavity with a heated wavy solid wall; the geometry is encountered in compact heat exchangers. Alumina nanoparticles are included in the water to enhance the heat exchange process. The incidental entropy generation is also studied to evaluate the thermodynamic irreversibility. The nanofluid flow is taken as laminar and incompressible while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The Darcy number (Da), porosity of the porous layer (ε ), number of undulations (N), and the nanoparticles volume fraction (ϕ ) are varied to assess the heat transfer and the incidental entropy generation. It is found that the waviness of the solid wall augments the average Nusselt number and minimizes the generation of entropy. The results show for some circumstances that the Nusselt number is augmented by 43.8% when N is raised from 0 (flat solid wall) to 4. It is also found that the porosity of the porous layer is a more crucial parameter than its permeability, where a 37.4% enhancement in the Nusselt number is achieved when the porosity is raised from 0.2 to 0.8. [ABSTRACT FROM AUTHOR]

The conjugate natural convection of a new type of hybrid nanofluid (Ag–MgO/water hybrid nanofluid) inside a square cavity is addressed. A thick layer of conductive solid is considered over the hot wall. The governing partial differential equations (PDEs) representing the physical model of the natural convection of the hybrid nanofluid along with the boundary conditions are reported. The thermophysical properties of the nanofluid are directly calculated using experimental data. The governing PDEs are transformed into a dimensionless form and solved by the finite element method. The effect of the variation of key parameters, such as the volume fraction of nanoparticles, Rayleigh number, and the ratio between the thermal conductivity of the wall and the thermal conductivity of the hybrid nanofluid (Rk), is studied. Furthermore, the effects of the key parameters are investigated on the temperature distribution, local Nusselt number, and average Nusselt number. The results of this study show that the heat transfer rate increases by adding hybrid nanoparticles for a conduction-dominant regime (low Rayleigh number). The heat transfer rate is an increasing function of both the Rayleigh number and the thermal conductivity ratio (Rk). In the case of a convective-dominant flow (high Rayleigh number flow) and an excellent thermally conductive wall, the local Nusselt number at the surface of the conjugate wall decreases substantially by moving from the bottom of the cavity toward the top. [ABSTRACT FROM AUTHOR]

The aim of the current study is to investigate the natural convection heat transfer in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. The governing equations that are expressed in dimensionless form are solved by means of control volume finite element method employing a validated FORTRAN code. The dimensionless controlling parameters of the present investigation are shape factor of nanoparticles (m), Hartmann number (Ha), Rayleigh number (Ra), and nanoparticle volume fraction (ϕ). In this study, the amplitude A and number of undulations N are fixed at a constant value of 0.2 and 8, respectively. The obtained results portray that in the presence of waves on the inner wall of the annulus, the heat transfer rate is an ascending function of Rayleigh number, nanoparticle volume fraction and less obvious function of their shape factor, while it is a descending function of the Hartmann number. [ABSTRACT FROM AUTHOR]

A numerical study is carried out on mixed convection and entropy generation of Al2O3/water nanofluid due to a rotating cylinder inside a square cavity. The numerical computations are performed taking the non-homogenous model of Buongiorno into consideration. The inner moving rotating circular cylinder is maintained at a constant hot temperature Th and the other left and right vertical walls of the cavity are maintained at a constant cold temperature Tc. The bottom and top horizontal walls are maintained as adiabatic. The Galerkin weighted residual method is implemented to numerically solve the governing equations. The Rayleigh number (104 ≤ Ra ≤ 107), angular rotational velocity (0 ≤Ω≤ 600) nanoparticles loading (0 ≤ ϕ ≤ 0.04) and the dimensionless radius of rotating cylinder (0.1 ≤ R ≤ 0.4) are the governing parameters of this study. Numerical results for the streamlines, isotherms, isentropic lines, nanoparticle loading, local and average Nusselt number and Bejan number are obtained and presented graphically. A detailed discussion of the results is performed to highlight the physics of the problem. [ABSTRACT FROM AUTHOR]

The natural-convection thermal performance of a dielectric liquid in a cubical module triggered by a varying rectangular heat generation source is numerically examined. The rectangular generating source is connected to the center of one vertical wall of the cubical module, which is constructed either vertically or horizontally. Two vertical walls neighboring the source-mounted wall are kept cold, and the remaining walls are insulated from the environment. The isotherms and the velocity contours are computed for a wide range of the Rayleigh number as well as the generating-source aspect ratio and the thermal conductivity ratio, demonstrating the variations of the thermal and stream structures inside the module. It is established that the thermal performance is more significant and is an increasing function of the heat generating-source aspect ratio and the Rayleigh number for the two altered alignments of the generating source. According to the practical demands of the thermal management of electronic devices, the heat transfer rate can be magnified or diminished by choosing the proper parameters such as thermal conductivity ratio, Rayleigh number, the aspect ratio and orientation of the generating source. [ABSTRACT FROM AUTHOR]

Mixed convective heat transfer of Cu–water nanofluid in a porous cavity with non-uniform temperature profiles on vertical sidewalls in the presence of thermal radiation and magnetic field is examined numerically. The vertical sidewalls are heated sinusoidally. Thermally insulated walls are considered at the remaining sides of the cavity. The magnetic field is applied parallel to the horizontal walls uniformly. The SIMPLE algorithm based on finite volume approach is applied to solve the governing equations. The numerical outcomes are discussed in the wide range of the parameters, Richardson number, phase deviation, amplitude ratio, Darcy number, Hartmann number, the thermal radiation, and the solid volume fraction. It is found that the average Nusselt number is decreased in value with the raise in the either Hartmann number or Richardson number in the presence of thermal radiation. The average heat transfer rate is enhanced with an augment in the solid volume fraction, and this enhancement is more effective in the presence of thermal radiation than that of in the absence of thermal radiation. The highest heat transfer rate is obtained for φ = 0 in the forced convection regime, whereas it is maximum at φ = 3 π / 4 in the mixed and free convection regimes. [ABSTRACT FROM AUTHOR]

In current attempt, nanoparticle Electrohydrodynamic transportation has been modeled numerically via control volume based finite element method. Mixture of Fe3O4 and Ethylene glycol is elected. Impact of radiation parameter (R d) , voltage supplied (Δ φ) , nanoparticle concentration, Permeability and Reynolds number have been displayed. Results display that permeability and thermal radiation can improve temperature gradient. [ABSTRACT FROM AUTHOR]

This study provides numerical analysis of the free convection of copper-water-based nanofluid filling a triangular cavity with semicircular bottom wall. The cavity sidewalls are maintained at cold temperature, while the semicircular wall is maintained at hot temperature. The other wall segments are thermally insulated. To control the energy transport within the cavity, a uniform magnetic field is applied horizontally. The physical domain is discretized according to the control volume finite element method which has been used to solve the governing equations. The physical and geometrical aspects of the current problem are investigated by inspecting the impacts of Rayleigh number, Hartman number, aspect ratio and the volume fraction of the Cu nanoparticles. Decreasing the radius of the hot semicircle enlarges the average Nusselt number at the absence of the magnetic field. When the magnetic field is applied, this effect is conversed within Ra ≤ 104. This conversed impact does not hold up when Ra is raised to 105. The numerical results are correlated in a sophisticated correlation of the average Nusselt number with other parameters. [ABSTRACT FROM AUTHOR]

This paper carries on investigation to study the effects of variable magnetic field and thermal radiation on free convective flow of an electrically conducting incompressible nanofluid over an exponential stretching sheet. The model implemented in the present study significantly enriches the thermal conductivity and hence more heat transfer capability of nanofluids. The transformed governing equations have been solved numerically using fourth-order Runge-Kutta method along with shooting technique. The influence of variable magnetic field and thermal radiation associated with thermal buoyancy on the dimensionless velocity, temperature, skin friction and Nusselt number have been analyzed. The obtained numerical results in the present study are validated and found to be in excellent agreement with some previous results seen in the literature. The present study contributes to the result that augmented Hartmann number belittles the fluid flow and enhances the fluid temperature and the related thermal boundary layer thickness. [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]