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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, 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 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]

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]

Exergy efficiency, Nusselt number, friction factor, pressure drop, thermal and frictional entropy generation of water-based nanodiamond + Fe3O4 nanofluid flow in a tube and with various coiled wire inserts have been studied experimentally under turbulent and constant heat flux boundary conditions. The experiments were conducted in the Reynolds number range from 2000 to 22,000, particle concentrations of 0.05%, 0.1% and 0.2% and coiled wire inserts of different p / d values of 3.67, 2.34 and 1.00, respectively. Results indicate that at 0.2% vol. and Reynolds number of 20,095, without coiled wire inserts, the heat transfer coefficient, Nusselt number, friction factor, pressure drop and pumping power are enhanced to 44.36%, 29.55%, 11.1%, 29.58% and 39.49% over the base fluid data. Similarly, at 0.2% vol. and Reynolds number of 20,095, with coiled wire inserts of p / d = 1, the heat transfer coefficient, Nusselt number, friction factor, pressure drop and pumping power are further enhanced to 107.19%, 66.36%, 38.84, 64.44% and 76.54% over the base fluid data without inserts. The thermal entropy generation is decreased to 30.80% and it is further decreased to 46.34% at 0.2% vol. and Reynolds number of 20,095 with coiled wire inserts of p / d = 1. The exergy efficiency of water is 18.95%, and it is increased to 24.06% for 0.2% vol. and it is further increased to 51.85% for 0.2% vol. and Reynolds number of 20,095 with coiled wire inserts of p / d = 1. The study indicates that the hybrid nanofluids with coiled wire inserts are guaranteed choice for augmenting the exergy efficiency of flow through tube. [ABSTRACT FROM AUTHOR]

The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction (ψ ) —vorticity (ζ ) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for R i = 0.01 , Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations. [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]

The current problem is performed to analyze the heatline visualization of the mixed convection mechanism and heat transfer in a double lid-driven square cavity having a heated wavy bottom surface. The moving vertical surfaces are under adiabatic conditions, and the top surface is at a cold temperature. The finite element method is employed to determine the dimensionless governing equations controlled by specific boundary conditions. The implications of the Reynolds number ( 10 ≤ Re ≤ 500 ), the directions of the constant moving wall ( λ l = ± 1 , λ r = ± 1 ), Richardson number ( 0.01 ≤ Ri ≤ 100 ), Prandtl number ( 0.015 ≤ Pr ≤ 10 ) and the number of oscillations ( 1 ≤ N ≤ 4 ) are visualized by the streamlines, isotherms and the heatlines. The same direction of lid-driven cases leads to two primary circulation cells. The Richardson number increases as it imposes the increment of the vertical temperature gradient. At a high Prandtl number, the convection mode of heat transfer is fully established, and heat conduction occurs at a low Prandtl number. Moreover, the number of oscillations has the most significant direct impact on the streamlines and the temperature distributions compared to the flat surface. Higher Reynolds and Prandtl numbers result in an increment in the local and average Nusselt numbers. The result shows that one oscillation of the wavy surface with a low Richardson number yields to have an optimum heat transfer in the cavity. [ABSTRACT FROM AUTHOR]

The present examination is considered to discuss the steady, two-dimensional flow of heat and mass transfer of nanofluid flow along with the variable suction under the influence of heat source/sink alongside the viscous dissipation. Because of the stretchable surface, flow is generated. Spectral relaxation technique is used to acquire the numerical solution for the altered nonlinear group of differential equations. Thereafter, outcomes which were obtained from the above numerical technique are validated by comparing with the available outcomes in the existing literature and also with MATLAB inbuilt solver bvp4c. All the acquired results from the above numerical system are shown through graphs and tables to discuss different resulting parameters related to the present analysis. The range of the physical parameters is taken as - 0.1 ≤ f w ≤ 0.5 , 0.1 ≤ N t ≤ 0.7 , 0.1 ≤ N b ≤ 0.7 , 0 ≤ E c ≤ 1.2 , - 0.5 ≤ Q ≤ 0.5 , 1 ≤ P r ≤ 10 , 1 ≤ L e ≤ 5. The main findings are as follows: For the effect of suction parameter, the profiles of velocity, temperature and mass friction are decreased, and the coefficient of skin friction and Nusselt number is declined for the impact of thermophoresis parameter. [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]

The present work aims to examine the thermal efficacy of half-sinusoidal nonuniform heating at different spatial frequencies for a porous natural convection system using Cu–Al2O3/water hybrid nanofluid and magnetic field. The system is presented utilizing a classical square enclosure heated nonuniformly at the bottom wall, and the sidewalls are allowed to exchange heat with the surroundings. The Brinkman–Forchheimer–Darcy model is adopted catering other additional terms for buoyant force and magnetic field. The governing equations are transformed into nondimensional forms and then solved numerically using a finite volume-based computing code. The importance and fundamental flow physics are explored in terms of the pertinent parameters such as the amplitude (I) and spatial frequency (f) of half-sinusoidal heating, Darcy–Rayleigh number (Ram), volume fraction of hybrid nanoparticles (ϕ ), and Hartmann number (Ha). The flow structure and heat transfer characteristics are analyzed and presented utilizing heatlines, streamlines and isotherms and average Nusselt number. The results show that the use of half-sinusoidal nonuniform heating along with hybrid nanofluid can be a viable method for enhancement and control of the overall thermal performance. The study indicates that half-sinusoidal heating could be a promising technique for better heat transfer even in the presence of flow dampening effects like porous media and magnetic fields. [ABSTRACT FROM AUTHOR]

The steady flow of a nanofluid (mixture of titanium dioxide and water) in a rectangular channel under the influence of an inclined magnetic field is studied. The channel contains an upstream hot splitter plate in alignment with the upper and lower plates of the channel. It may be said that two incoming channel flows merge to form a single channel flow. This setup may apply to the heating chamber in which titanium dioxide can be used to enhance the thermal transfer rate. It is observed that the position of the splitter plate (that may act as an electric heater) affects the velocity and temperature of the fluid. Therefore, in order to ensure these facts, the examination of the flow behavior and the temperature distributions in the channel if the splitter is placed at different positions in the upstream have been probed. In addition, the effect of nanoparticles on the convection process has been probed. The streamlines are almost similar for a clear fluid as well as for a nanofluid (for low values of solid volume fraction of nanoparticles (i.e. φ < 0.05 )) for all values of the Reynolds number. However, the rise in the temperature is noted for the nanofluid if the concentration of nanoparticles is increased. The increase in the Reynolds number also supports the enhancement of the Nusselt number and, hence, the thermal transfer rate of the nanofluid. The Nusselt number is dominant in the vicinity of the trailing edge of the splitter because the trailing edge exhibits as a stagnation point. In addition, the maximum Nusselt number for nanofluid at moderate Reynolds number (e.g., Re = 100) is enhanced to 0.3% with respect to the clear fluid. Moreover, obtained results for this particular case are compared with the existing literature, and the results compare well. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend. [ABSTRACT FROM AUTHOR]

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–ε turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles ( ϕ = 2 % ) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01. [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]

In this paper, the problem of steady forced convection heat transfer and fluid flow characteristics of a hybrid nanofluid flowing through an isothermally heated horizontal tube considering various nanoparticle shapes has been investigated numerically. The three dimensionless cylindrical coordinate equations are discretized using the finite volume method and solved via a FORTRAN program. A numerical parametric investigation is carried out for a tube filled with regular water, (TiO2/water) nanofluid and (Ag–TiO2/water) hybrid nanofluid. Four different types of nanoparticle shapes are considered in this study, spherical, cylindrical, platelets and blades, with different volume fractions ranging from 0 to 8% using water as a base liquid. The influence of nanoparticle shape, nanoparticle concentration and Reynolds number on the local Nusselt number and the friction factor is essentially examined. The results showed that the friction factor of both nanofluid and hybrid nanofluid flow was increased as the nanoparticle volume fraction increased for all kinds of nanoparticle shapes, whereas it decreased as the Reynolds number increased. Nusselt number increased with increase in the nanoparticle concentration and Reynolds number. The highest heat transfer rate was acquired for the maximum nanoparticle volume concentration by using blade nanoparticle shape followed by platelet shape, cylindrical shape and lastly the sphere shape. It was found that the maximum values of the friction factor were registered for platelet-shape nanoparticles. [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]

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 study ahead deals with the natural convection of MWCN–Fe3O4/water magnetic hybrid nanofluid flowing in a porous medium. The flow domain is affected by an inclined magnetic field influencing the dynamic viscosity. The dependency of the flow and heat transfer characteristics on Rayleigh number, Ra = 103–106; Hartman number, Ha = 0–50; inclination angle of the magnetic field, ϕ = 0°–180°; magnetic number, δ0 = 0–2.0; porosity, ε = 0.1–0.9; Darcy number, Da = 10−7–10−1;and volume fraction of the composite nanoparticles, φ = 0, 0.1 and 0.3% is studied numerically. At low Rayleigh number Ra = 104, dispersing the nanocomposite particles increases the average Nusselt number Nuavg, while that decreases the Nuavg when Ra = 105 and 106. The dependency of viscosity on the magnetic field decreases the Nuavg at 0° < ϕ < 135°, which is due to an increase in overall viscosity of the nanofluid. After that (ϕ ≥ 135°), the average Nusselt number is greatly enhanced by increasing ϕ from 135° up to 180°. There is no meaningful change in average Nusselt number of the hybrid nanofluid by increasing the inclination angle of magnetic field in the absence of magnetic field-dependent viscosity (δ0 = 0). [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]

The objective of the present study is to peruse the natural convection in the cavity containing inclined elliptical heater under shape factor of nanoparticles and magnetic field. The control volume-based finite element method is used for solving conservation equations. Numerical results show very good grid independency and very good compromise with other works. The result shows the heat transfer grows via mounting nanofluid volume fraction. The increment of Ra number also leads the heat transfer to ascend. Heat transfer of nanofluid with three different shapes of nanoparticles is studied, and results show the platelet nanoparticle is better than the other ones. The influence of magnetic field on heat transfer is also investigated and discussed. The obtained outcomes represent that at a certain Rayleigh number, the average Nusselt number descends with the ascendant of Hartmann number. Finally, the new correlation is reported for calculating the Nu number in these geometries. [ABSTRACT FROM AUTHOR]

The paper presents the mixed convection heat transfer and entropy generation of a nanofluid containing carbon nanotubes, flowing in a 3D rectangular channel, subjected to opposed buoyant forces. The governing equations, including the continuity, momentum and energy equations, have been numerically solved using the finite volume technique. The results, including the contours of the axial velocity and temperature, have been presented for different values of the opposed buoyancy parameter (− 300 < Ω < − 100). The outcomes show that with an increase in the opposed buoyancy parameter, the nanofluid velocity near the channel wall drastically reduces and, therefore, causes a reduction in the Nusselt number. In addition, due to the occurrence of backflow phenomenon, an increment of the opposed buoyancy parameter enhances the total entropy generation along the channel. In brief, the friction-induced entropy generation is negligible compared with the entropy generation due to heat transfer. Finally, by increasing the value of the opposed buoyancy parameter, the ratio of the heat transfer rate to irreversibility decreases within the system. [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]

Buongiorno model is applied to investigate nanofluid migration through a permeable duct in the presence of external forces. Influences of radiation and Joule heating on first law equation are added. Final formulas are solved via differential transform method. Roles of suction, thermophoretic, radiation and Brownian motion parameters, Schmidt number, Hartmann number, Eckert number were presented. Results show that temperature gradient improves with the enhancement of Reynolds number, suction and Radiation parameters. Nu augments with the augmentation of Hartmann and Eckert numbers, while reverse behavior is seen for skin friction coefficient. Also, it can be concluded that Nusselt number enhances with the increase in radiation parameter but it decreases with the increase in Brownian motion. [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 contemporary power engineering and microelectronics, the efficiency of cooling systems is of crucial importance. To meet this requirement, specialized approaches and the use of nanofluids are employed to improve the heat dissipation of heat-generating components. This study presents a methodology based on a numerical simulation investigation and statistical analysis using the Response Surface Methodology (RSM) to estimate the average Nusselt number (Nuavg) associated with mixed convection in a ventilated cavity. The study considered pure water and mixtures of nanoparticles (Cu, Ag, and TiO2) as heat transfer fluids, exploring various values of the Richardson number (0.1 to 100) and volume fractions (0 to 8%). Analysis of Variance (ANOVA) and the quadratic mathematical model developed by RSM effectively predicted the results of the numerical simulation with a coefficient of determination R2 close to 1. The results obtained from the 3D curves of the RSM show that the average Nusselt number (Nuavg) increases significantly with the Richardson number. Conversely, an increase in the volumetric fraction leads to a slight decrease in Nuavg. Furthermore, it is observed that the agent (Ag) generates higher Nuavg values compared to other materials such as copper (Cu) and TiO2. Combining the RSM method with the desirability function (DF) allows for achieving the optimal average Nusselt number (Nuavg). Validation of the values proposed by the DF and those obtained by simulation shows a very small relative error, less than 0.13%. [ABSTRACT FROM AUTHOR]