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The present work elucidates the hydrothermal characteristics within a non-Darcian porous complex wavy enclosure saturated with Al 2 O 3 –Cu– H 2 O hybrid nanofluid considering a uniform magnetic field. The left sidewall of the enclosure is wavy and heated isothermally, whereas the other sidewall is maintained at ambient temperature, all other walls are insulated. The Forchheimer–Brinkman-extended Darcy model is implemented to analyze the flow through porous media. The dimensionless transport equations are numerically solved following the finite volume-based in-house computational code with successive staggered non-uniform mesh distribution. The hydrothermal behaviors are investigated meticulously changing the dimensionless variables like undulation amplitude (λ ), Hartmann number (Ha), Darcy number (Da), and modified-Rayleigh number ( Ra m ). The remarkable results reveal that enhancing the heating surface area by heightening the amplitude of the undulation always leads to higher heat transfer, but does not always favor the growth of the flow strength. The heightening of the flow strength with amplitude is noted for higher Ra m only. The flow intensity, as well as heat transfer, increases with the growing Ra m . The same decreases with increasing Da and Ha. Local distribution of heat transfer characteristics shows complex behavior depending on the amplitude of the undulations and associated dimensionless numbers. [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]

The study investigates the approach to enhance the thermal management of battery cell module by attaching number of inverted triangular cavity to its casing. A sinusoidal heating is considered to battery cell module or a left wall of the cavity. The sinusoidal heated region is considered to be a function of amplitude ratio. The objective is to transfer the heat from module using natural convection process. The enhanced heat transfer is possible by adopting hybrid nanofluid in a triangular cavity due to its improved thermophysical properties. Thus, the investigation on natural convection heat transfer, fluid flow, and irreversibility within an inverted right-angled triangular porous cavity is conducted. Numerical results are obtained through an own-house FORTRAN coding, that uses the streamfunction–vorticity algorithm. The numerical results are derived for various values with Rayleigh number (103-106\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${10}^{3}-{10}^{6}$$\end{document}), Darcy number (10-5-10-1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${10}^{-5}-{10}^{-1})$$\end{document}, Hartmann number (0-50)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0-50)$$\end{document}, amplitude ratio (0.0-0.9\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.0-0.9$$\end{document}) and volume fraction of nanoparticles (0.01-0.04\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.01-0.04$$\end{document}), respectively. The irreversibility and flow results are compared with the various hybrid nanofluids. The study indicates that opting inverted right-angled triangular cavity rather than a square shape leads to an improvement in heat transfer. Accordingly, this inverted right-angled triangular cavity natural convective cooling can be considered as optimum design with the battery cell module for improved thermal management.Graphical abstract: The study investigates the approach to enhance the thermal management of battery cell module by attaching number of inverted triangular cavity to its casing. A sinusoidal heating is considered to battery cell module or a left wall of the cavity. The sinusoidal heated region is considered to be a function of amplitude ratio. The objective is to transfer the heat from module using natural convection process. The enhanced heat transfer is possible by adopting hybrid nanofluid in a triangular cavity due to its improved thermophysical properties. Thus, the investigation on natural convection heat transfer, fluid flow, and irreversibility within an inverted right-angled triangular porous cavity is conducted. Numerical results are obtained through an own-house FORTRAN coding, that uses the streamfunction–vorticity algorithm. The numerical results are derived for various values with Rayleigh number (103-106\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${10}^{3}-{10}^{6}$$\end{document}), Darcy number (10-5-10-1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${10}^{-5}-{10}^{-1})$$\end{document}, Hartmann number (0-50)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0-50)$$\end{document}, amplitude ratio (0.0-0.9\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.0-0.9$$\end{document}) and volume fraction of nanoparticles (0.01-0.04\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.01-0.04$$\end{document}), respectively. The irreversibility and flow results are compared with the various hybrid nanofluids. The study indicates that opting inverted right-angled triangular cavity rather than a square shape leads to an improvement in heat transfer. Accordingly, this inverted right-angled triangular cavity natural convective cooling can be considered as optimum design with the battery cell module for improved thermal management. [ABSTRACT FROM AUTHOR]

This paper aims to understand the characteristics of heat transfer and flow by natural convection of Al2O3–Cu/water-based hybrid nanofluid-filled square domain containing various configurations of a corrugated conducting solid under a horizontal magnetic field. The basic equations in their non-dimensional form are numerically solved using the finite volume discretization technique. The Corcione correlations are utilized to estimate the overall heat conductivity and overall viscosity of the hybrid nanoliquid when the nanoparticle's Brownian motion is taken into account. The dependency of different governing factors of the investigation, namely volume fraction of the combined nanoparticles, Rayleigh and Hartmann numbers, undulation number, undulation amplitude and the fluid/solid heat conductivity ratio, on thermohydrodynamic characteristics are delineated. Results stated that the maximum heat transmission rate was obtained for weak values of Hartmann, undulation number, undulation amplitude and high values of Rayleigh and nanoparticles volumic fraction. In addition, the fluid/solid heat conductivity ratio parameter was found to boost the heat transfer at weak Rayleigh while reducing it at high Rayleigh. [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 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]

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]

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]

In this work, the double-diffusive natural convection was studied in an open-ended cavity with the help of the lattice Boltzmann method. In this study, the driven force is developed by a change in the temperature gradient and concentration gradient on the left side of the cavity, which is the closed end. The temperature and concentration are maintained high at this end. The study is carried out for various parameters such as Rayleigh number (Ra) ranging from 103 to 106, aspect ratio (Ar) of 0.5, 1 and 2 and constant Prandtl number (Pr) of 0.7 and Lewis number (Le) of 2. The results are concentrated on for different buoyancy ratios (N = − 1, 0, 1) also. The results obtained are validated with existing literature results. The results show that when N value is negative, two buoyancy forces oppose each other and also the influence of concentration buoyancy force on fluid flow behavior gets dominant, and for aspect ratios 1 and 2, this effect was suppressed when Ra is increased but for the shallow cavity increasing in Ra helps the concentration force to become more dominant. [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]

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]

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]

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]

In this work, magneto-hydrodynamic natural convection of a nanofluid in a wavy cavity considering Brownian motion is studied numerically using the control volume finite element method. The effective viscosity and thermal conductivity of the nanofluid are defined by the correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered wavy cavity is heated from the left side and it cooled from the right side. Also, the top and bottom walls of the considered wavy cavity are assumed adiabatic. The impacts of various controlling parameters such as the Rayleigh number, wavy contraction ratio, Hartmann number and undulation number are examined on the contour maps of the streamlines and the isotherms. Further, the average and local Nusselt numbers are calculated and presented graphically and discussed. The findings narrate that the strength of the convective flow has a direct relationship with the Rayleigh number and also it has a reverse relationship with the wavy contraction ratio. [ABSTRACT FROM AUTHOR]

n analytical study of fluid flow and heat transfer in a composite channel is presented. The channel walls are maintained at different constant temperatures in such a way that the temperatures do not allow for free convection. The upper plate is considered to be moving and the lower plate is fixed. The flow is modeled using Darcy–Lapwood–Brinkman equation. The viscous and Darcy dissipation terms are included in the energy equation. By applying suitable matching and boundary conditions, an exact solution has been obtained for the velocity and temperature distributions in the two regions of the composite channel. The effects of various parameters such as the porous medium parameter, viscosity ratio, height ratio, conductivity ratio, Eckert number, and Prandtl number on the velocity and temperature fields are presented graphically and discussed. [ABSTRACT FROM AUTHOR]