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Heat transfer by natural convection for a centered inner adiabatic circular cylinder inside a trapezoidal enclosure filled with Ag-water nanofluid superposed saturated porous-nanofluid layer is numerically investigated. The inclined left and right walls of the trapezoidal enclosure are insulated. The bottom wall is partially heated at isotherm hot temperature, while the top wall is maintained at isotherm cold temperature. Finite element technique is used to numerically solve dimensionless Navier-Stoke equations for the nanofluid and porous-nanofluid media between inner adiabatic circular cylinder and trapezoidal enclosure. The numerical results are validated with those of Kim et al. [2008] in terms of streamlines and isotherms to check the accuracy of the present program. The validation illustrates a favorable agreement between the present work and Kim et al. The following parameters are studied: Rayleigh number (103 ≤ Ra ≤ 106 ), Darcy number (10-1 ≥ Da ≥ 10-5), nanoparticle volume fraction (0 ≤ ph ≤ 0.1), and porous layer thickness (0 ≤ Yp ≤ 100%).

In this study. The mixed convection in a square enclosure with a hot bottom wall and a conductive half-immersed rotating cylinder from its top wall is investigated numerically. The enclosure is filled with a copper-water nanofluid. The upper half of the cylinder is cooled by the surrounding air, whereas its solid lower half is exposed to the nanofluid. The two left and right sidewalls of the enclosure, together with the remaining regions of its top wall, are assumed to be adiabatic. The dimensionless governing equations are expressed for the velocity and the temperature formulation, and they are modeled by using COMSOL code based on the Galerkin finite element method. In the present work, the geometrical aspect ratio is considered to be varied as (0.2 ⤠R/L ⤠0.5), the thermal conductivity ratio is considered to be varied as 1 ⤠Kr ⤠10, the angular rotational velocity is considered to be varied as 0 â¤Î© ⤠1000, and the ambient convection heat transfer coefficient is considered to be varied as 5 ⤠h ⤠20. However, the solid volume fraction (Ï•), the Prandtl number (Pr), and the Rayleigh number (Ra) are considered to be fixed at Ï• = 0.02, Pr = 6.2, and Ra=105. It was found that the convection effect becomes more pronounced when the angular rotational velocity increases, whereas a reverse behavior is observed with an increase in the geometrical aspect ratio. Also, it was observed that the heat explorer depth begins to decrease as the angular rotational velocity increases until the increases of angular rotational velocity effect is diminishing therefore it may be the main target of the present research. This observation is seen for both considered values of the thermal conductivity ratio and the geometrical aspect ratio. Moreover, it was observed that both the local and the average Nusselt numbers increase as the geometrical aspect ratio increases. A comparison with a previously published numerical work is performed, and a good agreement between the results is observed. [ABSTRACT FROM AUTHOR]

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• The naturally cooled baffled U-shaped cavity is examined under the magnetic field. • The power-law non-Newtonian water-Fe 3 O 4 nanofluid is considered as coolant. • The average Nu rises with boosting aspect ratio and nanoparticle volume fraction. • The impact of n and Ra on average Nu is significant only for Ra =106. • The effect of Ha and n on average Nu is considerable only for the cases where Ha <30. This numerical work examines the impact of an external magnetic field on the hydrothermal aspects of natural convection of a power-law non-Newtonian nanofluid inside a baffled U-shape enclosure. The enclosure is heated from the bottom and cooled from the baffles while the other walls are thermally insulated. Sinusoidal profile is chosen to describe the temperature distribution along the bottom wall. A comprehensive analysis is conducted to study the influence of pertinent parameters including Rayleigh number (Ra), Hartmann number (Ha), nanoparticle volume fraction (ϕ), aspect ratio of cold baffles (AR), inclination angle, and power-law index (n) on the flow and heat transfer characteristics in detail by using Galerkin finite element method. The obtained results show that the impact of n on the Nusselt number (Nu) is considerable for Ra =106 and inappreciable below this value. The influence of n and Ha on the heat transfer is significant when Ha is smaller than 30. For Ha <30, there is a threshold value of nanoparticle after which the rise of n augments heat transfer, which is 5% for AR =0.4 and 7% for AR =0.6. The analysis of heat transfer and fluid flow in open cavities is important because of the diverse applications in thermal engineering. In this work, magnetic field, non-Newtonian power-law nanofluid, and sinusoidal heat flux are used to improve the performance of a naturally cooled U-shape cavity. It was found that the cooling performance of cavity augments with the rise of aspect ratio, nanoparticle volume fraction, Rayleigh number, while it reduces with boosting Hartmann number. Finally, it was revealed that the best cooling performance of cavity occurs at Ra =106, Ha= 0, ϕ =5% and AR =0.6 Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Study MHD mixed convection from two rotating cylinders in a porous trapezoid. • Study on Cu-water nanofluid in a porous medium with different Darcy numbers. • Higher effect of vertical magnetic on decreasing the stream function. • High effect of magnetic field angle on temperature and irreversibilities. The numerical simulation of MHD mixed convection due to a rotating circular solid cylinder in a trapezoidal enclosure filled with a Cu-water nanofluid saturated with a porous media was presented in the current paper. The midpoint of the top wall of the enclosure is considered as a center of a cylinder which has a different radius. The remaining of this wall is considered adiabatic. The bottom wall is heated with the temperature of T h and moving to the right hand, while sidewalls are kept isolated and stationary. The Hartmann number, thermal conductivity ratio, angular rotational velocity, Richardson number, inclination angle, cylinder radius, Darcy number, nanofluid concentration vary in the ranges of 0 to 100, 1 to 10, -5 to 5, 0.01 to 100, 0° to 90°, 0.2 to 0.4, 10 −5 to 10 −1 and 0 to 0.1, respectively. While the convection heat transfer coefficient is considered constant at (h = 5). It was found that, the vertical magnetic field decreases the stream function values more than the inclined and the horizontal fields. Also, the inclination angle of the magnetic field has a profound influence on the thermal performance inside the enclosure. The average Nusselt number rises by raising the Hartmann number, thermal conductivity ratio, cylinder radius and Darcy number, while it decreases by increasing the Richardson number. It was found also that, when the cylinder rotates in a counter clockwise direction (i.e., Ω = 5) and (K r = 10), the Nu ave decreases by about (90 %) when the (Ri) increases from 0.01 to 100. While, it increase by about (35 %) when the (Ha) increases from 0 to 100. Image, graphical abstract [ABSTRACT FROM AUTHOR]

The natural convection of heat transfer is presented numerically using a temperature gradient from the hot inner corrugated cylinder. Different inner corrugated numbers located inside a cooled wavy-walled enclosure filled with two layers were simulated. The right layer is filled with Ag nanofluid and the left with a fully saturated porous media with similar nanofluid. The porous media with the nanofluid was modeled using the Darcy–Brinkman model. The main dimensionless equations are solved numerically using the method of Galerkin. This study considered the following dimensionless parameters: the Rayleigh number (10 6 ≥ Ra ≥ 10 3 ), the Darcy number (0.1 ≥ Da ≥ 0.00001), the vertical location (0.2 ≥ H ≥ −0.2), the number of sinusoidal inner cylinders (6 ≥ N ≥ 3), fraction volume of the nanoparticle (0.1 ≥ ⱷ ≥ 0), and porous layer thickness (0.8 ≥ X P ≥ 0.2). Results suggest that to increase the fluid flow strength, the internal sinusoidal cylinder must move upward to increase the fluid flow strength. Increasing the thickness of the porous layer reduces the average heat transfer. Results indicate further that highest fluid flow strength occurs at N = 4 when the inner sinusoidal cylinder moves downward vertically. [ABSTRACT FROM AUTHOR]

The present work examines numerically the heat transfer and the buoyancy-driven flow within a U–shaped baffled enclosure filled with a nanofluid-saturated porous medium in the presence of an inclined magnetic field using a finite element scheme. The enclosure bottom wall is heated sinusoidally while the two baffles and the inner walls are maintained at a constant cold temperature. The rest walls of the enclosure are kept adiabatic. The parameters under investigation are Hartmann number (Ha), volume fraction (φ), Darcy number (Da), Rayleigh number (Ra), nanoparticles aspect ratio (AR), and the angle of applied magnetic field (γ). The results are crucial and illustrate that increasing the values of Ra, Da and the nanoparticles volume fraction enhances the heat transfer while the Hartmann number inversely affects the heat transfer augmentation. Moreover, the average Nusselt number (Nu ave) increases by increasing the enclosure aspect ratio. For the geometry under consideration and for a better heat transfer rate, it is recommended to choose an AR = 0.6 at Ha = 0 with a 0.1 vol fraction. [ABSTRACT FROM AUTHOR]