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The control and improvement of heat transfer in enclosures is very important in several engineering applications. In the current two-dimensional numerical study, the mixed convection and entropy generation of water flowing inside a square vented enclosure that contains four vibrating cylinders with relatively low frequencies fr = 1, 2, 3, 5 Hz in the vertical and horizontal directions are reported. The effects of Reynolds and Richardson numbers, vibration frequency, vibration amplitude, and the direction of the cylinders' vibration on heat transfer and entropy generation are presented for various cases. The horizontal walls of the enclosure are kept adiabatic while the vertical left and right walls are hot and cold, respectively. The linear regression analysis was used to reveal the rate of increase in the Nusselt number with the Reynolds and Richardson numbers number for each cases. Series of analyses show that the existence and the vibration of the cylinders increases heat transfer but the vibration in the horizontal direction is more effective since the top and bottom walls of the enclosure are adiabatic. It is found that the entropy generation due to heat transfer is low at the center of the enclosure. The direct relationship between the heat transfer and both Reynolds and Richardson numbers is reported. In terms of heat transfer, it is found that the critical vibration frequency and amplitude are fr = 4 and A = 0.05L and 0.075L. [ABSTRACT FROM AUTHOR]

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]

• 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]