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This research presents a novel approach by combining magnetohydrodynamic (MHD) flow with ohmic heating to investigate the conjugate mixed convective transport of ferrofluid in a discretely heated, smooth/wavy‐walled, square‐shaped porous compartment featuring a clockwise spinning cylindrical body positioned at various locations. It aims to maximize heat transfer efficiency and minimize entropy production. Numerical solutions are obtained using the Galerkin finite element weighted residual method to solve the two‐dimensional Navier–Stokes and heat energy equations. The parametric variations include Grashof number (10 6 ≤ Gr ≤ 10 8 ), Reynolds number (10 3 ≤ Re ≤ 10 4 ), and Hartmann number (31.62 ≤ Ha ≤ 100), dimensionless cylinder diameter (0.2 ≤ D ≤ 0.4), dimensionless cylinder vertical position (0.25 ≤ Y c ≤ 0.75), and dimensionless heater strip size (0.25 ≤ d h ≤ 0.75). The results are quantitatively expressed through the Nusselt number ( Nu ) of the hot wall, the mean fluid temperature, the overall entropy production, and the thermal performance criterion ( TPC ). Extensive analysis reveals that a transition from a conduction‐dominated region to a convection‐dominated region occurs at Gr = 3 × 10 7 , Re = 5477.23, and Ha = 74. Notably, the maximum values of Gr , Re , and Ha at d h = 0.25, D = 0.2, and Y c = 0.75 result in a 36.84% increase in the Nusselt number and a 64.89% reduction in TPC compared to those at d h = 0.75, thereby indicating optimal conditions. In contrast, the largest heater size yields the poorest performance, with a 26.93% drop in Nu and a 265.22% increase in TPC . Insights into the MHD mixed convective flow with a ferrofluid‐filled copper powder porous medium within a corrugated cavity at higher Grashof numbers contribute to a novel and deeper understanding of velocity and temperature distributions, heat transfer, and irreversibility, which mimics a nuclear reactor fuel channel and fluid‐chilling blankets.

In this study, mixed convection heat transfer of the non-Newtonian power-law nanofluid including CuO nanoparticles, inside a partially porous square enclosure with a concentric rotating cylinder and a hot side wall is numerically investigated. Two-phase mixture model is utilized for nanofluid flow simulation and the mixture viscosity and thermal conductivity are computed by Corcione’s correlation. The effect of different angular velocity (− 4000 ≤ Ω ≤ 4000) for various Rayleigh (10 4  ≤  Ra  ≤ 10 6 ), Darcy (10 −4  ≤  Da  ≤ 10 −1 ), power-law index (0.8 ≤  n  ≥ 1.2) and effective to base fluid thermal conductivity ratio ( k eff /k f = 16, 4) are studied on heat transfer. Results are presented and compared in terms of the average Nusselt number, and streamline and isotherm contours. Outcomes show that for different kinds of fluid, depending on the value of Ra , Da , k eff /k f and the amount and direction of angular velocity, heat transfer can be improved by augmenting heat convection and also can be deteriorated by increasing viscosity. Consequently, optimal values of Ra , Da , k eff /k f and Ω exist in order to maximize the average Nu number.

In this paper, we present the magnetohydrodynamic (MHD) equations for the flow between two concentric rotating cylinders. The primary objective is to investigate the instability and attractor bifurcation of the simplified governing equations. The analysis is based on recently developed theories, including the bifurcation theory for nonlinear dynamical systems and differential operators on 3-D Riemann manifolds. We begin by formulating the MHD equations coupled with temperature in cylindrical coordinates, defining the control parameters, which are related with the magnetic field, temperature difference, and the angular speeds of the inner and outer cylinders. It is shown that the system always undergoes a dynamical transition as control parameter equation crosses the first critical value λC . The type of transition is determined by the multiplicity of the critical eigenvalue. Then, we provide approximate expressions for the bifurcation and the structure of the attractor, along with necessary explanations for the obtained results. Finally, we present numerical computations to interpret the results of the theorem and provide a visual analysis of the velocity field and temperature distribution for the four stable nodes of the attractor through graphical representation.

Purpose This study aims to investigate magnetohydrodynamic (MHD) conjugate pure mixed convection considering interior heat production and resistive heating inside a square closed/open cavity featuring a rotating cylinder for aiding (clockwise) and opposing (counterclockwise) flow configurations. Moreover, the impacts of altering cylinder size and conductivity on the system’s overall performance to determine optimum conditions are examined in this investigation. Design/methodology/approach The closed chamber is differentially heated by keeping high and low temperatures at the vertical boundaries. In contrast, the open cavity has a heated left wall and an open right boundary. The Galerkin finite element method is used to solve the Navier–Stokes and the thermal energy equations, which construct the present study’s mathematical framework. Numerical simulations are conducted for the specified ranges of several controlling parameters: Reynolds (31.62 ≤ Re ≤ 1000), Grashof (103 ≤ Gr ≤ 106) and Hartmann numbers (0 ≤ Ha ≤ 31.62), and volumetric heat generation coefficient (Δ = 0, 3). Findings When Gr, Re and Ha simultaneously increase, the average Nusselt number along the warmed boundary rises accordingly. Conversely, interior heat production lowers heat transmission within the computational domain, which is also monitored regarding mean fluid temperature, overall entropy production and thermal performance criterion. Finally, the open cavity confirms better thermal performance than the closed cavity. Originality/value Comprehending the impacts of the magnetic field, Joule heating, internal heat generation and enclosed or open boundary on pure MHD combined free-forced convective flow offers valuable understandings of temperature fluctuations, velocity propagations, heat transport and irretrievable energy loss in numerous engineering applications.

Mixed convection inside a square cavity with internal rotating heater and cooler is analyzed numerically by simultaneous application of porous media and nanofluid as a heat transfer enhancement technique. Optimized multi-block porous foams are utilized to enhance the heat transfer. This type of medium could improve the heat transfer rate with manipulation and selection of porous regions’ pore size (or permeability) by amplifying the flow in critical regions and weakening it in non-effective areas. The whole cavity domain is assumed to be made of 25 distinct porous blocks. At first, the effects of the various rotation directions have been investigated and then the optimum distribution of pore size in the porous media is determined in a manner to maximize the heat transfer rate using the pattern search optimization algorithm. Finally, simultaneous effects of application of multi-block porous media and nanoparticle addition to the base fluid on the average Nusselt number are studied in various conditions. For this purpose, various volume fractions of the nanoparticles are implemented to investigate the effects of the different values of the volume fraction on Nu number. The optimization has done for different Ri and Ra numbers for achieving to the best distribution in each condition. In the best condition, 20.4% increase in the heat transfer is obtained.

The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied numerically. The fluid inside the enclosure is a CuO–water nanofluid layer in the top space of it, while the bottom space includes a CuO–water nanofluid saturated with a porous medium. Both the right and left sidewalls are assumed adiabatic, while the bottom and the top walls of the enclosure are maintained, respectively, at the hot and cold temperatures. The dimensionless governing equations are expressed for velocity and temperature formulation and modeled by using COMSOL code based on the Galerkin finite element method. Parametric studies on the effects of various significant parameters such as Rayleigh number, Darcy number, the inner cylinder radius, the porous layer thickness, the angular rotational velocity, the solid volume fraction and the number of undulations on the flow and thermal fields together with the heat transfer rate have been performed. The highest value of the stream function for (Ra = 103 and Ra = 105) is seen at (R = 0.2 and S = 0.2). The same thing is observed, when the bottom wall is considered wavy. For (Ra = 103 and N = 0) and (0.5 ≤ S ≤ 0.8), it can be seen that as the inner cylinder radius increases from (R = 0.1) to (R = 0.3), the stream function values increase continuously. It is found that the average Nusselt number increases as the Rayleigh and Darcy numbers, the solid volume fraction, inner cylinder radius and the angular rotational velocity of the cylinder increase, while it decreases as the porous layer thickness and the number of undulations increase. Comparisons with previously published numerical works are performed, and good agreements between the results are observed.

The integration of cavities designed with distinct specifications enhances the convective heat transfer, leads to improved performance of engineering systems. The current research focuses on numerical investigation of mixed convection within the cavity, which features a partially heated wall and a rotating cylinder. The cavity is filled with hybrid nanofluid comprising Al [Formula omitted]O [Formula omitted] and Cu nanoparticles suspended in water, serving as base fluid. The dimensionless governing equations were derived with a novel transformation of parameters along with consideration of the two-phase Buongiorno model. The input parameters examined included the Rayleigh number ( [Formula omitted]), the dimensionless radius of the cylinder ( [Formula omitted]), the angular rotational velocity of the cylinder ( [Formula omitted]), the concentration of nanoparticles ( [Formula omitted]), and the dimensionless length of partially heated wall. Utilizing COMSOL Multiphysics as a simulation platform, Galerkin's Weighted Residual Method is used to solve the governing equations. The impact of varying parameters is analyzed through the visualization of streamlines, dimensionless temperature with isothermal lines, normalized solid volume fraction, and their influence on both local and average Nusselt numbers. The observed results indicate an indirect relationship between average Nusselt number and the length of the partially heated wall. Moreover, the careful consideration of the varying parameters discussed leads to improved heat transfer performance of the hybrid nanofluid in the cavity. The highest value of Nusselt number attained is 8.9456 at [Formula omitted], [Formula omitted] and [Formula omitted], underscoring a notable achievement that surpasses the values reported in previous works. The findings of this study offer valuable implications for optimizing convective heat transfer in applications, such as heat exchangers and electronic cooling systems.

Mixed convection in a lid-driven square cavity with different walls temperature in the existence of four rotating cylinders having harmonic motion is simulated numerically for various parameters such as the solid volume fraction (0 ≤ ϕ ≤ 0.03), Richardson number (0.1 ≤ Ri ≤ 10) and type of motion for each cylinder. Cu–water nanofluids are considered as fluid inside the enclosure. A comparison of full rotation and harmonic rotation in steady and transient cases was made to get a better understanding of the effect of harmonic rotation. The consequences of this study are obtainable in terms of average and local Nusselt numbers, isotherm contours, streamlines contours, velocity profiles, PEC, and entropy generation profiles. Obtained results show that the heat transfer is dependent on the angular velocity of the cylinder, type of rotation, and the nanoparticle concentration. Adding nanoparticles causes to improve the heat transfer rate. However, the effect of the nanofluids on geometry has decreased for the PEC, except for Ri = 1 and a few particular cases. Also, according to the Nusselt number graphs, we can tell that the harmonic motion in this study did not have a considerable effect on the heat transfer rate.

Numerical simulations are carried out to investigate the vortex-induced vibrations of a two-degree-of-freedom (2DOF) near-wall rotating cylinder. Considering the effects of gap ratio, reduced velocity and rotational rate, the amplitude response, wake variations and fluid forces are analyzed, with the Reynolds number of 200 and the mass ratio set to 1.6. The correlative mechanism in the wake–hydrodynamics–vibration is revealed. The results show that the influence of the wall dominates the vortex-induced vibration of the cylinder. The effect of the wall on the vibration weakens as the gap ratio increases, and the effect of the wall on the vibration is negligible when H/D > 1.1. The forward rotation of the cylinder enhances the wall effect, while the backward rotation presents the reverse effect. The vortex-induced vibration of the cylinder is suppressed when 0 < α < 1, and the amplitude range is concentrated at Vr ∈ (3, 5). The wake mode can be divided into five modes, and the wake modes are clarified under different rotation rates and reduced velocities.

Control of flow past a circular cylinder using a rotating control rod is investigated by conducting two-dimensional numerical simulations with a Reynolds number of 200, a rod-to-cylinder diameter ratio of 0.2, a gap ratio of 0.2, position angles of the control rod between 0° and 180°, and rotation rates between −7 and 7. The rotation rate is positive if the cylinder rotates in the anticlockwise direction. The aim of this paper is to discover the effects of the position angle and the rotation rate on flow control. If the rod is placed at the side (position angle = 90°) or nearly to the side of the cylinder (position angle = 45° and 135°), the rotating rod affects the flow in three ways, depending on its rotation rate: (1) strong negative rotation of the rod weakens the negative free shear layers and reduces the lift; (2) flow through the gap interferes with vortex shedding when the rotation rate is small in either direction; and (3) strong positive rotation of the rod enhances the negative free shear layers and increases the lift coefficient. Placing a rotation rod immediately in front of or behind the cylinder (position angle = 0° or 180°) causes a reduction in the lift coefficient for all rotation rates.