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The current study investigates the influence of MHD on the natural heat transfer considering the irreversibility in a complex-shaped cavity with the existence of inner roundish heater with four attached fins utilizing finite element formulation. Three different cases are considered to figure out the major characteristics of temperature, stream function and total generated entropy, Nusselt number in addition to Bejan number. Concentrated attention is directed to the enclosure geometry modifications and the varied length of attached fins and their impacts. The parameters of study are ranged as follows; Rayleigh number 10 3 ≤ Ra ≤ 10 6 , Hartmann number 0 ≤ Ha ≤ 60 , fins' length 0.1 ≤ H ≤ 0.3 . The novelty of the present work is on studying all of these parameters in the complex enclosure considering three different cases of the shape of the outer walls so that the star-shaped enclosure is classified as case 1. With increasing the length that separated between the outer arc of the star enclosure, the octagonal-shaped enclosure will appear as denoted in case 2 and 3. It had been seen that at low Rayleigh number Ra = 10 4 , case one is the best choice in heat transfer bettering while it is the lowest case at high Rayleigh number Ra = 10 6 . Additionally, the influence of Hartmann number on the total entropy generation reduction percentage for case three is 63.57 % while it is 51.11% for case two while Hartmann number had negligible impact of entropy generation reduction for case one. Lastly, the highest Bejan number is at fin length H = 0.3 is recorded for case one. [ABSTRACT FROM AUTHOR]

Enhancing thermal performance and lowering heat loss in energy conversion systems are essential, especially for new and complicated products that make this requirement worse. In order to address this difficulty, this study looks at fluid flow and heat transmission using hybrid nanofluid and nanoporous materials in combination cavities. The numerical simulation of natural convection within a hollow two-dimensional cavity comprised of two connected tilted squares with a circular hollow at the center is investigated. The inner heated square is filled with a nanoporous material, whereas the rest of the cavity is filled with Cu-Al2O3 hybrid nanofluid. The COMSOL Multiphysics software is utilized to simulate the dimensionless governing equations. A comparison with previously published research showed a good agreement. Calculations are performed for different values of Ra number (Ra: 103, 104, 105, and 106), Darcy number (Da: 10–1, 10–2, 10–3, 10–4, and 10–5), volume fraction (φ: 0, 0.02, 0.04, and 0.06), width (W: 0, 0.1, 0.2, 0.3, and 0.4), and uniform porosity (ε: 0.2, 0.4, 0.6, and 0.8). The results demonstrated that the increase of the porosity leads to a decrease in the Nu number with the Rayleigh number increase. Darcy and Rayleigh numbers have a significant impact on the width (W) between the hybrid nanofluid and nanoporous layers. In addition to the above, the fluid flow slows down at Ra = 103, which causes S ˙ gen , T ⌣ and Be to increase. The rising of Ra from 104 to 105 causes no change in the S ˙ gen , T ⌣ because heat is primarily transported by conduction, but the maximum Be number is reduced. [ABSTRACT FROM AUTHOR]

The current work investigated numerically the natural convection within a square enclosure filled with nanofluid by examining four different types of attached fins (rigid fins, flexible oscillating in the same and opposing directions) and comparing it to the case without fins. The governing equations of heat and fluid flow (mass, energy and momentum) of fluid had been solved using the finite element scheme. The results are validated with the previous studies and presented in terms of streamlines, isotherm and Nusselt number. The influence of Rayleigh number (104 ≤ Ra ≤ 106), dimensionless time (10–4 ≤ τ ≤ 1), thermal conductivity ratios (1 ≤ ks ≤ 1000), the amplitude of the flexible fins (10–2 ≤ A ≤ 0.1) and frequency (0.05 ≤ λ ≤ 0.5) are studied. The governing parameters have been tested based upon their influence on fluid flow and heat transfer for the current study. The results are shown as contours of vortices, velocity, streamlines and isotherms as well as the local and average Nusselt number (Nuave). It is observed that the larger amounts of heat are transmitted by convection at higher thermal conductivity ratios, and the greater the magnitude of the Nusselt number demonstrates the pronounced effect of the fin oscillation. In addition, when the flexible fins oscillated in the same directions, the Nusselt number increased by 18.34% as compared to the case without fins. Furthermore, increasing the flexible fins' amplitude improves the oscillating motion of the fins inside the cavity, which improves fluid flow and heat transmission strength. [ABSTRACT FROM AUTHOR]

The current study focuses on the transient mixed convection within a vented square enclosure with differentially heated vertical walls and a flexible baffle coupled to a circular solid cylinder. In numerical analysis, the COMSOL Multiphysics tool is used to simulate and solve two-dimensional governing equations using the Galerkin finite element approach and the arbitrary Lagrange–Euler (ALE) method, as well as the coupling of structure deflection and fluid flow. This work considered the effects of changing locations of flexible baffles attached to a cylinder on thermal and flow structures. The effect of several parameters, such as Richardson number (10–1 ≤ Ri ≤ 102), Cauchy number (10–12 ≤ Ca ≤ 10–4), and Reynolds numbers, (50 ≤ Re ≤ 250) on convective heat transfer characteristics are investigated for time 0.01 to 10 s. It is observed that changing time steps leads to a continuous change in fluid flow intensity which reflects on the deformation direction of the flexible baffle. The results indicated that the cavity with flexible baffle has the best average Nusselt number compared to cavities with rigid baffle and without baffles, respectively. As Re is raised from 50 to 250, the percentage of the average Nusselt number increased to 40% at Ri = 0.1 and 59% at Ri = 200. [ABSTRACT FROM AUTHOR]

In the present paper, numerical investigations of the magnetohydrodynamics forced convection of CNT–water nanofluid inside a square enclosure with one inlet and one outlet were performed. The analysis was carried out for a wide range of Reynolds number ( 100 ≤ R e ≤ 1000 ), Hartmann number ( 0 ≤ H a ≤ 60 ), inclination angle of the magnetic field ( 0 ∘ ≤ γ ≤ 90 ∘ ), elasticity of the bottom and left walls of the enclosure ( 10 4 ≤ E ≤ 10 7 ), location of the center of the hexagonal body in horizontal directions ( 0.3 ≤ x 0 / L ≤ 0.7 ) and in normal directions ( 0.25 ≤ y 0 / L ≤ 0.75 ), size of the internal hexagonal body ( 0.1 ≤ a / L ≤ 0.3 ), and, finally, the volume fraction of the nanoparticles ( φ = 0 and 0.1). For the flexible walls of the enclosure, a series of coupled fluid–structure interaction (FSI) analyses were accomplished by utilizing the Arbitrary Lagrangian–Eulerian formulation. It has been revealed that the bottom wall of the enclosure is very sensitive to the elastic wall, while the Nusselt number on the top wall increases with Hartmann number no matter which wall is elastic. It is also the most contributor to the heat transfer at Reynolds numbers of R e = 100 and 500, while the contribution of other walls changes with Reynolds number. [ABSTRACT FROM AUTHOR]

The combination of nano fluid and changing cross-section mini-channel heat sink effects have become a remarkable choice for the use of thermal devices such as miniature electronic devices to be effectively cooled. In this paper, the comparison of three dimensional straight and wavy channel configuration with using different types nano fluids are numerically investigated. The effects of wave amplitude and A particular type of volume fraction of (Copper Oxide CuO, Dimond Al2O3, Iron Oxide Fe3O4, Titanium Oxide TiO2 and Silver Ag-nano fluids are offered. Three amplitudes of waves (0.15 mm, 0.2 mm and 0.25 mm) and Reynold's number from 200 to 1000 and concentration volume varieties from 0 to 0.075 are used. The effect on thermal resistance, pressures drop, factor of friction of the mini channel is displayed. It is observed that the mini-channel sink's heat transfer efficiency is greatly enhanced compared to the straight channel in an event of adding distilled water as accoolant. The results indicate that nano fluid and wavy mini-channel can boost the heat sink's hydrothermal efficiency and Ag- water nano fluid in term of heat transfer, it outperforms other nanofluids an enhancement in the Nusselt number reached to 54% at concentration volume 0.075. [ABSTRACT FROM AUTHOR]

In this study, Galerkin Finite Element Method or GFEM is used for the modeling of mixed convection with the entropy generation in wavy lid-driven porous enclosure filled by the CNT-water nanofluid under the magnetic field. Two different cases of boundary conditions for hot and cold walls are considered to study the fluid flow (streamlines) and heat transfer (local and average Nusselt numbers) as well as the entropy generation parameters. Richardson (Ri), Darcy (Da), Hartmann angle (γ), Amplitude (A), Number of peaks (N), Volume fraction (φ), Heat generation factor (λ), Hartmann number (Ha) and Reynolds number (Re) are studied parameters in this study which results indicated that at low Richardson numbers (< 1) increasing the inclined angle of magnetic field, decreases the Nu numbers, but at larger Richardson numbers (> 1) it improves the Nu numbers. [ABSTRACT FROM AUTHOR]

Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper. [ABSTRACT FROM AUTHOR]

In this paper, numerical Galerkin Finite Element Method (GFEM) is applied for conjugate heat-transfer of a rotating cylinder immersed in Fe3O4-water nanofluid under the heat-flux and magnetic field. The outer boundaries of the cavity were maintained at low temperatures while beside the cylinder were insulated. It is assumed that the cylinder rotates in both clockwise and counter-clockwise directions. The dimensionless governing equations such as velocity, pressure, and temperature formulation were analyzed by the GFEM. The results were evaluated using the governing parameters such as nanoparticles (NPs) volume fraction, Hartmann and Rayleigh numbers, magnetic field angle and NPs shapes. As a main result, the average Nusselt number increases by increasing the NPs volume fraction, inclination angle and thermal conductivity ratios, while increasing the Hartmann number decreased the Nusselt number. Furthermore, platelet NPs had the maximum average Nusselt number and spherical NPs made the minimum values of Nusselt numbers among examined NPs shapes. [ABSTRACT FROM AUTHOR]

In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle's core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ ε ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6 < n < 1.4), Darcy number (10−5 < Da < 10−1), volume fraction (0 < ∅ < 0.2), and undulation number (1 < N < 4) on the thermal performance of the cavity for Prandtl numbers (Pr) ranging from 0.015 to 13.4 and Rayleigh number (Ra) equal to 105. Results showed that increasing Prandtl and Darcy numbers raised the average Nusselt number. However, increasing the power-law index reduced the average Nusselt number. When the non-Newtonian fluid behaves as a shear-thinning fluid (n = 0.7) and Pr = 13.4, the effect of the undulations number of the sinusoidal vertical interface on average Nu is not evident for a given range of volume fraction. [ABSTRACT FROM AUTHOR]