Unsteady Flow of Hybrid Nanofluid with MagnetohydrodynamicsRadiation-Natural Convection Effects in a U-Shaped Wavy Porous Cavity

In this paper,the unsteady magnetohydrodynamic(MHD)-radiation-natural convection of a hybrid nanofluid within a U-shaped wavy porous cavity is investigated.This problem has relevant applications in optimizing thermal management systems in electronic devices,solar energy collectors,and other industrial applications where efficient heat transfer is very important.The study is based on the application of a numerical approach using the Finite Difference Method(FDM)for the resolution of the governing equations,which incorporates the Rosseland approximation for thermal radiation and the Darcy-Brinkman-Forchheimer model for porous media.It was found that the increase of Hartmann number(Ha)causes a reduction of the average Nusselt number(Nu),with a maximum decrease of 25%observed as Ha increases from 0 to 50.In addition,the influence of the wall’s wave amplitude and the heat source length on the heat transfer rate was quantified,and it was revealed that at high wave amplitude,the average Nu increases by up to 15%.These findings suggest that manipulating magnetic field strength and cavity geometry can significantly enhance thermal performance.The novelty of this is related to the exploration of a U-shaped wavy cavity,which is not covered in previous studies,and to the detailed examination of the combined effects of magnetic fields,radiation,and hybrid nanofluids.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.

Impact of Viscous Dissipation and Ohmic Heating on Natural Convection Heat Transfer in Thermo-Magneto Generated Plume

The present investigation centers on the impact of viscous dissipation and ohmic heating on the plume generated by a line heat source under the impact of an aligned magnetic field.In this study,the flow model is adapted to incorporate ohmic heating and viscous dissipation by including the respective terms in the energy equation.A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow problem.Subsequently,a numerical solution is derived with stream function formulation for the system of coupled partial differential equations,which transmutes it into ordinary differential equations.To achieve this,the numerical properties of the problem are established through the utilization of the Shooting method in tandem with the MATLAB tool bvp4c.The graphical representations of both missing and specified boundary conditions depict the effects of the magnetic parameter,viscous dissipation variable,magnetic force parameter,Prandtl number,and magnetic Prandtl number.These are accompanied by a discussion of their respective physical implications.The observed results claimed that the velocity,current density,and temperature distribution decrease for enhancing magnetic parameters.Meanwhile,the skin friction and magnetic flux drop while the heat transfer rate increases with an increment in magnetic parameters.These fluid flow and heat transfer characteristics were observed to decrease for increasing viscous dissipation.The current work is novel in incorporating ohmic heating viscous dissipation in energy equations coupled with Max-well and magnetic induction equations.

NUMERICAL STUDY ON NATURAL CONVECTION HEAT TRANSFER INSIDE RECTANGULAR ENCLOSURE FILLED WITH ANISOTROPIC POROUS MEDIA

Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed numerically by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that: (1)the permeability ratio (K*=Ky/Kx) is an important factor affecting natural convection heat transfer in the porous media. As K' decreases, the circulation intensity of the natural convectioncells increase significantly, resulting in an enhancement of heat transfer coefficient; (2)the increase of Darcy number (aa=Ky/H2) implies that the viscous effect is more significant. As Da≥10-, there exists a certain difference between the Darcy model and the Brinkman model. It is more significant at a lower permeability ratio. In particalar, with K*≤0. 25, the Nusselt number for Da=10-3 would differ form that of Darcy model up to an amount of 30K. The Darcy flow as depicted by Darcy model is no longer existing and an analysis neglecting the viscous effect will inevitably be of considerable error.

Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt

In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.

Simulation on scrap melting behavior and carbon diffusion under natural convection

A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reasonably well with experimental ones.Scrap melting was subdivided into four stages:formation of a solidified layer,rapid melting of the solidified layer,carburization,and carburization+normal melting.The carburization stage could not be ignored at low temperature because the carburization time for the sample investigated was 214 s at 1573 K compared to 12 s at 1723 K.The thickness of the boundary layer with significant concentration difference at 1573 K increased from 130μm at 5 s to 140μm at 60 s.The maximum velocity caused by natural convection decreased from 0.029 m·s^(−1)at 5 s to 0.009 m·s^(−1)at 634 s because the differences in temperature and density between the molten metal and scrap decreased with time.

Simulation on microstructure evolution of Al-Si alloy under effect of natural convection during solidification

The solidification microstructure of Al-Si alloy was observed in the experiment,the second dendrite arm spacing(SDAS)was measured,and the effect of temperature on the microstructure was analyzed.Phase-field(PF)model incorporating natural convection caused by gravity was employed to simulate the microstructure evolution of Al-Si alloy under the experimental conditions.Good agreements between the experimental and simulation results verified the reliability of the simulation approach proposed in this study.Based on the proposed model,a series of simulation cases(2D and 3D)were performed to investigate the evolution of columnar and equiaxed dendritic structures.It was found that the solute content of the alloy had little impact on the microstructure evolution,while the solute expansion coefficient had obvious effect on the dendrite tip velocities.Significant improvement of computational efficiency was achieved via novel algorithms,making it possible to perform massive simulation for studying the evolution of solidification microstructures,which is hard to be directly observed in experiments via synchrotron radiation for Al-Si alloy.

Effects of porous material on transient natural convection heat transfer of nano-fluids inside a triangular chamber

This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section.The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method,taking into account the Darcy–Brinkman model for porous medium.It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial,transient,and semi-steady.The features of each step are provided in detail.The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper)inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate.In contrast,as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide)inside the chamber increased,convection heat transfer rate improved.At the same time,it was observed that the use of both nano-fluids(single and hybrid)in the porous environment of the aluminum foam could improve convection.

Characterization of size effect of natural convection in melting process of phase change material in square cavity

The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phase change happens,and how to quantitatively describe such an influence is still challenging.On the other hand,the simulation of natural convection process is considerably difficult,involving complex fluid flow in a region changing with time,and is typically not operable in practice.To overcome these obstacles,the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation,and ultimately a correlation equation to represent its contribution is proposed.Firstly,the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently,a comprehensive investigation is performed numerically for various domain sizes.The results show that the melting behavior of paraffin is dominated by the thermal convection.When the melting time exceeds 50 s,a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall,and then its influencing range gradually increases to accelerate the melting of paraffin.However,its intensity gradually decreases as the distance between the melting front and the heating wall increases.Besides,it is found that the correlation between the total melting time and the domain size approximately exhibits a power law.When the domain size is less than 2 mm,the accelerating effect of natural convection becomes very weak and can be ignored in practice.Moreover,in order to simplify the complex calculation of natural convection,the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time,and an empirical correlation is given for engineering applications.

Parametric study of natural convection over horizontal annular finned tube

Natural convection heat transfer from annular finned tubes was studied numerically. Effects of fin spacing, temperature difference and tube diameter on flow pathlines and local heat transfer were also studied. It was shown that pathlines remain mostly circular for different geometries. Moreover, the contributions of fin periphery, fin side and bare tube to heat transfer were specified. It was shown that the heat transfer per unit area of fin periphery can be several times that of other parts. Moreover, in higher finspacing, the heat transfer from the bare tube can be more important than fin sides.

Enhancement of natural convection heat transfer from a fin by triangular perforation of bases parallel and toward its tip

This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations （their bases parallel and toward the fin tip） under natural convection. The fin＇s heat dissipation rate is compared to that of an equivalent solid one. The parameters considered are geometrical dimensions and thermal properties of the fin and the perforations. The gain in the heat transfer enhancement and the fin weight reduction due to the perforations are considered. The study shows that the heat dissipation from the perforated fin for a certain range of triangular perforation dimensions and spaces between perforations result in improvement in the heat transfer over the equivalent solid fin. The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thickness are increased.

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the con- sidered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylin- der of concentric annuli. The effects of the various phys- ical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap be- tween the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening ten- dency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.

Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux

The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das' nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls(wavy and undulation numbers)are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

Experimental investigation of chimney-enhanced natural convection in hexagonal honeycombs

The natural convective heat transfer performance of an aluminum hexagonal honeycomb acting as a novel heat sink for LED cooling is experi- mentally investigated. The concept of adding an adiabatic square chimney ex- tension for heat transfer enhancement is proposed, and the effects of chimney shape, height, and diameter are quantified. The average Nuav of a heated hon- eycomb with straight chimney is significantly higher than that without chimney, and the enhancement increases with increasing chimney height. At a given chim- ney height, honeycombs with divergent chimneys perform better than those with convergent ones. For a fixed divergent angle, the Nuav number increases mono- tonically with increasing chimney height. In contrast, with the convergent angle fixed, there exists an optimal chimney height to achieve maximum heat transfer.

NUMERICAL STUDY OF NATURAL CONVECTION FLOW IN A VERTICAL SLOT

The stability of convective motion, generated by a lateral temperature difference across a vertical slot, is studied numerically over a range ofGr=5000 to 1.5 × 105,Pr=0.01 to 10, andA=8,16 and 20. Various cellular flow structures and temperature patterns are illustrated. Several branches of solutions characterized by different numbers of the cells in the flow patterns as well as by both steady and unsteady multicellular patterns are found for low-Prandtl-number fluid in the vertical slot. Meanwhile, the behaviors of the temperature variation and heat transfer are also discussed.

Natural convection effects on TNT solidification inside a shaped charge mold

High Explosive Anti-Tank(HEAT) warheads and ammunitions are frequently produced by explosive casting inside an axis-symmetric mold with an inverted conical geometry in the basis. In order to prevent manufacturing defects, the solidification process must be controlled. In this study, a dimensionless solidification model has been proposed to investigate the heat transfer considering the natural convection inside the liquid explosive and the numerical simulations were performed by using COMSOL Multiphysics and Modeling Software, employing trinitrotoluene(TNT) thermophysical properties. The effect of three different boundary conditions on the top of the mold have been evaluated: convection, adiabatic and isothermal. It has been observed that solidification process was faster for convection case and slower for isothermal case, while an intermediary total solidification time value was found for adiabatic case.Moreover, liquid explosive was completely surrounded by solid explosive during the solidification process for convection case and also for adiabatic case through the end of the process. Otherwise, it was not observed for isothermal case. The natural convection effects promoted a vortex inside the liquid explosive, accelerating the heat transfer process. It has been concluded that isothermal mold top boundary condition should be preferred to prevent manufacturing defects, avoiding high thermal stress.

Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2O3-water nanofluid with discrete heating

We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al2O3-water).The upper and bottom walls of the cavity have a wavy shape.The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angleγ,an opposite clockwise direction.For the numerical simulation,the finite element technique is employed.The ranges of the characteristics are as follows:the Rayleigh number(10^3≤Ra≤10^5),the Hartmann number(0≤Ha≤100),the nanoparticle hybrid concentration(ϕAl2O3,ϕCu=0,0.025,0.05),the magnetic field orientation(0≤γ≤2π),and the Prandtl number Pr,the amplitude of wavy cavity A,and the number of waviness n are fixed at Pr=7,A=0.1,and n=3,respectively.The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement.The effects of the governing parameters on the energy transport and fluid flow parameters are studied.The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement.When the Rayleigh number is raised,the Nusselt number is increased,too.For moderate Rayleigh numbers,the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid,followed by the Al2O3-nanofluid.The nature of motion and energy transport parameters has been scrutinized.

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

The lattice Boltzmann method(LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90?. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.