Impacts of Heat Flux Distribution, Sloping Magnetic Field and Magnetic Nanoparticles on the Natural Convective Flow Contained in a Square Cavity

In the present paper,the effect of the heat flux distribution on the natural convective flow inside a square cavity in the presence of a sloping magnetic field and magnetic nanoparticles is explored numerically.The nondimensional governing equations are solved in the framework of a finite element method implemented using the Galerkin approach.The role played by numerous model parameters in influencing the emerging thermal and concentration fields is examined;among them are:the location of the heat source and its lengthH
,the magnitude of the thermal Rayleigh number,the nanoparticles shape and volume fraction,and the Hartmann number.It is found that the nanofluid velocity becomes higher when the thermal source length,the nanoparticles volume fraction and/or the thermal Rayleigh number are increased,while it decreases as the Hartmann number Ha grows and the position of the heat source moves toward the center of the lower wall of the cavity.Moreover,the temperature of the nanofluid grows with the extension of the thermal source and decreases slowly when the heat flux position moves toward the center of the lower wall.The outcomes of the research also indicate that the average Nusselt number becomes smaller on increasing Hartmann number Ha and heat source length H^(*).The addition of Fe_(3)O_(4) to engine oil leads to a higher rate of heat transfer with respect to the addition of SiO_(2) particles.Blade-shaped nanoparticles generate the highest value of the Nusselt number compared to all the other considered shapes.

Numerical Study of Natural Convective Heat Transfer in an Air Filled Square Cavity Heated from Below and Symmetrically Cooled from the Sides with a Partition in the Hot Wall

A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.

EFFECTS OF TRANSVERSE OSCILLATIONS ON NATURAL CONVECTIVE FLOW INDUCED BY COMBINED THERMAL AND MASS DIFFUSIONS IN POROUS MEDIA

This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suction velocity of fluids, The analytical results for the problem are obtained based on the method of small parameter, and show that the natural circulation in the porous medium is affected by this kind of oscillation.

Natural convective heat transfer in a square enclosure utilizing magnetic nanoparticles

In the present paper,unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically.The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated.The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations.In numerical simulations,four types of nanoparticles such as magnetite(Fe_(3)O_(4)),cobalt ferrite(CoFe_(2)O_(4)),Mn-Zn ferrite(Mn-ZnFe_(2)O_(4)),and silicon dioxide(SiO2),and three types of base fluids such as water(H_(2)O),engine oil(EO)and kerosene(Ke)have been considered.Comparisons with previously published work are performed and excellent agreement is obtained.The effects of various model parameters such as thermal Rayleigh number,nanoparticles volume fraction and nanoparticles shape factor are studied.The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify.The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles.

Laminar Natural Convective Heat Transfer in theEnclosed Evacuated Collector Tube with East-West Symmetric Heat Input

Heat transfer in the evacuated collector tube is a three-dimensional laminar natural convection prob-lem driven by buoyancy. Because of its complexity, no effective theoretical model is available despiteof limited experimental work which is confined to one aspect- The present work aims to depict theconvective heat transfer inside a tweended inclined tube with East-West symmetric heat input us-ing numerical methods. Based on reasonable assumptions, governing equations of the inside fluid areestabllshed. The corresponding discretizated equations are solved by employing numerical methods.The calculated results are displayed for velocity and temperature profiles on different cross-sectionalplanes, which present the flow pattern characterized by upflow and dowallow along the axial direc-tion and adherent flow along the peripheral direction, and the heat transfer process from the wall tothe center. Furthermore, the transient Nusselt number and average temperature level are shown anddiscussed. Finally, the parametric effects of the tube radius and the heat input on the flow and heattransfer are also given.

Natural Convective Heat and Mass Transfer on a Vertical Heated Plate for Water Flow Containing Metal Corrosion Particles

Corrosion products of structural materials when contained in water usually are in two states:soluble state and colloidal particles with diameter about 10^(-3)—10^(-1)μm.Deposits of such corrosion products on tube surfaces under high pressure will jeopardize the operating economy of power plant equipment and even result in accidents. A numerical study is reported in this paper of the natural convective heat and mass transfer on a vertical heated plate subject to the first or mixed kind of boundary conditions for high-pressure water(P=17MPa)containing metal corrosion products with consideration of variable thermophysical properties.

Natural Convective Heat and Mass Transfer of Water with Corrosion Products at Super-Critical Pressures under Cooling Conditions

A numerical study is reported of laminar natural convective heat and mass transfer on a vertical cooled plate for water containing metal corrosion products at super-critical pressures. The influence of variable properties at super-critical pressures on natural convection has been analyzed. The difference between heat and mass transfer under cooling or heating conditions is also discussed and some correlations for heat and mass transfer under cooling conditions are recommended.

Natural convective heat transfer and nanofluid flow in a cavity with top wavywall and corner heater

A numerical analysis of natural convection of nanofluid in a wavy-walled enclosure with an isothermal comer heater has been carried out. The cavity is heated from the left bottom comer and cooled from the top wavy wall while the rest walls are adiaba- tic. Mathematical model has been formulated using the single-phase nanofluid approach. Main efforts have been focused on the effects of the dimensionless time, Rayleigh number, undulation number, nanoparticle volume fraction and length of comer heaters on the fluid flow and heat transfer inside the cavity. Numerical results have been presented in the form of streamlines, isotherms, velocity and temperature profiles, local and average Nusselt numbers. It has been found that nanoparticle volume fraction essentially affects both fluid flow and heat transfer while undulation number changes significantly only the heat transfer rate.

Natural convective flow of a magneto-micropolar fluid along a vertical plate

This paper presents a numerical study of natural convective flow of an electrically conducting viscous micropolar fluid past a vertical plate. Internal heat generation (IHG) versus without IHG in the medium are discussed in the context of corresponding similarity solutions. Results are presented in terms of velocity, angular velocity, temperature, skin friction in tabular forms, local wall-coupled stress, and Nusselt number. Computations have been accomplished by parametrizing the micropolar, micro-rotation, magnetic field, suction parameters, and the Prandtl number. Several critical issues are addressed at the end of the paper with reference to a previous study by El-Hakiem. The study is relevant to high-temperature electromagnetic materials fabrication systems.

THE EXPERIMENTAL STUDY FOR NATURAL CONVECTIVE HEAT AND MASS TRANSFER IN POROUS MEDIA

An electrochemical method is employed to study experimentally natural convection driven by combined thermal and solutal buoyant forces in a fluid-saturated porous enclosure. The horizontal temperature and concentration gradients are imposed in such a way that their effects on the flow are either opposing or augmenting. The inside temperature profiles and heat and mass transfer characteristics on the vertical walls are experimentally determined. The effects of dimensionless parameter Ra, Le, N on flow, heat and mass transfer are discussed in details.

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.