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natural convection in an H-Shaped Porous EnclosureFilled with a Nanofluid

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Computers, Materials & Continua 2021年第3期66卷 3233-3251页

作者： Zehba A.S.Raizah Abdelraheem M.Aly Department of Mathematics College of ScienceKing Khalid UniversityAbha62529Saudi Arabia Department of Mathematics South Valley UniversityQena83523Egypt

This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using an incompressible smoothed particle hydrodynamics(ISPH)method.The right area of the H-shaped enclosure is saturated with non-Darcy porous media.The center variable partitions of the H-shaped enclosure walls are kept at a high-temperature Th.The left and right walls of the H-shaped enclosure are positioned at a low temperature Tc and the other walls are adiabatic.In ISPH method,the source term in pressure Poisson equation(PPE)is modified.The influences of the controlling parameters on the temperature distributions,the velocity field and average Nusselt number are discussed.The performed simulations proofed that the length of the heated partitions augments the velocity field and temperature distributions in an H-shaped enclosure.Rayleigh number rises the fluid velocity and heat transfer in an H-shaped enclosure.The porous layer on the right side of the H-shaped enclosure at a lower Darcy parameter causes a high resistance force for the fluid flow and heat transfer characteristic inside an H-shaped enclosure.Added nanoparticles reduces the velocity field and enhances the heat transfer inside an H-shaped enclosure.

关键词： H-shaped enclosure ISPH natural convection nanofluid porous medium

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

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Applied Mathematics and Mechanics(English Edition) 2018年第10期39卷 1425-1436页

作者： M.A.SHEREMET R.TRIMBITAS T.GROSAN2 I.POP Laboratory on Convective Heat and Mass Transfer Tomsk State UniversityTomsk 634050Russia Department of Mathematics Babes-Bolyai UniversityCluj-Napoca 400084Romania

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.

关键词： wavy cavity natural convection Al2O3-water nanofluid non-uniform heating numerical result

natural convection flow in a vertical annulus with time-periodic thermal boundary conditions

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Propulsion and Power Research 2019年第1期8卷 47-55页

作者： Basant K.Jha Michael O.Oni Department of Mathematics.Ahmadu Bello University Zaria.Nigeria

This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces.Closed-form expressions for velocity,temperature,skin-friction,mass flow rate and rate of heat transfer which is expressed as Nusselt number are obtained by solving the present mathematical model after separating into steady component and periodic regime.The effects of pertinent parameters such as Strouhal number(St),Prandtl number(Pr)and radius ratio(λ)are shown with the aid of contour and line graphs.Results indicate that the role of Strouhal number and Prandtl number is to decrease fluid velocity,temperature and skin-friction.Furthermore,increase in Strouhal number increases the temperature phase-lag.

关键词： natural convection Fully developed flow Time-periodic heating Vertical annulus Strouhal number

natural convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method

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Communications in Computational Physics 2021年第1期29卷 292-318页

作者： Hasan Sajjadi Amin Amiri Delouei Rasul Mohebbi Mohsen Izadi Sauro Succi Department of Mechanical Engineering Faculty of EngineeringUniversity of BojnordBojnordIran School of Engineering Damghan UniversityDamghanIran Mechanical Engineering Department Faculty of EngineeringLorestan UniversityKhorramabadIran Center for Life Nanoscience Italian Institute of TechnologyViale Regina Margherita 29500161RomaItaly Physics Department Harvard University29 Oxford StreetCambridgeMA 02138USA

In this study,natural convection flow in a porous cavity with sinusoidal temperature distribution has been analyzed by a new double multi relaxation time(MRT)Lattice Boltzmann method(LBM).We consider a copper/water nanofluid filling a porous cavity.For simulating the temperature and flow fields,D2Q5 and D2Q9 lattices are utilized respectively,and the effects of different Darcy numbers(Da)(0.001-0.1)and various Rayleigh numbers(Ra)(10^(3)-10^(5))for porosity(ε)between 0.4 and 0.9 have been considered.Phase deviation(θ)changed from 0 toπand the volume fraction of nanoparticles(∅)varied from 0 to 6%.The present results show a good agreement with the previous works,thus confirming the reliability the new numerical method proposed in this paper.It is indicated that the heat transfer rate increases at increasing Darcy number,porosity,Rayleigh number,the volume fraction of nanoparticles and phase deviation.However,the most sensitive parameter is the Rayleigh number.The maximum Nusselt deviation is 10%,32%and 33%for Ra=10^(3),10^(4) and 10^(5),respectively,withε=0.4 toε=0.9.It can be concluded that the effect of Darcy number on the heat transfer rate increases at increasing Rayleigh number,yielding a maximum enhancement of the average Nusselt number around 12%and 61%for Ra=10^(3) and Ra=10^(5),respectively.

关键词： Porous media double multi relaxation time-lattice Boltzmann method nanofluid natural convection sinusoidal temperature distribution

natural convection of SiO_2-water nanofluid in square cavity with thermal square column

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Applied Mathematics and Mechanics(English Edition) 2017年第4期38卷 585-602页

作者： Xiaopeng XIONG Sheng CHEN Bo YANG State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Institute for Modelling and Simulation in Fluodynamics Nanoscience and Industrial Mathematics "Gregorio Millan Barbany"Universidad Carlos III de Madrid Faculty of Engineering The University of NottinghamUniversity Park

A square with a thermal square column is a simple but nontrivial research prototype for nanofluid research. However, until now, the effects of the temperature of the square column on the heat and mass transfer of nanofluids have not been revealed comprehensively, especially on entropy generation. To deepen insight into this important field, the natural convection of the SiO2-water nanofluid in a square cavity with a square thermal column is studied numerically in this study. The effects of the thermal column temperature （T = 0.0, 0.5, 1.0, 1.5）, the Rayleigh number （ranging from 103 to 106）, and the volume fraction of the nanoparticle （varying from 0.01 to 0.04） on the fluid flow, heat transfer, and entropy generation are investigated, respectively. It is found that, no matter at a low or high Rayleigh number, the volume fraction of the nanoparticle shows no considerable effects on the flow field and temperature field for all the temperatures of the thermal column. With an increase in the volume fraction, the mean Nusselt number increases slightly. At the same time, it is found that, with an increase in the temperature of the thermal column, the average Nusselt number gradually decreases at all values of the Rayleigh number. Meanwhile, it is found that, at a high Rayleigh number, the heat transfer mechanism is the main parameter affecting the increase in the total entropy generation rather than the volume fraction. In addition, no matter at a high or low Rayleigh number, when T = 0.5, the total entropy generation is the minimum.

关键词： natural convection SiO2-water nanofluid Rayleigh number volume fraction entropy generation

Enhanced natural convection for Accelerating Melting of Phase Change Material in Cellular Structure through Inserting Fin

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Journal of Thermal Science 2024年第2期33卷 548-563页

作者： KONG Dekui ZHANG Yongcun LIU Shutian State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDalian University of TechnologyDalian116024China

The design of thermal conductivity enhancers(TCE) is quite critical to overcoming the disadvantage of the poor thermal conductivity of phase change materials(PCM).The main contribution of this study is firstly to discuss how to actively enhance natural convection of the melted PCM in cellular structure by the fin formed in the structure under the condition of the same metal mass,apart from simultaneously improving heat conduction,which can boost the heat transfer performance.Also,a tailored hybrid fin-lattice structure(HFS) as TCE is designed and fabricated by additive manufacturing(AM).A two-equation numerical method is applied to study the heat transfer of the PCM,and its feasibility is validated with the experimental data.The numerical results indicate that enhanced natural convection and improved heat conduction can be obtained simultaneously when a well-designed fin is embedded into a lattice structure.The enhanced natural convection results in the improved melting rate and the decreased wall temperature;e.g.,the complete melting time and the wall temperature are reduced by 11.6% and 19.7%,respectively,because of the fin for metal aluminum.Moreover,the parameters of HFS including the porosity,pore density,and fin dimension have a great impact on the heat transfer.The enhancement effect of the fin for HFS on the melting rate of the PCM increases as the thermal conductivity of the base material decreases.For example,when the fin is introduced into the lattice structure,the complete melting time is reduced by 24.1% for metal titanium.In summary,this study enables us to obtain a good understanding of the mechanism of the heat transfer and provides necessary experimental data for the structural design of HFS fabricated by AM.

关键词： natural convection heat transfer enhancement phase change material additive manufacturing hybrid fin-lattice structure

Simulation of inclined dendrites under natural convection by KKS phase field model based on CUDA

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中国铸造:英文版 2023年第5期20卷 432-442页

作者： Chang-sheng Zhu Tian-yu Li Bo-rui Zhao Cang-long Wang Zi-hao Gao College of Computer and Communication Lanzhou University of TechnologyLanzhou 730050China State Key Laboratory of Gansu Advanced Processing and Recycling of Non-Ferrous Metal Lanzhou University of TechnologyLanzhou 730050China Institute of Modern Physics Chinese Academy of SciencesLanzhou 730000China School of Nuclear Science and Technology University of Chinese Academy of SciencesBeijing 100049China Advanced Energy Science and Technology Guangdong Laboratory Huizhou 516000GuangdongChina

In this work,Al-4.5wt.%Cu was selected as the research object,and a phase field-lattice Boltzmann method(PF-LBM)model based on compute unified device architecture(CUDA)was established to solve the problem of low serial computing efficiency of a traditional CPU and achieve significant acceleration.This model was used to explore the evolution of dendrite growth under natural convection.Through the study of the tip velocities,it is found that the growth of the dendrite arms at the bottom is inhibited while the growth of the dendrite arms at the top is promoted by natural convection.In addition,research on the inclined dendrite under natural convection was conducted.It is observed that there is a deviation between the actual growth direction and the preferred angle of the inclined dendrite.With the increase of the preferred angle of the seed,the difference between the actual growth direction and the initial preferred angle of the inclined dendrite shows a trend of increasing at first and then decreasing.In the simulation area,the relative deflection directions of the primary dendrite arms in the top right corner and the bottom left corner of the same dendrite are almost counterclockwise,while the relative deflection directions of the other two primary dendrite arms are clockwise.

关键词： PF-LBM natural convection inclined dendrites CUDA

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

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Applied Mathematics and Mechanics(English Edition) 2013年第6期34卷 669-686页

作者： A. NOGHREHABADI A. BEHSERESHT M. GHALAMBAZ Department of Mechanical Engineering Shahid Chamran University of Ahvaz

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.

关键词： natural convection porous medium nanofluid surface heat flux surfacenanoparticle flux

Conjugate natural convection of non-Newtonian hybrid nanofluid in wavy-shaped enclosure

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Applied Mathematics and Mechanics(English Edition) 2022年第3期43卷 447-466页

作者： S.HUSSAIN T.TAYEBI T.ARMAGHANI A.M.RASHAD H.A.NABWEY Department of Mathematics Capital University of Science and TechnologyIslamabad 44000Pakistan Lehrstuhl III Department of MathematicsTechnical University of DortmundDortmund 44227Germany Faculty of Sciences and Technology University of Bordj Bou ArreridjEl-Anasser 34030Algeria Department of Engineering West Tehran BranchIslamic Azad UniversityTehran 11365Iran Department of Mathematics Aswan UniversityFaculty of ScienceAswan 81528Egypt Department of Mathematics College of Science and Humanities in Al-KharjPrince Sattam Bin Abdulaziz UniversityAl-Kharj 11942Saudi Arabia Department of Basic Engineering Science Faculty of EngineeringMenou¯a UniversityShebin El-Kom 32511Egypt

The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.

关键词： natural convection waved-shaped cavity magnetic field hybrid nanofluid higher order finite element method(FEM)