Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al_(2)O_(3) free convection in entropy determination

The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation,heat absorption,heat generation,and magnetic field(MF)is very vital due to its existence in various sectors of industry and engineering.The present research focuses on mathematical modeling to simulate the cooling of a hot component through power-law(PL)nanofluid convection flow.The temperature reduction of the hot component inside a two-dimensional(2D)inclined chamber with two different cold wall shapes is evaluated.The formulation of the problem is derived with the lattice Boltzmann method(LBM)by code writing via the FORTRAN language.The variables such as the radiation parameter(0–1),the Hartmann number(0–75),the heat absorption/generation coefficient(−5–5),the fluid behavioral index(0.8–1.2),the Rayleigh number(103–105),the imposed MF angle(0°–90°),the chamber inclination angle(−90°–90°),and the cavity cold wall shape(smooth and curved)are investigated.The findings indicate that the presence of radiation increases the mean Nusselt number value for the shear-thickening,Newtonian,and shear thinning fluids by about 6.2%,4%,and 2%,respectively.In most cases,the presence of nanoparticles improves the heat transfer(HT)rate,especially in the cases where thermal conduction dominates convection.There is the lowest cooling performance index and MF effect for the cavity placed at an angle of 90°.The application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical research.

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

In this paper,natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function(RBF).The nanofluids used were Cu-water or Al_(2)O_(3)-water mixture with nanoparticle volume fractions range of 0≤φ≤0.2.A system of continuity,momentum,and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids.Partial derivatives in the governing equations were approximated using the RBF method.The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations.Themain goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions.To assess the accuracy of the proposed method,several test cases of natural convection in square and triangular cavities were selected.For Rayleigh numbers ranging from 103 to 105,a validation test of natural convection of Cu-water in a square cavity was used.The numerical investigation was then extended to Rayleigh number 106,as well as Al_(2)O_(3)-water nanofluid with a volume fraction range of 0≤φ≤0.2.In a second investigation,the same nanofluids were used in a triangular cavitywith varying volume fractions to test the proposed meshless approach on non-rectangular geometries.The numerical results appear to be in agreement with those from earlier investigations.Furthermore,the suggested meshless method was found to be stable and accurate,demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries.

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.

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.

Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall

Natural convection in an open end cavity with a hot inclined wall is simulated based on the lattice Boltzmann method （LBM）. The physics of flow and energy transfer in open end cavities are addressed when the hot wall is inclined. The combination of the two topics （open cavity and inclined walls） is the main novelty of the present study. The effects of the angle of the hot inclined wall on the flow field and heat transfer are thoroughly investigated. The Prandtl number is fixed to 0.71 （air）. The Rayleigh number and the angle of the hot inclined wall are varied in the range of 10^4 to 10^6 and 60° to 85°, respectively. The results are presented for two different aspect ratios, i.e., A = 1 and 2. The results obtained with the LBM are also compared with those of the finite volume method （FVM）. The predicted results of the LBM conform to those of the FVM. The results show that by increasing the angle of the hot inclined wall and the aspect ratio of the cavity, the average Nusselt number decreases. The trend of the local Nusselt number on the inclined wall is also discussed.

A Study on Natural Convection of Air in a Square Cavity with Partially Thermally Active Side Walls

In this present work, we study heat transfer in a confined environment. We have to determine the thermal and dynamics fields of the cavity while observing the effect of the Rayleigh number which depends on the characteristics of the fluid and the temperatures imposed. The behavior of boundary layers in natural convection is analyzed along this square cavity. The central halves of its vertical walls are heated at different temperatures. The left active part is at a higher temperature than the one on the right wall. The remaining inactive parts and the horizontal walls (upper and lower) are adiabatic. The thermal and dynamic modeling of two-dimensional problem was done using a calculation code Fortran 90 and a visualization software ParaView based on the finite volume method. The equations governing this phenomenon of unsteady flow have thus been solved. This allows the modeling of both air flow and heat transfer with a numerical stabilization of the solution. So, we have presented our results of numerical simulations using a visualization tool. The results show the different velocity and temperature curves, velocity vectors and isotherms in laminar flow regime.

Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method

A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.

Numerical Study of Heat Transfer in a Differentially Heated Cavity

Laminar natural convection is studied in a square cavity filled with air whose two vertical sides are subject to a temperature difference, while the other two horizontal sides are adiabatic. The hot and cold wall temperatures are kept constant. We have presented a dynamic and thermal study of pure natural convection for different values of the Rayleigh number. The numerical simulation was carried out for Rayleigh numbers ranging from 102, 103, …, 105 and the Prandtl number is Pr = 0.71. We used the COMSOL Multiphysic 5.1 software, which allows us to simultaneously solve the coupled physical phenomena in a square enclosure containing air under the Boussinesq approximation. For the coupling of natural convection with radiation from radiative surfaces, both horizontal faces are subjected to radiative flux, and the emissivity of the surfaces varies from ε = 0.1 to 0.8. We have seen that a circulation process is involved. The fluid that is subjected to a high temperature near the hot wall rises to the ceiling and the fluid near the cold wall sinks. This movement continues until the fluid reaches thermal equilibrium. In a natural convection-surface radiation coupling, simulation results indicate that radiative exchange decreases as a function of the Rayleigh number. Surface radiation reduces the flow in the cavity.

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.

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

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.

Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM)

The lattice Boltzmann method （LBM） is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles： TiO2, Ag, Cu, and A1203. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical meth- ods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ =2.5 when Ra = 106 while at A = 1.5 for other Rayleigh numbers.

Unsteady Natural Convection between Two Eccentric Hemispheres

Natural convection heat transfer in open or closed cavities takes place in different engineering areas. The hemispherical cavity is a part of basic geometries although it is not widely studied. The present paper reports the numerical study of natural convection in a closed hemispherical annulus delimited by two vertically eccentric hemispheres filled with Newtonian fluid (air in this case with Pr = 0.7) is conducted. The inner hemisphere is heated by a heat flux of constant density and the outer one is maintained isothermal. Based on the Boussinesq assumptions, the governing equations are numerically studied using unsteady natural convection formulated with vorticity and stream-function variables. These equations are written by using bispherical coordinates system and solved by using a finite difference method. The effect of the control parameters such as the Rayleigh number (103 ≤ Ra ≤ 106) or the eccentricity (e = ±0.2, ±0.5, 0) in the dynamic and thermal behaviours of the fluid is investigated.

Effects of Rayleigh Number on MHD Heat Transfer and Fluid Flow in Two-Dimensional Open Square Cavity with Heat Generation

The present work is devoted to investigating heat transfer and fluid flow in a two dimensional square open cavity containing a heated circular cylinder at the centre. A constant heat flux is set at the left sidewall;high and low temperatures are fixed at the bottom and top walls of the cavity respectively. The right side of the cavity is open. Galerkin Weighted Residual Finite Element Analysis is used to visualize the heat transfer and fluid flow solving two-dimensional governing mass, momentum and energy equations for steady state, heat transfer and fluid flow in presence of magnetic field in side an open square cavity. A uniformly heated circular cylinder is placed at the centre of the cavity as a heat source. To find the effects of Rayleigh number (Ra) on the thermal fields and fluid flow in presence of magnetic field and a heated circular cylinder as heat source by visualization and line graphs is the objective of this study. Numerical results are presented in graphical and tabular form. The study is conducted for different values of Rayleigh number, some fixed Hartmann numbers (Ha) and heat flux (q). In the conclusion it has been observed that the temperature field and fluid flow pattern are functions of the parameters Rayleigh number and Hartmann number.

不同冷热壁面对方腔内对流换热影响的格子Boltzmann模拟

基于格子Boltzmann方法,选取多弛豫时间(MRT)模型对具有局部冷热壁面立体方腔中的三维自然对流换热进行模拟研究。分别采用三维D3Q19模型描述速度场,D3Q7模型描述温度场,研究不同瑞利数Ra(103≤Ra≤105)和局部冷热壁面位置变化对三维方腔内自然对流的影响。结果表明:冷热壁面的布置方式对流动换热有显著影响,且瑞利数Ra越大,其影响效果越明显。其中,冷热壁面均处于中间位置(工况5)的自然对流换热能力最强,并且随着Ra逐渐增大,自然对流能力增强,流线逐渐复杂。在相同工况条件下,随着Ra增大,平均努塞尔数Nuav也逐渐增加,换热能力增强。在相同Ra条件下,工况5的Nuav最大,表明其自然对流换热能力最强。

Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity

In this paper,the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is considered.The Buongiorno model is applied to descirbe the nanofluid behaviours.Both the top and bottom horizontal walls of the cavity are adiabatic,and there is a temperature difference between the left and right vertical walls.The non-dimensional governing equations are obtained when the stream-vorticity formulation of function is used,which are solved by the recently developed robust Coiflet wavelet homotopy analysis method.A rigid verification for the solver is given.Besides,the effects of various physics parameters including the Rayleigh number,the buoyancy ratio parameter,the bioconvection Rayleigh number,the Prandtl number,the Brownian motion parameter,the thermophoresis parameter,the heat generation parameter,the Lewis number,the bioconvection Peclet number and the Schmidt number on this complicated natural convection are examined.It is known that natural convection is closely related to our daily life owing to its wide existence in nature and engineering applications.We believe that our work will make a significant contribution to a better understanding of the natural convection of a complex fluid in a cavity with suspensions of both inorganic nanoparticles and organic microorganisms.

Analysis of Natural Convection in an Elliptical Cavity,Using a Dini Expansion

Analyzed is natural transient convection followed by steady-state convection in an elliptical cavity heated from below, using a spectral finite difference scheme in terms of a Dim expansion. The major or minor axis of the elliptic section of the cavity is assumed to be placed horizontally. As a thermal boundary condition, Dirichlet or Neumann condition is specified. Not only for nearly pure-heat conduction case at low Grashof numbers but also for strong convection flow with cellular patterns at larger Grashof numbers are found to be attained at least for some combination of Prandtl numbers and geometrical parameters.

Multiple Relaxation Time Lattice Boltzmann Simulation of 2D Natural Convection in a Square Cavity at High Rayleigh Numbers

Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time(MRT)lattice Boltzmann method(LBM)with a separate distribution function to solve the temperature.The Rayleigh numbers examined here range from Ra=103 to Ra=10^(8).For Rayleigh numbers below 10^(8),the flow remains stationary and transition occurs beyond Ra=2×10^(8).Unsteady results at higher Rayleigh numbers(Ra=10^(9) and Ra=10^(10))are also investigated.To the best of our knowledge,this is the first accurate study which involves the high Rayleigh numbers Ra=10^(9),10^(10).

Boussinesq近似与封闭腔体内自然对流的数值模拟

采用三种不同的密度处理方法对封闭方腔内自然对流换热进行数值模拟,得到了瑞利数Ra从103～106封闭方腔内空气的流动换热规律,所得到的数值模拟结果与研究文献做了对比分析,验证了其方法的准确性,同时对比分析了利用不可压理想气体、考虑气体密度随温度变化的情况,以及运用Boussinesq近似的数值模拟结果。计算结果表明,在所计算的问题中,如果小温差下采用Boussinesq近似可以一定程度上减小计算量,加速计算收敛结果,但在大温差下采用Boussinesq近似将造成计算结果误差相对很大。

基于热格子Boltzmann方法的自然对流数值模拟

对Eggels和Somers提出的热格子Boltzmann格式进行了改进.在不可压缩流动的假设下,提出了一种新的温度平衡分布函数,可以克服压缩性对温度统计的影响,并且相应地修正了统计宏观温度的方法.Eggels和Somers的方法对速度和温度均采用半步长反弹格式边界条件,适合无滑移的速度边界条件.但是对温度采用该边界条件在物理本质上显得不够准确,所以在边界上对二者统一采取算法既简单又容易实现的非平衡态外推格式,同时可以与Boltzmann格式的整体二阶精度保持一致.最后,利用改进的热格子Boltzmann方法（TLBM）模拟了Ra=10^6和Pr=0.71（空气）的方腔中的自然对流,模拟得到的流动参数与其它数值方法的结果吻合得很好,表明改进的热格子Boltzmann方法可以有效准确地模拟非等温流动.