Computational analysis of non-isothermal temperature distribution on natural convection in nanofluid filled enclosures

In this study, the problem of steady state natural convection in an enclosure filled with a nanofluid has been analyzed numerically by using heating and cooling by sinusoidal temperature profiles on one side. The governing partial differential equations, in terms of the dimensionless stream function–vorticity and temperature, are solved numerically using the finite volume method for various inclination angles 0^°≤?≤90^°$0^{°}\le ?\le 90^{°}$, different types of nanoparticles (TiO₂ and Al₂O₃) and fractions of nanoparticles 0≤φ≤0.1$0\le \phi \le 0.1$, whereas the range of the Rayleigh number Ra is 10³–10⁵. It is found that the addition of nanoparticles into water affects the fluid flow and temperature distribution especially for higher Rayleigh numbers. An enhancement in heat transfer rate was registered for the whole range of Rayleigh numbers. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers.     

Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid

Mixed convection flow of Cu–water nanofluid inside a lid-driven square cavity with adiabatic horizontal walls and sinusoidal heating on sidewalls has been investigated numerically. The effects of increase in shear force for a fixed buoyancy force and effects of increase in buoyancy force for a fixed shear force were investigated. Effects of variations of Richardson number, phase deviation of sinusoidal heating, and volume fraction of nanoparticles on flow and temperature field were studied. The obtained results showed that for a constant Grashof number at all Richardson numbers, a clockwise eddy was developed inside the cavity, also the rate of heat transfer increases with decrease in Richardson number and increase of volume fraction of nanoparticles. For a constant Reynolds number the clockwise eddy is observed up to Ri = 1. For Ri = 10 a multicellular flow pattern is formed inside the cavity. Moreover it was found that when the Reynolds number is kept constant, the rate of heat transfer increases with increase in Richardson number.     

Transient electrohydrodynamic convective flow and heat transfer of MWCNT - Dielectric nanofluid in a heated enclosure

A computational research was performed to analyze the electrohydrodynamic (EHD) convective heat transfer in a differentially heated dielectric-MWCNT nanofluid layer. The study was conducted on a square enclosure subjected to a temperature gradient between these two vertical walls as well as a potential difference between these horizontal walls. The enclosure was filled with MWCNT oil-based nanofluid; the MWCNT nanoparticles were dispersed in a perfectly insulating thermal oil with a volume fraction of hardly exceeded 0.4%. The governing equations were derived with the assumption of homogeneous nanofluid and were solved with employing finite volume method. Based on the obtained results, it was found that the increase of Rayleigh number, electric Rayleigh number and nanoparticle concentration enhanced the heat transfer. For high thermal and electric Rayleigh number values, the flow and heat transfer became time dependent and accordingly a frequency study was also performed. It was found that the inclusion of an electric field with the addition of nanoparticles led to a significant heat transfer enhancement of about 43%.     

Effect of thermal stratification on free convection in a square porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

Natural convection in a square porous cavity filled with a nanofluid in conditions of thermal stratification has been numerically studied. The mathematical model has been formulated in terms of the dimensionless stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das' nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids. Formulated partial differential equations along with the corresponding boundary conditions have been solved by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, thermal stratification parameter, porosity of the porous medium, solid volume fraction parameter of nanoparticles, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It has been observed an essential effect of thermal stratification parameter on heat and fluid flow fields.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method

A computational analysis has been performed on mixed convection in a double sided lid-driven cavity in the presence of volumetric heat generation or absorption. Effects of inclined magnetic field are also studied. The governing parameters are solved via Galerkin weighted residual finite element method in space and the Crank–Nicolson in time. Governing parameters are nanoparticle volume fraction (0.0?≤???≤?0.04), Richardson number (0.01?≤?Ri?≤?10), internal heat generation or absorption parameter $(?10\le q\le 10),$ inclination angle of magnetic field (0°?≤?γ?≤?90°) and Hartmann number (0?≤?Ha?≤?100). It is observed that the highest heat transfer is obtained in case of the maximum value of heat absorption. As a further finding, heat transfer decreases with increasing of Hartmann number and increases with increasing of nanoparticle volume fraction.     

封闭腔内纳米流体强化自然对流换热的数值模拟

采用F luen软件对封闭腔内Cu-H2O纳米流体强化自然对流换热进行了数值模拟,重点分析Cu纳米粒子添加量和Gr数对换热性能的影响,并解释其换热机理。研究结果表明:在水基液中加入Cu纳米粒子可以显著提高基液的自然对流换热特性。对于一给定的Gr数,随着纳米粒子质量分数的增加,纳米流体的速度组成部分增加,纳米流体质量分数越大,x方向和y方向的速度峰越大,因此加速了流体中能量传输。另一方面,随着Gr数的增加,流线图中旋涡逐渐变大,流线间强度增加,说明换热效果逐渐增强。当Gr数较小时,传热主要是由热壁和冷壁之间的热传导引起的,随着Gr数的增大,换热逐渐变为由对流换热占主导地位。     

Natural convection of CuO–water nanofluid filled in a partially heated corrugated cavity:KKL model approach

In this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for Cu O–water inside a partially heated domain by defining the constraint along the boundaries. For nanofluid analysis, the Koo and Kleinstreuer Li(KKL) model is implemented to deal with the effective thermal conductivity and viscosity. A heated thin rod is placed inside the corrugated cavity and the bottom portion of the corrugated cavity is partially heated. The dimensionless form of nonlinear partial differential equations are obtained through the compatible transformation along with the boundary constraint. The finite element method is executed to acquire the numerical solution of the obtained dimensional system. Streamlines, isotherms and heat transfers are analyzed for the flow field and temperature distribution. The Nusselt number is calculated at the surface of the partially heated domain for various numerical values of emerging parameters by considering the inner obstacle at cold, adiabatic and heated conditions. The computational simulation was performed by introducing various numerical values of emerging parameters. Important and significant results have been attained for temperature and velocities(in both x-and y-directions) at the vertically and horizontally mean positions of the corrugated duct.     

方腔内Cu/Al2O3水混合纳米流体自然对流的格子Boltzmann模拟

纳米流体作为一种较高的导热介质, 广泛应用于各个传热领域. 鉴于纳米颗粒导热系数和成本之间的矛盾, 本文提出了一种混合纳米流体. 为了研究混合纳米流体颗粒间相互作用机理和自然对流换热特性, 在考虑颗粒间相互作用力的基础上, 利用多尺度技术推导了纳米流体流场和温度场的格子Boltzmann方程, 通过耦合流动和温度场的演化方程, 建立了Cu/Al₂O₃水混合纳米流体的格子Boltzmann模型, 研究了混合纳米流体颗粒间的相互作用机理和纳米颗粒在腔体内的分布. 发现在颗粒间相互作用力中, 布朗力远远大于其他作用力, 温差驱动力和布朗力对纳米颗粒的分布影响最大. 分析了纳米颗粒组分、瑞利数对自然对流换热的影响, 对比了混合纳米流体(Cu/Al₂O₃-水)与单一金属颗粒纳米流体(Al₂O₃-水)的自然对流换热特性, 发现混合纳米流体具有更强的换热特性.     

Non-Darcy free convection of Fe3O4-water nanoliquid in a complex shaped enclosure under impact of uniform Lorentz force

Effect of Lorentz forces on natural convection in a complex shaped cavity filled with nanoliquid immersed in porous medium is investigated by means of Control volume based finite element method (CVFEM). Non Darcy model is taken into account for porous media. The working fluid is Fe₃O₄ –water and its viscosity considered as function of magnetic field. Figures are illustrated for different values of Darcy number (Da), Fe₃O₄ -water volume fraction (?), Rayleigh (Ra) and Hartmann (Ha) numbers. Results depict that enhancing in Lorentz forces results in reduce in nanofluid motion and increase the thickness of thermal boundary. Convective heat transfer enhances with rise of Darcy number.     

自然对流情形下激光辐照液体贮箱的机理

利用激光辐照靶目标时,被辐照部位可能是液体贮箱。通过实验测量与数值模拟的紧密结合,揭示了液体处于自然对流状态时激光辐照下贮箱侧壁温升及液体速度场的演化规律。结果表明：激光辐照初期,铝板中心温升率较高;随着壁面附近液体温度的升高,光斑附近速度边界层内的最大流速增大,传热强度亦增大,导致铝板温升率降低;当铝板吸收的激光能量能够基本被水的对流带走时,铝板中心的温升率趋于零。     

Convective heat transfer flow of nanofluid in a porous medium over wavy surface

In this letter, water base nanofluid flow over wavy surface in a porous medium of spherical packing beds is investigated. The copper oxides particles are taken into account. These properties are rehabilitated when fluid interacts with porous walls. For porous medium, Dupuit–Forchheimer model; an extension of Darcy's law model is utilized. The natures of velocity and temperature profiles of nanofluid are discussed graphically whereas the values of convection heat transfer coefficient in the presence of different nanoparticles concentrations in porous medium is presented in tabular form. The obtained results illustrate that convection heat transfer is improved by nanoparticles concentration but reduces when fluid attract to pores structured medium. On the other hand, when particles are added in fluid, convection heat transfer rate is improved but flow velocity is declined.     

KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel

Hydrothermal behavior of nanofluid fluid between two parallel plates is studied. One of the plates is externally heated, and the other plate, through which coolant fluid is injected, expands or contracts with time. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL correlation. The effects of the nanoparticle volume fraction, Reynolds number, Expansion ratio and power law index on Hydrothermal behavior are investigated. Results show that heat transfer enhancement has direct relationship with Reynolds number when power law index is equals to zero but opposite trend is observed for other values of power law index.     

Mathematical modelling of complex heat transfer in a rectangular enclosure

Numerical simulation of convective-radiative heat transfer in an enclosure with a heat source in the presence of heat-conducting walls of the finite thickness was carried out. The distributions of both local (streamlines, temperature fields) and integral (mean Nusselt numbers at typical interfaces) characteristics describing specific features of the investigated process in a real range of the variation of determining parameters were obtained. The radiation influence scales at thermal modes formation were determined. The effect of transient factor on the fields development of both hydrodynamic and thermodynamic characteristics was analysed. Correlation ratios for determining the mean Nusselt number at solid-gas interfaces were obtained depending on the Grashof number. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 08-08-00402-a).     

Experimental and numerical investigation of natural convection of magnetic fluids in a cubic cavity

In this article, natural convections of a magnetic fluid in a cubic cavity under a uniform magnetic field are investigated experimentally and numerically. Results obtained from experiments and numerical simulations reveal that the magnetic field and magnetization are influenced by temperature. There exist relative larger magnetization and magnetic forces in the regions near the upper wall and center inside the cavity than in the region near the bottom and side walls. A weak flow roll occurs inside cavity under the magnetic force, and it brings the low temperature fluid downward in the center region, and streams the high temperature fluid upward along the regions near the sidewalls. With the magnetic field imposed, the heat transfer inside the cavity is enhanced significantly compared to that without the magnetic field, and increasing the strength of the magnetic field the heat transfer is increased further.     

Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface

The effect of Marangoni convection on the flow and heat transfer within a power-law liquid film on an unsteady stretching sheet is examined. The governing equations are non-dimensionalized using suitable transformation variables and the resulting transformed PDEs are then solved numerically by an implicit finite-difference scheme. Results for the velocity and temperature distributions, the free-surface temperature, and the wall temperature gradient are presented for various values of the unsteadiness parameter S, the power-law index n, the thermo-capillarity number M, and the modified Prandtl number Pr. The velocity and temperature distributions in the film are affected significantly by the thermally-induced Marangoni convection adjacent to the free surface. A fluid with a smaller Pr is more sensitive to the Marangoni effect. For Pr less than a moderate value (e.g., at selected values of n and ξ  , Pr?1$\mathit{Pr}?1$ for S=0.8$S=0.8$ and Pr?10$\mathit{Pr}?10$ for S=1.2$S=1.2$), the Marangoni effect tends to increase the heat transfer rate; whereas this impact diminishes in the high Pr regime.     

Natural convection with damped thermal flux in a vertical circular cylinder

Natural convection flows of an incompressible Newtonian fluid inside a circular cylinder are studied. The heat transfer process is described by a generalized fractional constitutive equation for the thermal flux-temperature gradient. Caputo time-fractional derivative operator, which provides the damping of thermal flux, is considered into the studied model.Analytical solutions to the fluid temperature, thermal flux, fluid velocity and volume flow rate are obtained with the integral transforms method (Laplace transform and finite Hankel transform).Temperature behaviors for small and large values of the time t, as well as the post-transient and transient velocity components are determined. The influence of the memory parameter (the order of the time-fractional derivative) on the temperature, thermal flux, velocity and the volume flow rate is numerically and graphically studied.     

Investigation of a turbulent wall jet in forced convection issuing into a directed coflow stream

In the present paper, we have studied numerically the directed coflow stream effects on mean and turbulent flow properties of a turbulent plane wall jet in forced convection emerging into a directed coflow stream. The system of equations governing the studied configuration is solved with a finite difference scheme using a staggered grid for numerical stability, not uniform in the two directions of the flow. The modified version of the first-order low Reynolds number k–? turbulence model is used and compared to existing experimental findings. It is found that predicted results are in satisfactory agreement with the experimental data and that the wall jet fluid decays faster in presence of a directed coflow stream. Results show also that the increase of coflow deviation angles causes an increase of the growth rates of the dynamic and thermal half-width of the jet and enhances the turbulent mixing. It is found that the longitudinal development of normalised forms of the jet characteristics parameters at different directed coflow velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale.     

Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel

This study aimed at exploring influence of T-semi attached rib on the turbulent flow and heat transfer parameters of a silver-water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. For this purpose, convection heat transfer of the silver-water nanofluid in a ribbed microchannel was numerically studied under a constant heat flux on upper and lower walls as well as isolated side walls. Calculations were done for a range of Reynolds numbers between 10,000 and 16,000, and in four different sorts of serrations with proportion of rib width to hole of serration width (R/W). The results of this research are presented as the coefficient of friction, Nusselt number, heat transfer coefficient and thermal efficiency, four different R/W microchannels. The results of numerical modeling showed that the fluid's convection heat transfer coefficient is increased as the Reynolds number and volume fraction of solid nanoparticle are increased. For R/W=0.5, it was also maximum for all the volume fractions of nanoparticle and different Reynolds numbers in comparison to other similar R/W situations. That's while friction coefficient, pressure drop and pumping power is maximum for serration with R/W=0 compared to other serration ratios which lead to decreased fluid-heat transfer performance.