Numerical simulation of turbulent natural convection of nanofluid with thermal radiation inside a tall enclosure under the influence of magnetohydrodynamic

In the present study, the natural convective heat transfer in the turbulent flow of water/CuO nanofluid with volumetric radiation and magnetic field inside a tall enclosure has been numerically investigated. The thermophysical properties of nanofluid have been considered variable with temperature and the effects of Brownian motion of nanoparticles have been considered. The main objective of this work is an investigation of the effect of using water/CuO nanofluid and presence of magnetic field on turbulent natural convection in three types of enclosures (vertical, inclined, and horizontal) by considering the volumetric radiation. The governing equations on turbulent flow domain under the influence of the magnetic field and by considering the combination of volumetric radiation and natural convection have been solved by a coupled algorithm. For validating the present research, a comparison has been carried out with the laminar natural convection flow under the influence of the magnetic field and radiation effects and also, the natural turbulent convection flow of previous studies and a proper coincidence has been achieved. The results indicated that by increasing volume fraction and Hartmann number the average Nusselt number enhances and reduces, respectively. By adding 1% CuO nanoparticles to the base fluid, heat transfer improves from 10.59% to 17.05%. However, by increasing the volume fraction from 1% to 4%, heat transfer improves from 1.35% to 4.90%. By increasing Hartmann number from 0 to 600, heat transfer reduces from 9.29% to 22.07%. Also, the results show that the ratio of deviation angle of the enclosure to the horizontal surface has considerable effects on heat transfer performance. Therefore, in similar conditions, the inclined enclosure with a deviation angle of 45° compared to the vertical and horizontal enclosure has better thermal performance.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

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

INTRODUCTIONNaturalconvectioninanellipticalcavityheatedfrombelowwastreatednumericallybyM..him.ull],usingaFourierspectralfinitedifferencemethod,anditseffectivenesswasshownasinRef.[2].AlsopossibilityoftheextensiontovarioustypesofboundaryconditionsforthespectralfinitedeferenceschemewasproposedinReL[2-3].HerethespectralfinitedifferenceschemeisbeingextendedtoadoptDimexpansions(akindofBesselexpansions).NUMERICALANAlySISBasicAssumptionsbleatedistransiellttwo--dimensionalnaturallaminarco…     

Computation of a turbulent natural convection in a rectangular cavity with the elliptic-blending second-moment closure

A numerical study of a turbulent natural convection in an enclosure with the elliptic-blending second-moment closure (EBM) is presented. The primary emphasis of the study is placed on an investigation of the accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent natural convection flow. The turbulent heat fluxes in this model are treated by the general gradient diffusion hypothesis (GGDH). The model is applied to the prediction of a natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for a validation of the turbulence models. The results are also compared with those by the two-layer model, the SST model, the V2-f model and the second-moment differential stress and flux model. It is shown that the elliptic blending model predicts as good as or better than the existing models for the mean velocity and turbulent quantities although this model employs a simpler GGDH for treating the turbulent heat fluxes.     

辐射侧加热腔内自然对流传热特性研究

为了明确辐射侧加热封闭方腔内半透明流体的自然对流传热现象及规律,采用有限体积法进行数值模拟研究,分析了瑞利数和光学厚度对流场、温度场以及传热特性的影响。结果表明：与传统侧壁加热腔内自然对流相比,辐射侧加热腔内等温线和流场分布规律不一致;随着瑞利数和光学厚度增加,涡心由中心位置沿直线向辐射入射侧斜上方偏移;随着瑞利数增加,等温线变得更均匀;随着光学厚度增加,等温线变密,努塞尔数Nu与瑞利数RaT的标度律指数减小,当光学厚度增加到一定时标度律不再变化,此时传热标度律与传统恒壁温侧加热腔内自然对流相当,满足Nu~Ra0.29T。     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Computation of combined natural-convection and radiation heat-transfer in a cavity having a square body at its center

This paper describes a numerical study of the radiation-natural convection interactions in a differentially-heated cavity with an inner body. A specifically developed numerical model, based on the finite-volume method, is used for the solutions of the governing differential-equations. The SIMPLER algorithm for the pressure–velocity coupling is adopted. The fluid (air) is perfectly transparent to the radiation. The surface emissivity ε, the Rayleigh number Ra, and the thermal conductivity ratio R_k were varied parametrically. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of isotherms, streamlines, average Nusselt-numbers across the enclosure, local Nusselt-numbers at the hot and cold walls, vertical and horizontal median velocities and horizontal walls, temperature distributions. It is found that: (i) the radiation exchange homogenizes the temperature inside the cavity and produces an increase in the average Nusselt-number, particularly when R_k and Ra are high and (ii) the average Nusselt-number increases with increasing surface emissivity, especially at high Rayleigh numbers.     

Suppression of natural convection heat transfer along a vertical flat plate with concavities

To clarify the effect of the suppression of natural heat transfer, the local heat transfer coefficients on a vertical cooled flat plate with circular grooves were measured by a multi‐type thermocouple method. Two flat plates with and without periodic circular grooves were tested in this experiment. The characteristics of heat transfer along the plate for both plates were compared. The local heat transfer coefficients on the periodic grooved plate became smaller than that of the flat plate. The flow pattern was changed when it passed over the grooves, and circulation was generated in the grooves in the downstream. As a result, the thickness of the thermal boundary layer on the grooved plate was more developed than the normal flat plate. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20294     

Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity

Turbulent double-diffusive natural convection is of fundamental interest and practical importance. In the present work we investigate systematically the effects of thermal Rayleigh number (Ra), ratio of buoyancy forces (N) and aspect ratio (A) on entropy generation of turbulent double-diffusive natural convection in a rectangle cavity. Several conclusions are obtained: (1) The total entropy generation number (S_total) increases with Ra, and the relative total entropy generation rates are nearly insensitive to Ra when Ra ≤ 10⁹; (2) Since N > 1, S_total increases quickly and linearly with N and the relative total entropy generation rate due to diffusive irreversibility becomes the dominant irreversibility; and (3) S_total increases nearly linearly with A. The relative total entropy generation rate due to diffusive and thermal irreversibilities both are monotonic decreasing functions against A while that due to viscous irreversibility is a monotonic increasing function with A. More important, through the present work we observe a new phenomenon named as “spatial self-copy” in such convectional flow. The “spatial self-copy” phenomenon implies that large-scale regular patterns may emerge through small-scale irregular and stochastic distributions. But it is still an open question required further investigation to reveal the physical meanings hidden behind it.     

Study of combined effect of natural convection and radiation heat transfer from annular finned vertical cylinder

The present numerical study reports the combined effect of natural convection and radiation heat from a vertical cylinder with annular fins. The study involves simulation for laminar as well as turbulent regimes. For the present study, Rayleigh's number is varied in the range ${10}^8-{10}^{12}$, emissivity in the range $0.2-0.8$, and the fin spacing ratio (s/d) in the range $0.1-10$. The radiation heat transfer has been found to share a considerable amount in the total heat transfer of the system for the laminar regime, but in the turbulent regime, its effect is minimal and can be neglected. When the fin spacing ratio is reduced, the total heat transfer increases for both the turbulent and laminar flow conditions. But the radiation heat increases with a reduction in fin spacing ratio for laminar and in case of turbulent flow radiation heat rate reduces with a reduction in s/d ratio. For the range of Rayleigh numbers considered in the present study, the Nusselt number increases with the increment of the fin spacing ratio. Thus, it can be concluded that there is a remarkable enhancement in the heat transfer rate in laminar cases with the fins. For turbulent cases, the fin efficiency lies between 40% and 50%.     

Heat transfer enhancement of turbulent natural convection adjacent to a vertical heated plate

Enhancement of heat transfer was investigated experimentally on natural convection adjacent to a vertical heated plate. In order to promote heat transfer from the heated plate, a V-shaped promoter of which the edge faced upstream was attached onto the surface of the vertical plate. The promoter redirects high-temperature fluids toward both sides of the promoter and also introduces low-temperature ambient fluids behind the promoter. These two mechanisms enhance heat transfer, in particular, in the region behind the promoter. Local heat transfer coefficients around the promoter were measured using water as the test fluid. These coefficients behind the promoter reached 2.5 times of those without the promoter. The optimal heights and attack angles of the promoter that maximize the heat transfer were also studied experimentally. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res. 25(1): 39–50, 1996     

Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate

The combined free convection boundary layer flow with thermal radiation and mass transfer past a permeable vertical plate is studied when the plate moves in its own plane. The plate is maintained at a uniform temperature with uniform species concentration and the fluid is considered to be gray, absorbing–emitting. The coupled unsteady non-linear momentum, energy and concentration equations governing the problem is obtained and made similar by introducing a time-dependent length scale. The similarity equations are solved numerically using superposition method. The resulting velocity, temperature and concentration distributions are shown graphically for different values of parameters entering into the problem. The numerical values of the local wall shear stress, local surface heat and mass flux are shown in tabular form.     

Numerical calculation of turbulent natural convection in a cylindrical transformer enclosure

Numerical calculations of turbulent natural convection in the enclosure of the 20 kVA oil-immersed transformer model are presented. The transformer is modeled as two concentric cylinders with different heights and diameters. The correlating equation between the mean Nusselt number and the Rayleigh number can be obtained for Ra = 10⁸ to 10⁹. The thermal boundary layers are well represented in the temperature distributions along the wall of the transformer model. The flow stratification between the hot and cold walls cannot be seen in the transformer model. The turbulence eddy viscosity has its maximum at the center of the core and its maximum values at the top of the core are slightly larger than those at the bottom of the core. © 1999 Scripta Technica, Heat Transfer Asian Res, 28(6): 429–441, 1999     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat‐flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71,Ra = 10⁶ is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ω_c = 350, which corresponds to the angular velocity of internal gravity wave ω_r estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 10⁵,Ra ≥ 10⁶ for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 309–322, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20122     

Combined convection heat transfer in a lid driven cavity filled with nanofluids

A simulation study is performed of laminar steady combined convection heat transfer in a lid-driven cavity containing various types of nanofluid (CuO–water nanofluid and Al₂O₃–water nanofluid) at various boundary conditions. The influence of two different types of temperature distributions applied to the cavity's bottom wall is investigated. There are two types of temperature distributions: constant temperature (T_h) and a sinusoidal temperature distribution applied to the bottom wall, which has a higher temperature than the top moving wall (T_c). In both circumstances, the sidewalls are kept adiabatic. The finite element method is utilized for the current issue. The influence of the Richardson number, which ranges from 0.01 to 10, and the volume fraction of nanoparticles, which ranges from 0 to 0.1, on the heat transfer rate has been explored. The influence of the sinusoidal temperature distribution's amplitude and phase angle is also examined. The isotherm and streamline patterns within the cavity are diverse with distinct nanoparticle volume fractions, and the Richardson numbers are presented and analyzed. The numerical findings showed that lowering the Richardson number raises the average Nusselt number. Also, the existence of nanoparticles in pure water increases heat transmission. Additionally, raising the sinusoidal temperature's amplitude increases the average Nusselt number. The results show that the increase of average Nusselt number at (φ = 0, Gr = 10⁴, Pr = 1, Ɣ = 3π/2) for amplitude 0.25, 0.5, 0.75, and 1 is 0.53, 0.9, 1.3, and 1.87, respectively.     

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core (Part 1: numerical analysis)

Combined heat transfer characteristics were obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. We assumed that the porous layer was both homogeneous and isotropic. The pure Darcy law for fluid flow and Rosseland's approximation for radiation were used. The numerical methodology was based on an algebraic coordinate transformation technique and the transformed governing equations were solved using the SIMPLE algorithm. The effect of radiation on the heat transfer characteristics was investigated over a wide range of radiation numbers and temperature ratios for two Darcy-Rayleigh number values (Ra^* = 100 and 1000) and for a fixed aspect ratio of H/L = 1. The results are presented in the form of combined radiation and convection heat transfer coefficients and are compared with the corresponding values for pure natural convection. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 278–294, 1999