Natural convective heat transfer and fluid flow in a porous medium filled corrugated enclosure: Effect of discrete heat sources

In this work, we investigate the two-dimensional unsteady natural convective fluid flow problem in a porous-corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation-free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10⁻⁵ ≤ Da ≤ 10⁻¹), Rayleigh (10³ ≤ Ra ≤ 10⁶), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non-miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy-driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.     

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.     

开口方腔内混合对流换热的数值模拟

研究了两种不同外界来流方向的开口方腔内的混合对流换热问题。对不同的格拉晓夫数、R e以及纵横比进行了数值模拟。计算结果表明了与它们相对应的不同流型及换热效果,同时表明通过增加流速可以减小方腔与周围环境的热量交换。     

Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous medium

Two-dimensional double-diffusive natural convective heat and mass transfer in an inclined rectangular porous medium has been investigated numerically. Two opposing walls of the cavity are maintained at fixed but different temperatures and concentrations; while the other two walls are adiabatic. The generalized model with the Boussinesq approximation is used to solve the governing equations. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. A finite volume approach has been used to solve the non-dimensional governing equations and the pressure velocity coupling is treated via the SIMPLER algorithm. The results are presented in streamline, isothermal, iso-concentration, Nusselt and Sherwood contours for different values of the non-dimensional governing parameters. A wide range of non-dimensional parameters have been used including, aspect ratio (2 ≤ A ≤ 5), angle of inclination of the cavity (0 ≤ ? ≤ 85), Lewis number (0.1 ≤ Le ≤ 10), and the buoyancy ratio (− 5 ≤ N ≤ 5).     

Natural convective flow of a chemically reacting fluid in an annulus

We examine the heat transfer and flow properties induced by natural convection in an annulus between a square enclosure and a circular cylinder filled with a chemically reacting fluid. During the exothermic reaction process in the reacting fluid, there generates heat that induces natural convection in the annulus. The problem is developed defining the vorticity‐stream function. We solve it with the use of the finite difference method. The results show that two counter‐rotating vortices generate in each half about the vertical symmetry line through the center of the inner cylinder. The lower eddies of the inner vortices get closer and closer with the decrease of the aspect ratio and the increase of the Rayleigh number, Frank‐Kamenetskii number, buoyancy force parameter, and Lewis number. Besides this, the eyes of the outer vortices expose similar characteristics for increasing values of the Rayleigh number and buoyancy force parameter, and for decreasing values of the aspect ratio and the Lewis number. It is remarkable that the flow field and the Nusselt number demonstrate completely distinct characteristics for the Lewis number unity, the aspect ratio equal to 0.1, and in the absence of the buoyancy force parameter.     

Mixed convective heat transfer enhancement in a ventilated cavity by flow modulation via rotating plate

The present study numerically explores the mixed convection phenomena in a differentially heated ventilated square cavity with active flow modulation via a rotating plate. Forced convection flow in the cavity is attained by maintaining external fluid flow through an opening at the bottom of the left cavity wall while leaving it through another opening at the right cavity wall. A counter-clockwise rotating plate at the center of the cavity acts as an active flow modulator. Moving mesh approach is used for the rotation of the plate and the numerical solution is achieved using arbitrary Lagrangian-Eulerian finite element formulation with a quadrilateral discretization scheme. Transient parametric simulations have been performed for various frequency of the rotating plate for a fixed Reynolds number (Re) of 100 based on maximum inlet flow velocity while the Richardson number (Ri) is maintained at unity. Heat transfer performance has been evaluated in terms of spatially averaged Nusselt number and time-averaged Nusselt number along the heated wall. Power spectrum analysis in the frequency domain obtained from the fast Fourier transform analysis indicates that thermal frequency and plate frequency start to deviate from each other at higher values of velocity ratio (>4).     

Laminar Natural Convective Heat Transfer in the Enclosed Evacuated Collector Tube with East—West Symmetric Heat Input

INTR0DUCTI0NNaturalconvectioninenclosureshasbeenfoundinavariety0fapplications,suchassolarcollectors,nu-cleartechn0logies,thecoolingofelectronicalcircuits,etc.Amongthemnaturalconvectioninsideanen-closedrectangularcavityisthemostclassicalproblem.Correspondinglyagreatdealofexperimentalandnumericalworkhasbeendoneinsuchafieldwiththe"clean"boundaryCPnditi0nsofuniformwalltem-perature(UWT)anduniformheatflch(UHF).Re-celltlymoreattelltionispaidontheconvectioninthecirculartube.HwangandLai[11inves…     

Three-dimensional flow of a viscous fluid with heat and mass transfer

Three-dimensional unsteady free convection and mass transfer flow of an incompressible, viscous liquid through a porous medium past an infinite vertical flat plate subjected to a time-dependent suction velocity normal to the plate is studied. The equations encountered into the problem are solved using perturbation technique to obtain the velocity, temperature and concentration fields considering as reference parameter. Expressions for the skin-friction, rate of heat and mass transfers are also obtained. Two cases of most common interest viz. cooling case (G_r > 0) and heating case (G_r < 0) are discussed.     

Three－Dimensional Numerical Simulation of Natural Convection Heat Transfer in an Inclined Cylindrical Annulus

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Fluid flow and heat transfer in the transition process of natural convection over an inclined plate

The present study deals with fluid flow and heat transfer in the transition process of natural convection over an inclined plate. In order to examine the mechanism of the transition process, experiments on the flow and heat transfer were performed for various plate inclination angles in the range of 20 to 75°. The wall temperature and fluid flow fields were visualized using a liquid crystal sheet and fluorescent paint, respectively. The visualization confirmed that separation of a boundary layer flow took place, and the onset point of streaks appeared over the plate wall when the modified Rayleigh number exceeded a characteristic value for each inclination angle. The local Nusselt number in the transition range was proportional to the one‐third power of the local modified Rayleigh number. By introducing a nondimensional parameter, a new correlation between visualizations of the flow and temperature fields and heat transfer was proposed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 648–659, 2001     

Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection

Numerical investigations of transient natural convection flow through a fluid-saturated porous medium in a rectangular cavity with a convection surface condition were conducted. Physical problem consists of a rectangular cavity filled with porous medium. The cavity is insulated except the top wall that is partially exposed to an outside ambient. The exposed surface allows convective transport through the porous medium, generating a thermal stratification and flow circulations. The formulation of differential equations is non-dimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite different equation handling the boundary condition of the open top surface is derived. The two-dimensional flow is characterized mainly by two symmetrical vortices driven by the effect of buoyancy. A lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. Unsteady effects of associated parameters were examined. It was found that the heat transfer coefficient, Rayleigh number and Darcy number considerably influenced characteristics of flow and heat transfer mechanisms. Furthermore, the flow pattern is found to have a local effect on the heat convection rate.     

辐射引起密闭容器内半透过性流体的自然对流对传热的影响

用数值方法研究了密闭容器内半透过性流体在辐射光的照射下产生的自然对流对传热的影响。基于二维假设下的流体流动和热量传递的动态数学模型，并用有限差分方向交替法进行数值求解，得到了稳态下的对流换热系数。结果表明，流体的自然对流受倾斜角度和光学厚度的影响，而传热又受自然对流的影响，对流换热系数的大小与密闭容器内自然对流的强度密切相关。局部换热系数沿透过板内侧的分布与密闭容器的放置角度有关，垂直放置时为从下至上逐渐增大，水平放置时，呈波浪形分布，倾斜角度从π／2减少至0时，由从下至上逐渐增大的分布变为波浪形的分布，垂直和水平放置时的平均换热系数都随光学厚度的增大而增大。     

Conjugate natural convection heat transfer in an inclined square cavity containing a conducting block

The present work is concerned with computation of natural convection flow in a square enclosure with a centered internal conducting square block both of which are given an inclination angle. Finite volume method through the concepts of staggered grid and SIMPLE algorithm have been applied. Deferred QUICK scheme has been used to discretize the convective fluxes and central difference for diffusive fluxes. The problem of conjugate natural convection has been taken up for validating the code. The abrupt variation in the properties at the solid/fluid interface are taken care of with the harmonic mean formulation. Solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been performed for Ra = 10³–10⁶, angle of inclination varying from 15° to 90° in steps of 15° and ratio of solid to fluid thermal conductivities of 0.2 and 5.0. Results are presented in terms of streamlines, isotherms, local and average Nusselt number.     

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。     

Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate

The fluid flow and heat transfer induced by the combined effects of the mechanically driven lid and the buoyancy force within rectangular enclosures were investigated in this work. The fluid filled enclosures are heated and lid-driven either on the upper or on the lower horizontal wall, thermally isolated on the right vertical wall, and cooled on the other walls. The basis of the investigation was the numerical solutions of the equations for the conservation of mass, momentum, and energy transport using the finite difference method. The effects of the flow governing parameters including the Richardson and the Prandtl numbers, and the length-to-height aspect ratio, respectively, in the range 10⁻²  Ri  10², 10⁻³  Pr  10, and 1  AR  4 for a fixed Reynolds number, Re = 100, were studied. The results are presented in the form of the hydrodynamic and thermal fields, and the profiles for vertical and horizontal components of velocity, temperature, and the local heat flux. The fluid flow and energy distributions within the enclosures and heat flux on the heated wall are enhanced by the increase in the Richardson number. While an increase in the Prandtl number improves the heat flux on the heated wall, an increase in aspect ratio suppresses it. The results can be used as base line data in the design of systems in which mixed convection heat transfer in rectangular enclosures occurs.     

Enhancement of natural convective heat transfer from tall,vertical heated plate to water

An enhancement technique was developed for natural convection heat transfer from a tall, vertical heated plate to water. Rectangular grid fins attached to the base plate were utilized as a heat transfer promoter. These grid fins redirect the high‐temperature fluid ascending along the base plate toward the outside of the boundary layer and introduce the low‐temperature ambient fluid toward the base plate instead. The heat transfer coefficients of thus‐treated surfaces were measured and compared with a nontreated surface and a surface with conventional vertical plate‐fins. The highest performance was achieved for the experimental surfaces. In particular, the experimental surfaces with 5‐mm‐high, nonconducting grids and with 10‐mm‐high, conducting grid fins show 27% and 80% higher heat transfer coefficients compared to the turbulent heat transfer coefficients of the nontreated surface, respectively. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(2): 178–190, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10083     

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

Fluid flow and heat transfer of natural convection around array of vertical heated plates

Natural convective flows around an array of vertical heated plates were investigated experimentally. Main concerns were directed to the influences of plate numbers on the heat transfer characteristics of the plates. Both surfaces of the test plates were heated with constant and equal heat fluxes and their local heat transfer coefficients were measured. The results showed that the coefficients of the surfaces of the array facing outward became higher than those facing inward. The flow fields around the bottom of the plate array were visualized with smoke. The result showed that the ambient flow is directed from the sides to the center of the array and enters the parallel channel obliquely. These flows cause the above difference in the coefficients. While the difference gradually diminished in between the plates placed in the central section of the array, their coefficients asymptotically approach those of the analytical correlation that assumed a uniform velocity at the channel inlet. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20232     

Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080