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.     

Effect of nanofluid variable properties on natural convection in enclosures

In this work, the heat transfer enhancement in a differentially heated enclosure using variable thermal conductivity and variable viscosity of Al₂O₃–water and CuO–water nanofluids is investigated. The results are presented over a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 9%), and aspect ratios (½ ≤ A ≤ 2). For an enclosure with unity aspect ratio, the average Nusselt number of a Al₂O₃–water nanofluid at high Rayleigh numbers was reduced by increasing the volume fraction of nanoparticles above 5%. However, at low Rayleigh numbers, the average Nusselt number was slightly enhanced by increasing the volume fraction of nanoparticles. At high Rayleigh numbers, CuO–water nanofluids manifest a continuous decrease in Nusselt number as the volume fraction of nanoparticles is increased. However, the Nusselt number was not sensitive to the volume fraction at low Rayleigh numbers. The Nusselt number demonstrates to be sensitive to the aspect ratio. It was observed that enclosures, having high aspect ratios, experience more deterioration in the average Nusselt number when compared to enclosures having low aspect ratios. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett model and the Brinkman model. It was found that at high Rayleigh numbers the average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models.     

Transient double-diffusive convection in an enclosure with large density variations

An extension of a slightly compressible flow model to double-diffusive convection of binary mixtures of ideal gases enclosed in a cavity is presented. The problem formulation is based on a low-Mach number approximation and the impermeable surface assumption is not invoked. The main objectives of this work are the statement of the mathematical model used, and the analysis of some significant results showing the influence of density variation on transient solutions for pure thermal or pure solutal convection as well as for thermosolutal convection in the special case where the thermal and solutal buoyancy forces are equal in intensity either for aiding or for opposing cases.     

Stability of buoyancy and surface tension driven convection in a horizontal double-diffusive fluid layer

Linear stability analysis has been applied to examine the stability of convection in a horizontal double-diffusive fluid layer driven by the combined effects of buoyancy and surface tension. Such a convective flow may serve as an idealized model of the horizontal Bridgman process for crystallization or solidification of liquid melts. Results show that salt-finger instability is excited over a wide range of thermal and solutal Grashof numbers. Travelling wave instabilities caused by surface tension effects are excited when the effective Marangoni number becomes large.     

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。     

Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients

The finite-difference method is used to predict numerically the characteristics of hydromagnetic double-diffusive convective flow of a binary gas mixture in a rectangular enclosure with the upper and lower walls being insulated. Constant temperatures and concentrations are imposed along the left and right walls of the enclosure and a uniform magnetic field is applied in the x-direction. Consistent with what is reported by previous investigators, an oscillation in the flow is observed in the absence of the magnetic field for a specific range of buoyancy ratio values where the Prandtl number Pr=1, the Lewis number Le=2, the thermal Rayleigh number Ra_T=10⁵, and the aspect ratio A=2 for the enclosure. In the presence of the magnetic field, however, no oscillatory behavior is observed. Numerical results are reported for the effect of the heat generation or absorption coefficient and the Hartmann number on the contours of streamline, temperature, concentration and density. In addition, results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. In this study, the thermal and compositional buoyancy forces are assumed to be opposite.     

Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model

Linear stability analysis has been carried out to predict the onset of double-diffusive convection in superposed fluid and porous layers using a one-equation model. The eigenvalue problem is solved numerically by a finite difference scheme. Results have been obtained for the thermal convection and salt-finger cases. Comparing with the results obtained for the same problems by Chen and Chen [F. Chen, C.F. Chen, J. Heat Transfer 110 (1988) 403–409] using a two-equation model, we find that these two methods give the same general characteristics of the marginal stability curves, however, there are differences in the critical conditions and the flow streamlines at onset. Carefully conducted experiments are needed to determine which model gives the more realistic results.     

Non-Darcy effects on conjugate double-diffusive natural convection in a variable porous layer sandwiched by finite thickness walls

Steady conjugate double-diffusive natural convective heat and mass transfer in a two-dimensional variable porosity layer sandwiched between two walls has been studied numerically. The Forchheimer–Brinkman–extended Darcy model has been used to solve the governing equations in the saturated porous region. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. An exponential variation of the porosity near the hot wall is considered. The vertical walls are impermeable and subjected to a horizontal gradient of both temperature and concentration while the horizontal walls are adiabatic. A finite volume approach has been used to solve the dimensionless governing equations and the pressure velocity coupling is treated with the SIMPLE algorithm. The model has been validated with available experimental, analytical/computational studies.     

Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid

The Prandtl number dependence of unsteady laminar natural convection along an infinite vertical plate in a thermally stratified fluid is investigated. Flows are induced by an impulsive (step) change in plate temperature and by a suddenly imposed plate heat flux. Analytical solutions of the viscous equations of motion and thermodynamic energy are obtained for Prandtl numbers near unity by the method of Laplace transforms and a regular perturbation expansion. The zeroth-, first- and second-order terms in the expansion are obtained for an impulsive change in plate temperature, while the zeroth- and first-order terms are obtained for a sudden application of a plate heat flux. The developing boundary layers are thicker, more vigorous, and more sensitive to the Prandtl number at smaller Prandtl numbers (<1) than at larger Prandtl numbers (>1). The analytical results are confirmed and extended with results from numerical simulations for Prandtl numbers strongly deviating from unity.     

Numerical study of turbulent double-diffusive natural convection in a square cavity by LES-based lattice Boltzmann model

Turbulent double-diffusive natural convection in a square cavity represents numerous important problems in practice as well as in fundamental. However up to date the study on it is quite sparse and most previous studies just focus on laminar regime. To the best knowledge of the present authors, only several k–? models were developed to investigate turbulent double-diffusive convection and there is no attempt to use Large Eddy Simulation (LES). In order to deepen our knowledge on turbulent double-diffusive convection in a square cavity, we propose a novel LES-based lattice Boltzmann (LB) model to simulate such turbulent convectional flow. Previous LES-based LB models can be recovered from the present model. We find that the symmetry of the fluid circulation becomes broken since the Rayleigh number Ra = 10⁸, although the asymmetry is more clear when Ra ? 10¹⁰. More important, in the present study we find the power-law relationship among the Nusselt (Nu), the ratio of buoyancy forces (N) and the Rayleigh number (Ra) still exists in turbulent regime. The formula among them can be concluded as Nu = a × (Ra × ∣1 ? N∣)^b + c. The values of parameters a, b and c are given in this work.     

Effect of the days scrolling on the natural convection in an open ended storage silo

The problem of unsteady natural convection heat transfer in a vertical, open ended, porous cylinder heated laterally with a sinusoidal time variation of the temperature has been investigated numerically. The model considered is the classical Darcian flow coupled with the energy equation. In the case of constant wall temperature, two types of chimney flows take place, with and without fluid recirculation. The present problem depends on the filtration Rayleigh number (Ra), the aspect ratio (A) and the inlet–outlet conditions (Bi). For low dimensionless temperature amplitudes (XA < 0.5) in the sinusoidal time variation, the resulting heat transfer is found to be globally equivalent to the case of constant wall temperature. The observed relative difference between sinusoidal and constant wall temperature is less than 5%. This difference decreases as the Ra is reduced.     

Effect of natural convection on oscillating flow in a pipe with cryogenic temperature difference across the ends

The effect of natural convection on the oscillatory flow in an open-ended pipe driven by a timewise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Two cases, namely, one with natural convection acting downwards and the other, with natural convection acting upwards, are considered. The full set of compressible flow equations with axissymmetry are solved using a pressure correction algorithm. Parametric studies are conducted with frequencies in the range 5–15 Hz for an end-to-end temperature difference of 200 and 50 K. Results are obtained for the variation of velocity, temperature, Nusselt number and the phase relationship between mass flow rate and temperature. It is found that the Rayleigh number has a minimal effect on the time averaged Nusselt number and phase angle. However, it does influence the local variation of velocity and Nusselt number over one cycle. The natural convection and pressure amplitude have influence on the energy flow through the gas and solid.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Minimizing hot spot temperature of porous stackings in natural convection

Due to their large surface of heat transfer per volume, porous structures such as metallic foams are considered as an interesting alternative to fins. In this paper, we investigate the optimal configuration of a porous medium structure with the objective to minimize the hot spot temperature in natural convection. The heat sink is adjacent to a heat-generating plate, and consists of a stacking of porous layers, in which a cooling fluid circulates strictly driven by natural convection. The objective of this work is to minimize the hot spot temperature of the system. The design variables are the porosity and the material of each layer. The thermal performance is evaluated with a CFD code based on a finite volume approach. The hot spot temperature minimization is pursued with a genetic algorithm (GA) under global mass and cost constraints. The GA determines the optimal porosity and selects the most appropriate material of each layer. Furthermore, the optimal total length of the stacking is indirectly determined by the GA as layers can be added or removed in order to improve the global performance and/or satisfy the constraints. A mapping of the designs generated by the GA as a function of the mass and cost constraint combination reveals that an appropriate distribution of porosity and material benefits the overall thermal performance of the layered porous medium.     

A numerical study on natural convection of a heat-generating fluid in rectangular enclosures

Unsteady natural convection of a heat-generating fluid in the enclosures of a rectangular section with isothermal or adiabatic rigid walls is investigated numerically in the present work. Using the high-performance finite-difference scheme in the 2D stream function-vorticity formulation, developed by the authors, the peculiarities of convective heat transfer are studied in a wide range of thermal and geometric parameters for the laminar regime of fluid motion. Steady-state as well as oscillating solutions obtained in this work are compared with available numerical and experimental results of other researchers.     

自然对流温度场节能改造

本文通过热流理论分析和传热计算,指出了某一运行多年的自然对流温度场的不足,为了节能增效,采取了快捷的改造措施。工程竣工后试运转表明节能率可达50%,对所有自然对流温度场的改造具有普遍指导意义和重要参考借鉴作用。     

Effect of natural convection on freezing of water around an isothermal,horizontal cylinder

Freezing of superheated water around an isothermal, horizontal cylinder has been studied experimentally. The shadowgraph technique was used to visualize the flow (plume) development in the water, and the contour of the ice layer around the heat sink was recorded photographically. Freezing of water was always accompanied by natural convection and produced nonuniform ice growth. Benard-Goertler instabilities resulted in secondary flows which produced waviness (nonuniform) ice growth along the axis of the cylinder. The number, location and magnitude of the ripples were found to depend on the initial water superheat and on the heat sink temperature.     

Electrothermal convection in a rotating dielectric fluid layer: Effect of velocity and temperature boundary conditions

The simultaneous effect of a vertical AC electric field and rotation on the onset of thermal convective instability in a horizontal rotating dielectric fluid layer is studied by performing linear stability analysis. The lower and upper boundaries of the fluid layer are considered to be either rigid or free and either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free–free isothermal boundaries. It is observed that the oscillatory convection is not a preferred mode of instability for dielectric fluids and the necessary conditions for its occurrence are independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. The similarities and differences between the results of isothermal and insulated boundaries are highlighted. It is noted that the effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hence to hasten the onset of convection. To the contrary, the effect of rotation is to delay the electrothermal convection for a fixed type of boundary conditions. Although the rigid–rigid boundaries enhance the stability when compared to rigid–free and free–free boundaries up to moderate values of Taylor number, the situation is reversed at high Taylor number domain. This trend depends on the temperature boundary conditions as well.