Modeling of double diffusive buoyant flow in a solar collector with water‐CuO nanofluid

The behavior of a prism‐shaped solar collector with a right triangular cross sectional area is investigated numerically. The water‐CuO nanofluid is taken as the functioning liquid through the solar collector. The leading differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The performance of parameters in terms of temperature, mass, velocity distributions, radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid height horizontal‐vertical velocities, and sub‐domain average velocity field are investigated systematically. These parameters include the Rayleigh number Ra and the solid volume fraction φ. The outcome explains that the performance of the solar collector can be enhanced with the largest Ra and φ. The code validation shows excellent concurrence with the hypothetical outcome obtainable in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21039     

Cross flow on transient double‐diffusive natural convection in inclined porous trapezoidal enclosures

This paper investigates the cross‐diffusion effects subject to exponential variable boundary conditions on transient double‐diffusive natural convection flow in an enclosure. The flow domain is a two‐dimensional inclined trapezoidal cavity filled with a porous medium. The top wall is assumed to be insulated and permeable, while the enclosure's bottom wall is subject to exponential varying temperature and concentration. The prescribed temperature and concentration are different at the vertical walls. Conservation equations are used as the governing equations. The finite element Galerkin weighted residual method, in association with the Newton‐Raphson scheme is employed to solve the system of coupled nondimensional equations. The numerical tests are confirmed with existing literature and are found to be in excellent agreement. The simulations results for stream functions, isotherms, and isoconcentrations are discussed for the various flow parameters. A sensitivity analysis using the response surface method suggests that the average Nusselt and Sherwood numbers are more sensitive to the cross‐diffusion effects. It is further observed that the cross‐diffusion terms stabilize the sensitivity to the angle of inclination.     

Theoretical study and practical application of the capillary film solar distiller

In the south of Algeria, to supply sufficient fresh water for the population, desalination is necessary because water resources (underground and geothermal) are brackish.This paper presents the theoretical study and the results of experiments carried out with a capillary film multi-effect distiller installed in the south of Algeria (in a village near Touggourt, where the temperature of the groundwater is about 65°C at the source). The name of this device is DIFICAP (stiller with a lm in illary motion).The aim of our study is to improve the efficiency of this distiller. The research and development of this desalination process is carried out under the following aspects: modelisation of heat and mass transfer, experimentation under direct solar radiation in South Algeria and technical development to aim to optimize the efficiency of this distiller.The theoretical and experimental results show that the efficiency of this distiller increases when the temperature of the brackish water, the intensity of the solar radiation and the number of stages increase.     

Numerical research of double‐diffusive natural convection in elliptical cylinders: Effect of thermal Rayleigh number

This paper is the first part of a two‐part study, and it presented numerical research of double‐diffusive natural convection within an annulus area, situated in two horizontal confocal elliptic solids charged by a Newtonian fluid. The elliptical coordinates were used to transform the physical domain into a rectangular one. To resolve the governing equations and the boundary layer conditions, a calculator code based on the finite volume approach was developed. The details of the influences of thermal Rayleigh number on heat and mass transfer were investigated. Results obtained were compared with those existing in other reasearch works.     

Influence of Lewis number on double‐diffusive convection in a square cavity filled with a binary gas

This paper considers double‐diffusive convection in a square cavity filled with a binary gas, due to horizontal opposing temperature and concentration gradients. The effect of Lewis number was considered under the conditions of Prandtl number Pr = 1, buoyancy ratio N = 1, and thermal Rayleigh numbers R_aT = 10⁴ and 10⁵. Numerical solutions are obtained by a Chebyshev collocation technique with high resolution. Depending on the Lewis number, three kinds of flow structures are identified: symmetric steady flow, asymmetric oscillatory flow, and symmetric oscillatory flow. Oscillatory flow occurs in the regime of thermal dominant flow, and leads to a periodic change between stable and unstable states in species stratification due to the thermo‐solutal interaction. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 63–75, 2001     

Influence of Lewis number on double‐diffusive convection in a square cavity filled with binary gas

This paper presents double‐diffusive convection in a square cavity filled with binary gas, due to horizontal opposing temperature and concentration gradients. The effect of Lewis number was considered under the conditions of Prandtl number Pr = 1, buoyancy ratio N = 1, and thermal Rayleigh number Ra_T = 10⁴ and 10⁵. Numerical solutions are obtained by a Chebyshev collocation technique with high resolution. Depending on the Lewis number, three kinds of flow structures are identified: symmetric steady flow, asymmetric oscillatory flow, and symmetric oscillatory flow. Oscillatory flow occurs in the regime of thermal dominant flow and it leads to a periodic change between stable and unstable states in species stratification due to the thermo‐solutal interaction. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 85–97, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10073     

Numerical analysis of entropy generation in mixed convection flow with viscous dissipation effects in vertical channel

A numerical investigation is performed into the entropy generated within a mixed convection flow with viscous dissipation effects in a parallel-plate vertical channel. In performing the analysis, it is assumed that the flow within the channel is steady, laminar and fully developed. The governing equations for the velocity and temperature fields in the channel are solved using the differential transformation method. The numerical results for the velocity and temperature fields are found to be in good agreement with the analytical solutions. The entropy generation number (N_s), irreversibility distribution ratio (Φ) and Bejan number (B_e) of the mixed convection flow are obtained by solving the entropy generation equation using the corresponding velocity and temperature data.     

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.     

Double‐diffusive natural convection in a partially heated enclosure using a nanofluid

This paper analyzes numerically the effect of double‐diffusive natural convection of a water–Al₂O₃ nanofluid in a partially heated enclosure with Soret and Dufour coefficients. The top horizontal wall has constant temperature T_c, while the bottom wall is partially heated T_h, with T_h > T_c . The concentration in the top wall is maintained higher than the bottom wall C_c < C_h. The remaining bottom wall and the two vertical walls are considered adiabatic. Water is considered as the base fluid. The governing equations are solved by the Penalty Finite Element Method using Galerkin's weighted residual scheme. The effect of the parameters, namely, Rayleigh number and solid volume fraction of the nanoparticles on the flow pattern and heat and mass transfer has been depicted. Comprehensive average Nusselt and Sherwood numbers, average temperature and concentration, and mid‐height horizontal and vertical velocities at the middle of the cavity are presented as functions of the governing parameters mentioned above. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21010     

Double diffusive convection of a micropolar fluid saturated in a sparsely packed porous medium

This study examines the double diffusive convection of a sparsely packed micropolar fluid‐saturated porous medium by using a linear stability analysis. The Darcy–Brinkman–Forchheimer model is employed for the porous fluid layer. The stability criterion is sought analytically with the simple free‐free, iso‐thermal, and iso‐solutal boundary conditions. The dependence of stationary or oscillatory convection on the porous parameter, Lewis number, solutal Rayleigh number, and parameters involved in micropolar fluids is drawn and discussed. The results show that the critical wave number is found to be insensitive to the variation of governing parameters except for the porous parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21052     

Combined free and forced convection flow through a porous medium

Local similarity solutions of the forced and free convection flow past a porous medium bounded by a semi-infinite vertical porous plate are obtained numerically.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.     

含体积热源方腔的耦合自然对流换热数值模拟

对具有内热源方腔的稳态层流耦合自然对流换热进行了三维的数值模拟,采用的模拟代码基于连续介质计算力学的开源库OpenFoam,解决了自然对流换热与固体传热的耦合问题。对外壁面为常温、方腔内充满含体积热源流体的自然对流计算结果表明,温度场、速度场与非耦合的工况有很大差异。Ra的变化从10^5到10^9。     

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values.     

Numerical simulation of three-dimensional flow dynamics in a hot water storage tank

A hot water storage device is one of the most common household appliances yet it is also one of the biggest sources of energy consumption. With natural resources fading, it is imperative that typical high-energy users such as hot water systems are made as energy efficient as possible. Research has shown that the thermal performance of a hot water system can be increased by maximising the level of thermal stratification within the storage tank, which could lead to huge energy saving. To analyse the effects of tank geometry and operating conditions on the thermal stratification within a storage tank, seven three-dimensional models have been numerically simulated by using the computational fluid dynamics program Fluent with realistic boundary and initial conditions applied. The level of thermal stratification in each model has been quantified using exergy analyses. The results show that increasing the tanks height/diameter aspect ratio, decreasing inlet/outlet flow rates and moving the inlet/outlet to the outer extremities of the tank all result in increasing levels of thermal stratification.     

Employing exergy-optimized pin fins in the design of an absorber in a solar air heater

Fins serve as heat transfer augmentation features in solar air heaters however they increase pressure drop in flow channels. Pin fins are relatively good heat transfer augmentation features with superior aerodynamic performance and as a result find application in some solar air heaters. The exergy optimization method is employed in sizing the pin fin. Results indicate that high efficiency of the optimized fin improves the heat absorption and dissipation potential of a solar air heater. With optimum fin efficiency and superior absorptive coating quality, useful energy losses can be minimized. Some important observations pertinent in design are made.     

A review on entropy generation in natural and mixed convection heat transfer for energy systems

This paper reviews the second law analysis of thermodynamics in enclosures due to buoyancy-induced flow for energy systems. It defines entropy generation minimization or thermodynamic optimization. In addition, the article summarizes the recent works on entropy generation in buoyancy-induced flows in cavity and channels. Studies on mixed convection were also included in the study. Presentation was performed for flow in porous media and viscous fluid filled media at different shaped enclosures and duct under buoyancy-induced force.     

Numerical simulation of double diffusive mixed convection in an open enclosure with different cylinder locations

This article reports numerical simulation of the double diffusive mixed convection around a cylinder in an open enclosure with an inlet and exit ports. The temperature and mass concentration of the cylinder are higher than those of the inlet flow and the cylinder can be at three different locations (lower, middle and upper) in the enclosure. The inlet flow with low temperature and mass concentration is located at the lower-left wall of the enclosure and the exit is at the upper-right wall. Other walls are assumed to be adiabatic. Effects of Lewis number Le, buoyancy ratio Br, and cylinder locations on the double diffusive mixed convection are investigated at Richardson number Ri = 1.0 and 0.01 while Prandtl number Pr is kept at 0.7. Streamlines, isotherms, isoconcentrations, and the average and local Sherwood number at different parameters are reported to characterize the double diffusive mixed convection phenomena in the open enclosure.     

双层壁幕墙传热特性的数值模拟

建立了双层壁中层空间的流体动力学和传热学二维稳态数学模型。将内、外层玻璃幕墙的传热模型、遮阳板的传热模型相耦合计算出双层壁的热力性能。给出了不同高度上的温度和速度分布数据。计算结果与相关文献中的实验数据较吻合。     

Three-dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

The present article provides a three-dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (${10}^3\le \mathit{Ra}\le {10}^7$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from $\mathit{Ra}={10}^3$ to ${10}^7$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient $\mathit{\phi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number ($\mathit{Ra}={10}^3$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of $\mathit{Ra}={10}^4$ and ${10}^5$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large ($\mathit{Ra}{\ge 10}^6$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.