Search

Mixed convection in the lid-driven cavity model widely represented real engineering applications, especially electronic cooling and wind across buildings. In past decades, avalanche experiments and numerical calculations have been done on the lid-driven cavity model. Unfortunately, one unusual flow behavior in the cavity mixed convections—multiple steady solutions, i.e., identical boundary conditions and governing parameters whereas different initial conditions or loading perturbations may lead to two or more flow states, and it was hardly investigated. Multiple steady enclosure flow behaviors essentially complicate the convective transport of heat and air, which has been vividly analyzed by streamlines, heatlines and isotherms. In the present work, the flow mechanisms and evolution driven by mixed convections in lid-driven cavities for multiple aspect ratios will be investigated through the numerical methodology of computational fluid dynamics. The effects of dimensionless parameter (Grashof number, Reynolds number, and Richardson number) on multiple flow motions have been disclosed, regarding of hysteresis effect and their destabilization mechanism. Investigations on these complicated flow motions essentially facilitate the optimization of engineering flows similar to lid driven enclosures, whatever mechanical cooling of electronics, or wind across street canyons. [ABSTRACT FROM AUTHOR]

The present study presents a comprehensive analysis of effects of porous fins on mixed convection heat transfer in lid-driven square cavities, where the top lid has the two-way movement. Porous medium with varying permeability, instead of the solid one, could widely modify its baffling effect on fluid flow and could also be utilized to control fluid flow and heat transfer. Fluid flow within the cavity was solved through the Navier–Stokes equations, while that within a saturated porous medium was governed by the Darcy–Forchheimer model. Numerical results indicate that the adding porous fins with excellent permeability could enhance heat transfer dramatically, especially for more fins. The rate of heat transfer enhancement due to an increase in Darcy number decreases, and similar trends were observed for the quantitative variations of porous fins. Besides, positions of porous fins have significant effects on fluid flow and heat transfer. The correlations of average Nusselt numbers, as functions of various governing parameters, have been proposed. The present investigations could be beneficial to the design of the microelectronic cooling through the installation of porous-alike materials or modules. [ABSTRACT FROM AUTHOR]

The effects of porous fins on mixed convection inside lid-driven square enclosures were reported in the present work. The porous medium with varying permeability, instead of the solid one, could widely change the baffling performance on the fluid flow, where this characteristic could be beneficial for controlling fluid flow and energy transport, typically electronic cooling process. The top lid could have the two-way movement. The working fluid in the cavity was governed by the N-S equations while that within porous medium was determined by the non-Darcy model called the Darcy-Forchheimer model based on representative element-averaging method. Relevant governing parameters, including Richardson number, Darcy number, quantities, length and distribution ratio of porous fins, are sensitively varied to identify their effects and roles on mixed convection heat transfer. Numerical results illustrate that the mechanism of main circulation development is modified by the additional fins. The adding porous fins with excellent permeability enhance heat transfer dramatically, while these fins with tiny Darcy number deteriorate heat transfer rate. The rate of heat transfer enhancement due to the increasing of the length and quantities of fins decreases. Furthermore, the distribution ratio shows the significant effects on the fluid flow and heat transfer. Present investigations could benefit the microelectronic cooling through the installation of porous-alike materials or modules. [ABSTRACT FROM AUTHOR]

In former theoretical researches of nanofluid flows, numerical investigations could not agree with experimental observations, particularly regarding whether the mixing nanoparticles will enhance or deteriorate the heat transfer. In the present work, thermal driven buoyancy flows of nanofluids in a square enclosure were modeled by the use of homogeneous assumptions and the effective kinematic viscosity and thermal conductivity formulas. Thoroughly developed heat transfer coefficient is subsequently proposed, aiming to critically evaluate the performance of nanofluid heat transport. Numerical results are presented over a wide range of thermal Rayleigh number (103 ≤ Ra ≤ 106) and nanoparticles volume fraction (0.001 ≤ φ ≤ 0.04). Present modeling results accurately predict both the enhancement and deterioration of the natural convection heat transfer, fully validated by former experimental observations. Overall, mathematical models and Nusselt number definitions proposed in the present work effectively enhance the reliability of numerical modeling researches on the nanofluid heat transfer. Present clarification research on the Nusselt unifications could benefit future development of thermal carrier fluid enhanced by nano-particles. [ABSTRACT FROM AUTHOR]

Thermal buoyancy-driven natural convection in partial enclosures with multiple free openings is investigated regarding the coupling of the pressure correction algorithm with inner-loop iterations of the pressure correction equation. Unexpected steady flow phenomena, i.e., nonunique steady flow states, are observed when different inner-loop iterations m and relaxation factorsαof the pressure correction equation are implemented, after the appropriate assumptions on the free opening boundary conditions are made. Numerical experiments and benchmark exercises confirm that definitions on the free openings could be too weak to ensure global similarity to the results of extended domain methodology. Furthermore, inner-loop iteration m and relaxation factorαcould have similar effects on the nonunique steady flow results. As thermal Rayleigh number is relatively low, a linear relationship could be established among inner-loop iteration m, relaxation factorα, and mass exchange rate,MER. In addition, harmonic arrangements on the iteration residuals of the momentum equation and the pressure correction equation could accelerate convergence of the whole pressure correction algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Slot ventilated enclosure flows have been simulated, respectively in displacement ventilation and mixed ventilation covering from the forced convection dominated flow to the natural convection dominated flow. Direct convection simulation together with the turbulent streamlines and turbulent heatlines demonstrate that the enclosure flow pattern, indoor thermal level and heat transfer potential will depend on the interactions of external forced flow and thermal buoyancy driven flows, i.e., Reynolds number and Grashof number. In subsequent inverse convection modeling, the inverse determination of enclosure wall heat flux profiles was conducted by the use of adjoint methodology, in which the direct, sensitivity and adjoint problems are formulated and solved by finite volume method. The effects of the supplying air flow rate, thermal source strength, ventilation mode, flux functional forms, and the measurement errors on the accuracy of inverse turbulent convection estimation have been investigated. The inverse solutions of turbulent convections are of low level accuracy as the flow becomes thermal-driven turbulent flows, and they deteriorate as the noise levels increase. This work is of fundamental importance for the room air flow design and measurements involving the turbulent thermal convections. [Copyright &y& Elsevier]

Abstract: Simultaneous transport of heat and moisture by conjugate natural convection in a partial enclosure with a solid wall is investigated numerically. Moist air motions are driven by the external temperature and concentration differences imposed across enclosures with different ambient moisture conditions. The Prandtl number and Schmidt number used are 0.7 and 0.6, respectively. The fluid, heat and moisture transports through the cavity and solid wall are, respectively, analyzed using the streamlines, heatlines and masslines, and the heat and mass transfer potentials are also explained by the variations of overall Nusselt and Sherwood numbers. The numerical simulations presented here span a wide range of the main parameters (heat and mass diffusion coefficient ratios, solid wall thickness and thermal Rayleigh numbers) in the domain of aiding and opposing buoyancy-driven flows. It is shown that the heat transfer potential, mass transfer potential, and volume flow rate can be promoted or inhibited, depending strongly on the wall materials and size, thermal and moisture Rayleigh numbers. [Copyright &y& Elsevier]

Abstract: The numerical study presented in this work describes the direct and inverse mixed convection problems in a slot-ventilated enclosure subjected to an unknown heat flux on one side. Particularly, the interaction of internal natural convection with the cold ventilated flow leads to various flow fields depending on the Richardson number, Reynolds number, and the functional form of the imposed boundary heat flux. Fluid and heat transport structures across the enclosure are visualized by the streamlines and heatlines, respectively. Subsequently, an iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined for a domain of arbitrary geometries. In this approach, no a priori information is needed about the unknown boundary heat fluxes to be determined. The accuracy of the heat flux profile solutions is shown to depend strongly on the values of Reynolds number and flux functional forms. Effects of measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the natural convection and forced convection. [Copyright &y& Elsevier]

Abstract: The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy–Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher–Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated. [Copyright &y& Elsevier]

Abstract: This paper reports a numerical study of double-diffusive convective flow of a binary mixture in a porous enclosure subject to localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy–Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. The set of coupled equations is solved using the SIMPLE algorithm. An extensive series of numerical simulations is conducted in the range of , , and , where N, Le, Da and L are the buoyancy ratio, Lewis number, Darcy number and the segment location. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present model as limiting cases. Streamlines, heatlines, masslines, isotherms and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed overall Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment. [Copyright &y& Elsevier]

Present work numerically and theoretically investigates the fluid flow and heat transfer in an inclined solar chimney induced by thermal buoyancy within a range of thermal Rayleigh numbers (Ra) and chimney inclination angles (α). Transport paths of fluid and heat were visualized by streamlines and heatlines, respectively. Backflow could be observed in the solar chimney when Ra increases beyond a certain value, and it directly paralyses the ventilation of the chimney. Numerical results further demonstrate that the larger the inclination angle α is, the smaller the corresponding critical Ra number of the reverse flow occurs at the glass side is. The larger the inclination angle α is, the greater Nusselt (Nu) value of the absorber wall is, while its increment rate decreases gradually with the increase of the inclination angle α, when thermal Ra is maintained. As α varies from 30° to 90°, corresponding critical Ra for reversal flows gradually decreases; furthermore, these critical values obtained by the theoretical solutions were higher than those from simulation. Volume flow rates increase positively with Ra when α is no more than 30°; however, they increase initially and then decline with Ra when α is no less than 45°. In order to enhance ventilation performance, a solar chimney flush attached with discrete heating sources on the glazing wall is proposed. The numerical results indicated that modified inclined solar chimney with discrete heating sources could enhancing its ventilation performance by preventing reverse flow occurring in the channel. Our investigations also showed that the optimal inclination angle for maximum volume flow rate heavily depends on Ra. This research could provide necessary technical support and guidance for solar energy utilization and building energy conservation through air channel in building envelopes. • Thermal buoyancy driven natural convection occurred in the inclined solar chimney. • Reverse flows observed at the outlet strengthen with increasing inclination angle. • Optimal inclination angle for maximum volume flow rate heavily depends upon Ra. • Heat transfer rates and volume flow rates were influenced by discrete heating sources. • Solar chimney with discrete heat sources could improve ventilation performance. [ABSTRACT FROM AUTHOR]

Slot-ventilated enclosure flows occurr in many engineering problems, including microelectronic cooling, cardiovascular blood flow, airborne transmission, built ventilation, etc. Inverse models on such slot-ventilated flows have consistently been observed, straightforwardly representing that boundary wall conditions are missing or unknown, whereas temperatures at certain internal points could be known as priors. In present work, the direct and inverse models on the slot-ventilated enclosure flows were established successively. For direct flow problems, enclosure flows covering from forced convection dominated flow to natural convection dominated flow are fully simulated, varying some dominant parameters, Richardson number, Reynolds number, and the functional forms of the imposed boundary heat flux. In subsequent inverse convection modeling within a mixed convection domain, multiple unknown heat fluxes and their profiles were creatively identified using the adjoint methodology, in which direct, sensitivity, and adjoint problems were formulated and solved jointly by finite volume method. The impacts of Reynolds number, Richardson number, flux functional forms, and measurement errors on the accuracy of inverse solutions have been thoroughly examined. Inverse solutions accuracy becomes poor as the field flow is dominated by mechanical ventilation, and their accuracy further deteriorates as the noise levels increase. The results demonstrate that the current inverse problem approach could yield highly accurate estimations for multiple arbitrary unknown heat flux functions within the enclosure, without any priori information. This versatile approach was applicable to a range of mixed convection control or reconstruction problems, offering substantial contributions to electronic cooling design and the optimization of enclosed air environments. [ABSTRACT FROM AUTHOR]

Convection resonance could be significant for strengthening heat and mass transfer rates in enclosure flows, such as electronic cooling, built air environment and green energy harvest. This paper presented a numerical investigation on the coupled heat and moisture transport and resonance phenomena in enclosures packed with discrete porous media, where natural convection dominated, mixing convection, and forced convection dominated domains could be covered. Various physical parameters were extensively investigated, including buoyancy ratio (−10 ≤ Br ≤ 10), permeability (10−6 ≤ Da ≤ 101), Richardson number (10−1 ≤ Ri ≤ 5), Reynolds number (50 ≤ Re ≤ 1000), enclosure tilting angle (0° ≤ Φ ≤ 180°), thermal conductivity (0.1 ≤ Kr ≤ 10), and frequency (10−2 ≤ ω ≤ 5). Present results showed that in a vertical enclosure, reduction of porous medium permeability and promotion of the ratio of Richardson number to floating force could enhance heat and mass transfer rates. In an inclined enclosure, the effect of buoyancy and inclination angle on heat and mass transfer processes and rates exhibits a centrally symmetric distribution. In addition, a dense porous media and cooperative heat and mass buoyancy force ratio were beneficial to reducing the total entropy production. Finally, the transient heat and moisture transport and resonance phenomena in discrete distributed porous media were investigated. The system exhibits significant self-excited oscillations at ω = 100, being evident whatever sparse or dense porous media. Heat and mass transfer pulse amplitude in a periodically varying heat source enclosure decays with increasing porous medium thermal conductivity ratio, whereas it increases with increasing buoyancy ratio and Reynolds numbers. The most significant heat and moisture resonance occurs in a mixed convection system with Da = 10 and Br = 4. Present oscillation and resonance researches could contribute to the development of electronic cooling or built ventilation with much low or free cost of thermal management. • Heat and moisture transports inside in an inclined porous enclosure were modelled. • Transient, oscillatory, and resonant states were observed for mixed convections. • Reduction of porous permeability and promotion of Ri and Br enhanced transport rates. • Dense porous media and cooperative Br aided entropy production in inclined enclosure. • Self-excited oscillation and resonance were fully analyzed by various parameters. [ABSTRACT FROM AUTHOR]

Abstract Fluid flow and heat transfer mechanism in a solar chimney induced by thermal buoyancy within a range of Ra numbers are reported by numerical and experimental investigations. The transport paths followed respectively by air and heat are visualized by streamlines and heatlines. Numerical results demonstrate that the reverse flow not only slows down the volume flow rate but also accelerates backflow presented in the solar chimney when Ra increases beyond a certain value, which makes the solar chimney lost its role of ventilation. In order to suppress the reverse flow and enhance ventilation performance, a solar chimney with multiple discrete sources flush attached the glazing wall is proposed. The effects of the sizes, positions, and numbers of those discrete heat sources on the system heat transfer rate and volume flow rate are discussed. After comparing with conventional solar chimney, the modified solar chimney with discrete heat source of height D 0 = 1 and position S 0 = 1 could perform better, not only preventing reverse flow but also enhancing the ventilation performance. The results obtained by the lab experimental measurements were agreed well with former numerical simulations. Temperature distributions along the heated wall for different heat input at ambient temperature illustrate the temperatures on the heated wall do not increase linearly and even drop near the top exit. This research could be significant for solar energy utilization and building energy conservation. Highlights • Thermal buoyancy driven natural convection in the solar chimney channel was modeled. • Heatlines clearly delineate heat transport structures, similar to streamlines. • Heat transfer rates and volume flow rates could be influenced by discrete heat sources. • Reverse flow evolves into backflow, at which solar chimney loses the role of ventilation. • Solar chimney with discrete heat sources improves ventilation performance significantly. [ABSTRACT FROM AUTHOR]

Two component conjugate natural convection in a rectangular inclined enclosure having a partition with finite thickness and imposing heat and mass fluxes on the long end walls is studied both analytically and numerically, representative of heat and moist vapor transport across modern building enclosures. Contours of stream function, heat function and mass function are presented to clearly scrutinize the mechanism of heat and moisture transports. Present research covers the range of Ra from 10 3 to 10 7 , N from −10.0 to 10.0, d from 0 to 0.2 and Φ from −90° to 90°. In most of treated situations, the analytical solution, based on the parallel flow approximation, is founded to be in good agreement with a numerical solution. For the vertical case, thermal Nusselt and species Sherwood numbers arrive at the minimum as N = −1.0, which is helpful to determine the optimized buoyancy ratio in engineering applications. The results also show that the presence of a partition suppress the intensity of convection. Similar trends are also observed in the inclined enclosure. Furthermore, the combined effect of opposed buoyancy ratio and negative angle of inclination is identical to that of cooperate buoyancy ratio and positive angle. Upward solutions, downward solutions and rest solutions have been exemplified with varying N and inclination angles. Dual solution branches could be sustained in the vicinity of N = −1.0, while the rest solutions obtained from rest states are completely coinciding with former continuous solutions. [ABSTRACT FROM AUTHOR]

Inverse conjugate natural convection problem with multiple unknown heating fluxes is examined in this study by conjugate gradient method based on temperature measurements inside the enclosure. The direct problem, as well as the auxiliary problems, required for the solution of the inverse problem with the CGM is formulated in terms of the Cartesian coordinates. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Some parameters affect the fluid and heat transport significantly, which have been vividly analyzed by streamlines and heatlines, respectively. The effect of thermal Rayleigh number, body size, thermal conductivity of solid-to-fluid, number of blocks, heat flux profiles, measurement errors and the number of sensors on the inverse solution accuracy are respectively addressed. Inverse solutions obtained with simulated temperature measurements reveal that extremely accurate estimations could be obtained for the unknown heat flux functions with the present inverse problem approach. This research could be significant for the design of electronic cooling and enclosed air environment. [ABSTRACT FROM AUTHOR]

Double-diffusive natural convection in a vertical enclosure containing various solid block arrays is numerically and analytically investigated in present work, where heat and species source and sink are simultaneously attached on the walls. Rayleigh number, buoyancy force ratio, number of inner solid blocks, solid thermal conductivity and mass diffusion coefficient have been varied to observe inherent flow structures and mechanism of thermal and mass transports, regarding of different levels of solid-to-fluid volume ratios. Correlations have been presented for different flow regimes, namely thermal buoyancy driven flow and solutal buoyancy driven flow. Simulation and correlation results demonstrate that influences of thermal conductivity and mass diffusion coefficient of the solid block arrays on average Nusselt and Sherwood numbers are not evident compared with that of Rayleigh number. Furthermore, there is a positive correlation between average Nusselt number and Sherwood number. In addition, under certain values of Rayleigh number, absolute values of buoyancy force ratio close to unity will cause multiple steady solutions in pure natural convection. This research could benefit the future thermal and species management for electronics and built environment. • Electronic cooling and pollutant transport are driven by the natural convection. • Multiple steady solutions of pure natural convection inside the enclosure were disclosed. • Thermal conductivity and mass diffusion coefficient of solid matrix were broadly tested. • Rayleigh number, buoyancy ratio, volume and number of solid blocks put effects on the convection. • Convective heat lines and mass lines were presented to identify the characteristics of transports. [ABSTRACT FROM AUTHOR]

This paper deals with thermosolutal convection in an inclined enclosure inserted with heat-generating porous blocks under the influence of magnetic field. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the enclosure. An extensive series of numerical simulations is investigated in the range of parameters 0 ≤ Ha ≤ 150, 103 ≤ Ra ≤ 107, −10.0 ≤ N ≤ 10.0, 10−9 ≤ Da ≤ 10−1, 0.1 ≤ Kr ≤ 10 and −90° ≤ Φ ≤ 90°. Streamline, isotherms, isoconcentrations and masslines are produced to illustrate the fluid, heat and moisture flow structures. It is founded that overall Nusselt number is an increasing function of Ra , N , Da and Kr in the vertical enclosure, while decreasing with Ha. The permeability and thermal conductivity of porous blocks have no significant effect on moisture transfer rate. The Nusselt and Sherwood curves for different inclination angle are presented to be parabolic, and the maximum are near at Ф = −10° and 30°, respectively. In addition, correlations of the overall Nusselt and Sherwood numbers depending on thermal Rayleigh number, buoyancy ratio, Hartmann number and inclination angle have been obtained, which are beneficial to determine heat and moisture transfer rates in electrical devices. • Heat and moisture transfer processes occurred in cooling of multiple electronic devices • Disconnected porous blocks with internal energy generation are inserted in the enclosure. • Overall Nusselt number increases with Ra , N , Da and Kr , while decreases with Ha. • Permeability and thermal conductivity of porous blocks hardly influence the moisture transfer rate. • Correlations of the overall Nusselt and Sherwood numbers have been obtained. [ABSTRACT FROM AUTHOR]

The application of porous media for electronic cooling process, instead of solid one, generally strengthens heat conduction while weakens convection insignificantly at high Darcy number. In the present work, effects of morphology and topology of porous fins on the laminar natural convection heat transfer were investigated in a differentially heated enclosure. Volume averaged Darcy-Forchheimer model was applied to solve the transport process within the porous media while the Navier-Stokes equations were employed within pure fluid region. Relevant governing parameters, including thermal Rayleigh number, Darcy number, thermal conductivity of the porous matrix, designs of porous fins, are sensitively varied to identify their effects and roles on the natural convection flows. Depending on thousands of numerical data, the correlation has been developed for all designs of porous fins. Numerical results illustrate that the adding porous fins with excellent permeability and heat conduction contribute to the remarkable heat transfer enhancement while the adding fins, acting like solid ones and having poor heat conduction, could result in an increase of thermal resistance and the deterioration of heat transfer. Numerical results further show that there exists an optimal design of porous fins to achieve the best performance of heat transfer if some conditions were satisfied. Overall, this study could benefit the electronic cooling by the installation of porous-alike materials. • Electronic passive cooling is modeled by the natural convection in an enclosure. • Thermal conductivity and Darcy number of porous matrix were broadly tested. • Morphology and topology of porous fins on the natural flow were analyzed. • Porous fins flush mounted on the hot wall affect heat transfer rates significantly. • Porous fins maximize the heat transfer rate if some conditions were satisfied. [ABSTRACT FROM AUTHOR]