Effects of variable properties and non-uniform heating on natural convection flows in vertical channels

The effects of variable properties and non-uniform heating on laminar air flows induced by natural convection in vertical channels are investigated numerically. A full-elliptic model which accounts for variations in viscosity and thermal conductivity with temperature and which determines the density from the state equation has been applied to cases in which variable property effects cannot be neglected (including conditions for which flow reversals may occur). The influence of the Rayleigh number and non-uniformity of the wall heat flux distribution on the critical heat per unit time transferred from the walls in symmetric and asymmetric channels is analyzed for a wide range of Rayleigh numbers. It is shown that the maximum wall temperature can be reduced substantially by selecting an appropriate wall heat flux distribution, although at the cost of slightly more restrictive critical conditions.     

Routes to chaos of natural convection flows in vertical channels

The aim of the present study is the analysis of the transition to turbulence of natural convection flows between two infinite vertical plates. For the study of the problem, a number of Direct Numerical Simulations (DNSs) have been performed. The continuity, momentum and energy equations, cast under the Boussinesq assumption, are tackled numerically by means of a pseudospectral method, through which the three-dimensional domain is decomposed with Chebychev polynomials in the wall-normal direction and with Fourier modes in the wall-parallel directions. For low Rayleigh number values, the predictions of the flow regimes are consistent with the classical analytical results and linear stability analyses. In particular, the first bifurcation (Ra ≈ 5800) from the so-called laminar conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the flow regime becomes chaotic. This transition to chaos is found to be related with the amplification of spanwise instabilities occurring at scales larger than the channel gap, H. The study of the return of the system from the chaotic regime to the laminar base flow reveals a phenomenon of hysteresis, i.e. the chaotic regime persists even at Ra-values lower than the second critical value. From a numerical point of view, the predicted flow regimes appear to be extremely sensitive to the domain size, grid resolution and perturbation amplitude. These aspects are shown to be of crucial importance for the prediction of the heat transfer performance, and, hence, should be taken into consideration when numerical methods are used for the simulation of real-world problems.     

Radiative effects on natural convection in vertical convergent channels

Natural convection in air, in a convergent channel, uniformly heated at the principal walls, is experimentally investigated, in order to analyze the effects of the radiative heat transfer. Results in terms of wall temperature profiles as a function of the walls inclination angle, the spacing between the walls, the heat flux, are given for two values of the wall emissivity. Flow visualization is carried out to show the peculiar pattern of the flow between the plates in several configurations. The comparison between two wall emissivity values, 0.10 and 0.90, shows that the effect of thermal radiation is more pronounced for larger convergence angles. For a wall emissivity equal to 0.90 and for small values of the minimum channel spacing, heat transfer in slightly convergent vertical channels is stronger than in a vertical parallel channel. Flow visualization points out a recirculating zone in the upper part of the channel for small values of the minimum channel spacing and for converging angles equal to 5° and 10°. Nusselt numbers and dimensionless maximum temperatures are then evaluated and correlated to the Rayleigh number, in the investigated range from 5 to 5 × 10⁸ and 0° ? θ ? 10°. A very good agreement between experimental data and correlations is observed for the dimensionless parameters based on the maximum channel spacing. Comparisons between experimental and numerical data are also performed and a good relationship is observed.     

Investigation of natural convection in convergent vertical channels

Using air as the working fluid, natural convection heat transfer in a uniform wall temperature convergent vertical channel has been investigated numerically. The investigation encompassed half angles of convergence between 0° (parallel-walled channel) and 10° and the solutions were performed for (S/L) Ra_s range of 1 to 2 × 10⁴. In order to find a correlation format which will merge the convergent channel results for low Rayleigh number ranges (Ra′ < 10²) with those for the parallel-walled channel ones, the minimum (S_min), mean (S_avg), and maximum (S_max) interval spacing between channel walls were used as characteristic dimensions. It was found that merging was best achieved by the use of maximum interval spacing (S_max) as the characteristic dimension. These numerical findings agree with those for high Rayleigh number ranges (RA′ > 10²) reported in the literature.     

Numerical simulation for natural convection in vertical channels

The investigation of laminar natural convection in vertical obstructed channels is conducted using an h-adaptive finite element algorithm. The adaptive model uses an L₂ norm based a-posteriori error estimator with a semi-implicit, time-stepping projection technique. The advection terms are treated using an explicit Adams Bashforth method while the diffusion terms are advanced by an implicit Euler scheme. By using the adaptive algorithm, mesh independent studies can be avoided. Results are obtained for thermal and flow patterns including average Nusselt numbers for different parameters (Rayleigh number, aspect ratio and locations of obstructions) in both smooth and obstructed channels.     

Distribution of heat sources in vertical open channels with natural convection

In this paper we use the constructal method to determine the optimal distribution and sizes of discrete heat sources in a vertical open channel cooled by natural convection. Two classes of geometries are considered: (i) heat sources with fixed size and fixed heat flux, and (ii) single heat source with variable size and fixed total heat current. In both classes, the objective is the maximization of the global thermal conductance between the discretely heated wall and the cold fluid. This objective is equivalent to minimizing temperature of the hot spot that occurs at a point on the wall. The numerical results show that for low Rayleigh numbers (∼10²), the heat sources select as optimal location the inlet plane of the channel. For configuration (i), the optimal location changes as the Rayleigh number increases, and the last (downstream) heat source tends to migrate toward the exit plane, which results in a non-uniform distribution of heat sources on the wall. For configuration (ii) we also show that at low and moderate Rayleigh numbers (Ra_M ∼ 10² and 10³) the thermal performance is maximized when the heat source does not cover the entire wall. As the flow intensity increases, the optimal heat source size approaches the height of the wall. The importance to free the flow geometry to morph toward the configuration of minimal global resistance (maximal flow access) is also discussed.     

Numerical modeling of the electrohydrodynamic effect to natural convection in vertical channels

The electrohydrodynamic effect to natural convection inside the vertical channels is numerically investigated by computational fluid dynamics technique. The range of parameters considered are 10⁴ = Ra = 10⁷, 7.5 = V₀ = 17.5 kV, and 2 = aspect ratio = 10. Flow and temperature distributions are affected with supplied voltage at the wire electrodes, and the heat transfer enhancement is significantly influenced at low Rayleigh number. The augmented volume flow rate of fluid is indicated in relation with the number of electrodes. Moreover, heat transfer enhancement also depended on the electrode arrangement while the number of electrodes is initially fixed. The relation between channel aspect ratio and number of electrodes that performs the maximum heat transfer is expressed incorporating with the optimum concerning parameters.     

Transient effects in natural convection cooling of vertical parallel plates

This work presents results from a numerical study of transient natural convection between vertical parallel plates. Two boundary conditions – uniform wall temperature and uniform heat flux – are considered. Results presented include the rate of heat transfer for uniform wall temperature and the maximum wall temperature for uniform heat flux. Also presented are simple correlations to calculate the minimum heat transfer and the maximum wall temperature during the transient period. It is found that for uniform wall temperature the ratio of the minimum heat transfer to the steady state heat transfer decreases with length of the channel, and for uniform heat flux the maximum transient temperature has a maximum of about 9% over the steady state temperature.     

The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion

This paper concerns the laminar flows which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels are assumed small, as is typical for many processes in water and in atmospheric air. The usual Boussinesq approximations yield a set of equations which are shown to have solutions of similarity form for combined buoyancy effects, for vertical flows adjacent to surfaces and in plumes. This similarity is of the same form as that found for single buoyancy mechanism flows. The resulting equations were integrated for air and water for various practical values of the Schmidt number and for multiple buoyancy effects aiding and opposing. The results show many interesting effects on velocity, heat and mass transfer, and on laminar stability. A comparison of the results with those of integral method analysis shows the limits and reasons for failure of these approximate calculations in the more complicated of such combined buoyancy mechanism flows.     

Laminar natural convection in a vertical stack of parallelogrammic partial enclosures with variable geometry

A numerical study is conducted for laminar natural convection heat transfer occurring in a vertical stack of parallelogrammic partial enclosures. The partitions separating adjacent enclosures are always parallel to each other, however their angle relative to the horizontal can change. The length of each partition is less than the width of the main enclosure, which has an aspect ratio of 5. Adjacent enclosures are thermally linked through the fluid exchange, and through the finite thermal conductivity of the partitions. The thermal diode effect offered by the geometry is analyzed in terms of the partitions’ inclination angle and materials for different thermal boundary conditions/operating conditions. The thermal diode effect, and even its actuating direction, can be changed by changing the inclination angle of the partitions. The main focus of the present work deals with the heat transfer analysis based on the overall Nusselt number, and the visualization of the flow field and heat transfer mechanisms, by using the isotherms, the streamlines and the heatlines. Results clearly indicate the high potential of this configuration, based on the thermal diode effect, to be used as an effective heat transfer device in real situations of thermal engineering. The number of governing parameters is high, and the results are presented only for situations selected on the basis of their relevance. For computational expediency, it is analyzed the solution obtained for one single parallelogrammic partial enclosure of the stack, which is thermally linked with its adjacent enclosures by using vertical cyclic boundary conditions. This procedure has some potential, since it yields results with good accuracy to predict the overall thermal behavior of the stack.     

Dual mixed convection flows in a vertical channel

The classical problem of the fully developed mixed convection flow with frictional heat generation in a vertical channel bounded by isothermal plane walls having the same temperature is revisited in this paper. The existence of dual solutions of the local balance equations is pointed out. They are either columnar upflows or cellular down–up–down flows. Below a maximum value Ξ_max of the governing parameter Ξ = Ge Pr Re (the product of the Gebhart, Prandtl and Reynolds numbers), for any given Ξ a pair of different solutions occurs. The value Ξ_max corresponds to a maximum value of the Reynolds number above which no laminar solution can be found. At this maximum value, the two solution branches bifurcate from each other. In the neighborhood of the bifurcation point Ξ_max even small perturbations can cause transitions from one flow regime to the other. In the paper, the mechanical and thermal characteristics of the dual flow regimes are discussed in detail both analytically and numerically.     

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.     

Turbulent large-scale structures in natural convection vertical channel flow

We analyzed a database of a direct numerical simulation of natural convection in a vertical channel. The flow is driven by a constant temperature difference imposed at the walls (Ra = 5.4 × 10⁵, Pr = 0.7). The averaged flow and turbulent statistics are in good agreement with previous direct numerical simulations reported in the literature. Contrary to forced convection flows, the fluctuations of the heat transfer rate are uncorrelated with the fluctuations of the wall shear stress, which exhibit a symmetric probability density function. At the low Rayleigh number considered, the large-scale structures, which consist mainly in two counter-rotating vortices, with sizes comparable to the separation of the walls, are responsible for the extreme fluctuations of the wall heat transfer rate. The occurrence and the averaged topology of these structures have been determined using a conditional sampling technique.     

Constructal design of vertical multiscale triangular fins in natural convection

Constructal design of vertical multiscale triangular fins in natural convection is investigated in this paper. The design consists of two parts. The first part is for single-scale triangular fins. The objective in the first design is to reach to the highest heat transfer density from the fins for three fin angles (15°, 30°, and 45°). The single-scale fins are placed in a horizontal array and considered as isothermal fins. The degrees of freedom are the fin angle, and the fin-to-fin spacing. The constraint is the fin height. The second part is for multiscale fins where small fins are placed between the large fins which are optimized in the first part. In the second part, the angles of the large and small scales fins are kept constant at (15°). The optimal fin-to-fin spacing which is obtained in the first part is considered a constraint in the second part. The Rayleigh numbers in this design are (Ra = 10³, 10⁴, and 10⁵). The two-dimensional mass, momentum, and energy equations for natural convection are solved with the finite volume method. The results show that there is a benefit of placing the small-scale fins where the percentage increase in the heat transfer density is (10.22%) at (Ra = 10³), and (50.6%) at (Ra = 10⁵) due to existence of the small fins between the large fins.     

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.     

Thermophoresis-induced oscillatory natural convection flows of water-based nanofluids in tilted cavities

A two-phase model based on the double-diffusive approach is used to perform a numerical study on the natural convection of water-based nanofluids in differentially heated square cavities, inclined with respect to gravity so that the heated wall is positioned below the cooled wall, assuming that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum, and energy for the nanofluid, and continuity for the nanoparticles, is solved through a computational code that incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on several sets of literature experimental data. Pressure–velocity coupling is handled by the way of the SIMPLE-C algorithm. Numerical simulations are executed for tilting angles in the range 50?70 deg, such that the nonuniform distribution of the suspended solid phase gives rise to a nonnegligible solutal buoyancy force, whose effects are investigated using the nanoparticle diameter and average volume fraction, the cavity width, the nanofluid average temperature, and the temperature difference imposed across the cavity, as independent variables. It is found that the competition between the solutal and thermal buoyancy forces results in an oscillatory flow, with an oscillation amplitude that increases on increasing the cavity size and the imposed temperature difference. Moreover, the impact of the nanoparticle dispersion into the base liquid is found to be higher at higher average temperatures, whereas, by contrast, the other variables have moderate or negligible effects.     

Transient natural convection in an enclosure with vertical solutal gradients

Transient natural convection in an enclosure with vertical solutal gradients has been studied in this paper. Transfers in a rectangular cavity configuration translating hydrodynamic and thermal phenomena are numerically predicted by means of computational fluid dynamics (CFD) in transient regime.The objective of this numerical study is to give a fine knowledge of the hydrodynamic and thermal characteristics during energy storage in an enclosure filled with water stratified by downward salinity gradient. The enclosure is divided into three zones with different salinity level such as salt gradient pond (SGP). Water is heated by a heating device at the bottom of the cavity.The Navier–Stokes, energy and mass equations are discretized using finite-volume method, and a two-dimensional analysis of the hydrodynamic and thermal behaviors generated in transient regime in the cavity are performed. The mathematical modelling has allowed the prediction of the storage performances by developing parametrical study in view to search the convective heat transfer coefficient at the bottom of the enclosure. Velocity vector fields show the presence of recirculation zones caused only in the lower region and permit to explain the increase of the temperature in the lower convective zone (LCZ).This study shows also the importance of the salinity in the preservation of the high temperature in the bottom of the cavity, and the important reduction of the phenomenon of thermal transfer across the non-convective zone (NCZ).     

Heat transfer by natural convection in a vertical porous layer

Heat transfer by a natural convection in a vertical porous layer heated from below and cooled from above is studied analytically. In the case of linear theory, the normal mode technique is used to find the criteria for the onset of convection and it is shown that convection sets in when the cirtical Reyleigh number exceeds π². The nonlinear theory is investigated using normal mode technique combined with the orthonormal sequences which determines the amplitudes and hence the heat transfer. It is shown that uni-cellular pattern exist and the corresponding heat transfer increases with Rayleigh number.