Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids

Heat transfer enhancement in horizontal annuli using nanofluids is investigated. Water-based nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂ nanoparticles is used. The addition of the different types and different volume fractions of nanoparticles were found to have adverse effects on heat transfer characteristics. For high values of Rayleigh number and high L/D ratio, nanoparticles with high thermal conductivity cause significant enhancement of heat transfer characteristics. On the other hand, for intermediate values of Rayleigh number, nanoparticles with low thermal conductivity cause a reduction in heat transfer. For Ra = 10³ and Ra = 10⁵ the addition of Al₂O₃ nanoparticles improves heat transfer. However, for Ra = 10⁴, the addition of nanoparticles has a very minor effect on heat transfer characteristics.     

Convection naturelle dans une boîte rectangulaire légèrement inclinée contenant un milieu poreuxNatural convection in a slightly slanted rectangular box filled with a porous medium

Steady natural convection in a rectangular slightly inclined box filled with a porous medium is studied. If the lower plate is heated and the aspect ratio large, the structure of the flow is simple as long as the Rayleigh number remains sub-critical. If the upper plate is heated, a boundary layer regime appears provided that the Rayleigh number is high. The Nusselt number is calculated by the Galerkin method and shown to approximate in this particular case to the following expression: Nu= 1 + 0,16k^3/2Ra*^1/42     

Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses

Entropy generation due to conjugate natural convection heat transfer and fluid flow has been studied inside an enclosure with bounded by two solid massive walls from vertical sides at different thicknesses. Enclosure is differentially heated from vertical walls and horizontal walls are adiabatic. Governing equations which are written in streamfunction-vorticity form solved by finite difference technique for the governing parameters as Rayleigh number, 10³ ≤ Ra ≤ 10⁶, length ratio of solid walls as ₁ (for left vertical wall) and ₂ (for right vertical wall) and thermal conductivity ratio of solid to fluid (k), 1 ≤ k ≤ 10. Entropy generation contours due to fluid friction and heat transfer irreversibility, isotherms, streamlines, Nusselt numbers and velocity profiles were obtained. It is found that entropy generation increases with increasing of thermal conductivity ratio and thicknesses of the walls. Entropy generation due to heat transfer is more significant than that of fluid flow irreversibility for all values of thickness of the solid vertical walls.     

Turbulent natural convection in a porous square cavity computed with a macroscopic κ–ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ–ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Computations covered the range 10 < Ra_m < 10⁶ and 10⁻⁷ < Da  < 10⁻¹⁰ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m and for Ra_m less than a certain critical Rayleigh number, Ra_cr. This convergence of results as Ra_m decreases can be seen as a characterization of the laminarization phenomenon. For Ra_m values less than around 10⁴, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra_m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra_m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.     

Estimation of convective mass transfer in solar distillation systems

In this article a thermal model has been developed to determine the convective mass transfer for different Grashof Number range in solar distillatiOn process. The model is based on simple regression analysis. Based on the experimental data obtained from the rigorous outdoor experimentation on passive and active distillation systems for summer climatic conditions, the values of C and n have been calculated. The modified values of C and n for Nu=C(GrPr)ⁿ, are proposed as C=0.0322; N=0.4114 for 1.794 × 10⁶6 in a passive solar still and C=0.0538; N=0.383 for 5.498 × 10⁶6 in an active solar still. The percentage deviation between experimental and theoretical results are found within an accuracy of 12%.     

Effect of temperature dependence of electrical resistivity on the cooling performance of a single thermoelectric element

The coefficients of performance (COP) φ₀ and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (ΔT) and thermoelectric figure of merit (ZT) from the conventional thermal rate equations and the new thermal rate ones proposed here, respectively. We made an attempt to take the differences in the Seebeck coefficient , electrical resistivity ρ and thermal conductivity κ of TE materials at the hot and cold sides of a TE element into the thermal rate equations on the assumption that their TE properties change linearly with temperature. However, the difference in κ was neglected even in the new thermal rate equations because its temperature dependence was too small when φ was applied to the high-performance Bi–Te alloys. The normalized temperature dependences at 300 K of and ρ were denoted by A and B, respectively. The term of A in the thermal rate equations was canceled out by the Thomson coefficient, but that of B remained. When B > 0 K⁻¹, φ/φ₀ is enhanced more significantly with an increase of B at larger ΔT and lower ZT, and it reached about 1.20 at ΔT = 80 K for Bi–Te alloys with B ≈ 5 × 10⁻³ K⁻¹. It was thus found that the COP of a cooling module is also affected strongly by B as well as ZT.     

Chimney effect in a “T” form cavity with heated isothermal blocks: The blocks height effect

In this paper, a numerical study of natural convection from a two dimensional “T” form cavity with rectangular heated blocks is conducted. The blocks are identical, and the domain presents a symmetry with respect to a vertical axis passing through the middle of the opening. The governing equations are solved using a control volume method, and the SIMPLER algorithm for the velocity–pressure coupling is employed. Special emphasis is given to detail the effect of Rayleigh number and block height on the heat transfer and the flow rate generated by the chimney effect. The results are given for the parameters of control as, 10⁴Ra3×10⁶, Pr=0.71, opening diameter (C=l^′/H^′=0.15), blocks gap (D=d^′/H^′=0.5) and blocks height (1/8B=h^′/H^′1/2). These results show that the heat transfer variation with Ra is in the same manner as those met in the case of the vertical smooth or ribbed channels.     

A group of improved heat and mass transfer correlations in solar stills

Based on the analogy of heat and mass transfer and an empirical correlation, a group of improved heat and mass transfer correlations in basin type solar stills is established. In order to validate the correlation group, a multi-stage stacked tray solar still with basin area of 0.665×0.650 m² is constructed of aluminum sheets. By comparison of the calculated results with the measurement results, which were obtained from our steady state simulated experiments and reported in previous literature, it is found that the correlation group developed in this work can provide better predictions for the evaporation rate of basin type solar stills at the wide range of Rayleigh number (3.5×10³<Ra<2.26×10⁷) and temperature (35<T_w<86 °C).     

Experimental study of mixed convection and pressure drop in helically dimpled tubes for laminar and transition flow

This paper presents the experimental results carried out in dimpled tubes for laminar and transition flows and completes a previous work of the authors focused on the turbulent region. It was observed that laminar flow heat transfer through horizontal dimpled tubes is produced in mixed convection, where Nusselt number depends on both the natural convection and the entry region. Employing water and ethylene glycol as test fluids, the following flow range was covered: x^*=10⁻⁴–10⁻² and Ra=10⁶–10⁸.

The experimental results of isothermal pressure drop for laminar flow showed dimpled tube friction factors between 10% and 30% higher than the smooth tube ones. Moreover, it was perceived that roughness accelerates transition to critical Reynolds numbers down to 1400. Correlations for the laminar friction factor f=f(Re,h/d) and for the critical Reynolds Re_crit=Re_crit(h/d) are proposed. The hydraulic behaviour of dimpled tubes was found to depend mainly on dimple height.

In mixed convection, high temperature differences in the cross section were measured and therefore heat transfer was evaluated by a circumferentially averaged Nusselt number. Experimenal correlations for the local and the fully developed Nusselt numbers and are given. Results showed that at low Rayleigh numbers, heat transfer is similar to the smooth tube one whereas at high Rayleigh, enhancement produced by dimpled tubes can be up to 30%.     

A correlation for heat transfer by natural convection from horizontal cylinders that accounts for viscous dissipation

Eight previously published correlation equations plus one new correlation for heat transfer by natural convection from horizontal isothermal cylinders are tested against a fairly extensive body of experimental data culled from the literature for 10⁻⁸ < Ra < 10⁸ and 0.7 < Pr < 4 × 10⁴. The new equation, which represents the Nusselt number as a function of the Prandtl and Rayleigh numbers plus an additional dimensionless parameter that accounts for viscous dissipation, is shown to correlate the experimental data more accurately than does any one of the eight previously published equations. It is concluded that viscous dissipation may not be neglected in all cases of natural convection from horizontal cylinders, and further, that the inclusion of a viscous dissipation term in certain related problems, such as natural convection in porous media, may lead to more accurate correlation equations.     

Natural convection in an inclined rectangular channel at various aspect ratios and angles—experimental measurements

Rates of heat transfer were measured for laminar natural convection in silicone oil and air in a long rectangular channel. The aspect ratio (width/height) of the cross-section of the channel was varied over 1, 2, 3, 4·2, 8·4 and 15·5, and the Rayleigh number from 3 × 10³ to 10⁵. The channel was heated from below and cooled from above while the other two sides were insulated. The channel was then rotated about the long axis in steps through 180 degrees. The effect of inclination and of the aspect ratio on the rate of heat transfer was measured experimentally.A minimum and a maximum rate of heat transfer occurred as the angle of inclination was increased from 0 to 180 degrees. The angle of inclination at these critical conditions was found to be a strong function of the aspect ratio and a weak function of the Rayleigh number. A transition in the mode of circulation occurred at the angle corresponding to the minimum rate of heat transfer.     

A simple analytical treatment of edge-illuminated VMJ silicon solar cells

The series connected silicon vertical multi-junctions (VMJs) solar cells have been suggested as means for ensuring high voltage high efficiency solar cells. This study includes a review of some previously published work concerning the edge-illuminated VMJs solar cells. We introduce a simple one-dimensional analysis to study the high voltage series connected silicon VMJs solar cells. The cell, under study, consists of 40 VMJs. Each junction (unit cell) has dimensions of 250 μm × 0.78 cm × 500 μm. We calculate the short circuit current, the open circuit voltage and the efficiency for an ideal cell, having perfect carrier collection at short circuit conditions, and for real cells. An optimization with respect to the base doping, the emitter doping, the surface recombination velocity and the number of junctions is done for the real cell. A conversion efficiency of 20% has been calculated under AM1.5 light spectrum for real cells having a base doping of 10¹⁶ cm⁻³ and an emitter doping of 10¹⁷ cm⁻³.     

Laminar natural convection in inclined open shallow cavities

Laminar steady state natural convection in inclined shallow cavities has been numerically studied. The side facing the opening is heated by a constant heat flux, sides perpendicular to the heated side are insulated and the opening is in contact with a fluid at constant temperature and pressure. Equations of mass, momentum and energy are solved using constant properties and Boussinesq approximation and assuming an approximate boundary conditions at the opening. Isotherms and streamlines are produced, heat and mass transfer is calculated for Rayleigh numbers from 10³ to 10¹⁰, cavity aspect ratio A=H/L from 1 to 0.125. The results show that flow and heat transfer are governed by Rayleigh number, aspect ratio and the inclination. Heat transfer approaches asymptotic values at Rayleigh numbers independent of the aspect ratio. The asymptotic values are close to that for a flat plate with constant heat flux. The effect of elongation of open cavities is to delay this asymptotic behavior. It is also found that the inclination angle of the heated plate is an important parameter affecting volumetric flow rate and the heat transfer.     

Surface tension driven instability of a liquid film flow down a heated incline

The onset of surface tension driven stationary circulation in a thin film flow down a heated incline is studied by use of linear theory. In the limiting case of a horizontal liquid film, the onset of circulation takes place at finite critical wave numbers and Marangoni numbers for a large range of relevant flow parameters if the stabilizing effect of gravity neglected by previous workers is taken into account. If the angle of inclination Φ of the incline is so small that sin Φ 1 and if the Rayleigh number is of order sin³ Φ, then the flow structure corresponding to the neutrally stable state is that of stream-wise oriented vorticies. The critical Marangoni number of the film on a heated incline is smaller than that of the corresponding horizontal film by an amount sin² Φ F where F depends on relevant flow parameters.     

太阳能在污水处理厂中的运行模式

我国太阳能资源丰富,陆地表面每年接收太阳能辐射总量达3.4×10³ ~ 8.4×10³ MJ /m²。污水处理厂因其占地面积大、高能耗等特点,与太阳能应用具有潜在的共生优势。文章主要通过污水处理厂两大处理内容——污水处理和污泥处置过程中的不同环节介绍了相应的太阳能应用技术,并通过实际案例及相应模拟计算,分析了污水处理厂的整体能耗及经济效益。结果表明,太阳能应用于污水处理厂中可大大降低其能耗和运营成本。     

Natural convection in composite wall collectors with porous absorber

Steady natural convection heat transfer has been studied in a modified Trombe wall solar collector with a porous medium used as an absorber. The boundary conditions were: Two isothermal walls at different temperatures, two horizontal bounding adiabatic walls and either uniform or nonuniform heat generating porous layer with orifices. The aspect ratio A was from 5 to 10. The influence of orifice opening and position as well as the nonuniform heat generation within the porous medium have been studied in detail with the Darcy number varying from 10⁻⁸ to 10⁻². The results are presented in terms of practical parameters (θ, θ_max, q) as a function of Ra, Da and other nondimensional geometrical parameters. The isotherms and stream lines within the cavity are also produced. The overall results indicate that Da and geometrical parameters are the most important parameters affecting system performance.     

A simple model for computing diffuse solar radiation

In this paper a very simple model for predicting the daily diffuse solar radiation at any Italian location using as input few extensively measured meteorological parameters is proposed. In fact the daily diffuse radiation D, MJ.m⁻².day⁻¹, here is correlated with only the relative sunshine duration s/S and the noon altitude of the sun on the 15th of the month h_n, degrees, by the following equation:

D=7(s/S⁻(sinh_n)^1.55

.

The validity of this formula is verified using monthly mean daily data from four Italian stations displaced at various latitudes or altitudes or geographical situations (inland or coastal site). The test results show that the deviations between the measured and the computed values of D are generally low; the maximum standard per cent error of estimate Φ (%) is less than 10. Moreover a comparison of the values of D computed for each tested station by the present formula and the others considered correlations with experimental data is showed. This comparison points out that the standard per cent error of estimate Φ (%) referring to the present equation is better than ones obtained for the other considerd correlations for Adrano, Palermo and Genova whereas it is almost equal for Macerata. Consequently the very simple model herein proposed results independent of the latitude, the altitude and the geographical situation of the place and reasonably it can be considered valid and useful to predict the daily diffuse solar radiation at all Italian locations lacking in data records of diffuse radiation with good reliability.     

2D natural convection flows in tilted cavities: Porous media and homogeneous fluids

Natural convection flows are studied numerically for porous media and homogeneous fluids inside a rectangular cavity with inclination. These thermal fluid flows are considered under the respective two-dimensional unsteady Boussinesq approximation in stream function and vorticity variables. The study depends on the Rayleigh number, angle of inclination, and the aspect ratio of the cavity. At the validation stage our results are in good agreement with those reported by other authors. Results suppose to be new are presented either for angles of inclination not reported before or for high Rayleigh numbers with large aspect ratios. In rectangular porous cavities with Rayleigh number 10² multiple cells appear for some angles. In homogeneous fluids, for Rayleigh numbers of the order of 10⁵–10⁶ in large enough vertical cavities at most secondary cells appear for some angles and the flow becomes more complex and looks like to be oscillatory.     

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10³ to 3.1 × 10⁴ by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.     

Prediction of natural convection in horizontal annular enclosures at high Rayleigh numbers

This paper presents numerical results of natural convection at high Rayleigh numbers in annuli formed by concentric and vertically eccentric horizontal cylinders. Solutions are obtained in a numerically generated boundary-fitted coordinate system in which coordinate lines are coincident with the enclosure boundaries. Results obtained reveal the effects of eccentricity and Rayleigh number on convective heat transfer. Results are presented in the form of vector plots of velocity, local heat transfer data in addition to contours for temperature, turbulent kinetic energy, and turbulent viscosity. All results presented are for a fluid of Prandtl number 0.7 and Rayleigh numbers in the range of 10⁵ to 2×10⁷.