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.     

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.     

Heat transfer from a pulsed laminar impinging jet

A numerical investigation has been performed to study the effect of flow pulsations on time-averaged Nusselt number under a laminar impinging jet. The parameters considered are as follows: time-averaged jet Reynolds number (100 ≤ Re ≤ 1000), frequency of pulsation (1 ≤ f ≤ 20 Hz), and nozzle-to-target spacing (4 ≤ H/d ≤ 9). The combination of Re = 300, f = 5 Hz and H/d = 9 was found to give the best heat transfer performance. Interestingly, it was found that the onset of separation at the wall jet region of pulsating impinging jet is associated with the point of constant Nusselt number during the oscillation cycle. Downstream of the separation point in the wall jet region, the Nusselt number waveform fluctuates out of phase with the inlet velocity. Within one oscillation, large vortices existing during the minimum velocity state are broken into two smaller vortices when the flow is accelerated to reach the maximum velocity, after which the two vortices merge again when the flow decelerates back to the minimum velocity.     

Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.     

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.     

A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream

The problem of laminar mixed convection from a horizontal isothermal cylinder is considered. The free stream direction is assumed to be horizontal and perpendicular to the cylinder axis. The study is based on the solution of the full Navier-Stokes and energy equations for 2-dim. flow of a Boussinesq fluid. The free stream is assumed to start impulsively from rest and the velocity and thermal boundary layers are developed in time until reaching steady conditions. The investigation covered the ranges of Reynolds number 1 < Re < 40 and Grashof numbers up to Gr = 5 Re² while keeping Prandtl number at a constant value of 0.7. Comparison of results with previous experimental correlations shows a good agreement. The streamline and isotherm patterns are plotted and different aspects of the phenomenon are discussed.     

A new method for estimating solar radiation from bright sunshine data

Daily values of H/H₀, the ratio of total horizontal radiation to that outside the atmosphere has been correlated with s/S, bright sunshine as a fraction of daylength for 3 yr measurements in Adana and Ankara, Turkey. Using a maximum-likelihood quadratic fit, we show that monthly averages s/S and its standard deviation σ_s/S can be used to estimate the monthly average H/H₀ as

H/H₀ = 0.204 + 0.758s/S − 0.250[s/S² + σ²_s/S.

Comparison of the estimations of the above equation with measurements from different regions of Turkey indicate that less than 5 per cent relative error is possible. A further correlation σ²_s/S with s/S makes it possible to estimate H/H₀ with just the knowledge of s/S.     

An experimental study of mixed convection around a rotating isothermal cylinder

The mixed convective flows generated by a heated rotating horizontal cylinder have been investigated experimentally. The presence of rotation represents an important complication and extension of previous studies on convective flow and heat transfer around heated stationary horizontal cylinders in an otherwise quiescent medium. Significant qualitative, as well as quantitative, differences in the heat transfer characteristics and flow patterns generated by the rotating cylinders are observed as compared to those for stationary cylinders. When the Reynolds number reaches a value corresponding to the rotational parameter σ ≡ Gr/Re² being just below unity, the thermal plume becomes unstable and eventually breaks down. This event corresponds to the onset of a secondary mean flow which appears to be periodic in the axial direction. Mean Nusselt number measurements are presented, which show a dramatic increase in heat transfer at the onset of the secondary flow. Also, the structure of the secondary flow and the behavior of the plume are elucidated through Schlieren photography.     

Reliable one dimensional 46-CPWTR model applied to two dimensional heat transfer problem of insulated triangular duct

In this study, the heat transfer characteristics of an insulated long triangular duct are analyzed by using the one dimensional plane wedge thermal resistance (PWTR) and plate thermal resistance (PTR) models. It is found that the errors produced by the PWTR model are all positive, but the errors produced by the PTR model are all negative. Thus, the combined plate wedge thermal resistance (CPWTR) model generated by paralleling PWTR and PTR models with the proportion factors of  = 0.4 vs. β = 0.6 (46-CPWTR model) is capable of neutralizing the positive and negative errors and returning very accurate results in comparison with the two dimensional numerical solutions analyzed by CFD software. The errors generated by the one dimensional 46-CPWTR model are within 1% for practical insulation thickness (t/R₂ < 0.5). In the rare situations of thicker insulation (0.5  t/R₂  2), most of the errors returned by the one dimensional 55-CPWTR model are within 2%. Thus, engineers can obtain very reliable heat transfer results by applying the one dimensional 46-CPWTR or 55-CPWTR models to an insulated triangular duct. Meanwhile, the PTR model can still be used to estimate the highest surface temperature for a hot fluid duct or the lowest surface temperature for a cool fluid duct.     

Combined heat and mass transfer by natural convection at horizontal cylinder electrodes

Simultaneous heat and mass transfer in free convection at horizontal cylinder electrodes has been investigated experimentally using the electrochemical limiting diffusion current technique. The convective flow patterns occuring have been observed using Schlieren photography. The results confirmed the use of a combined Grashof number (GR_m) to account for thermal and concentration buoyancy effects. Various combinations of electroactive species concentration, cylinder diameter and cylinder surface temperature have been used. Results have been successfully correlated by the equations , 7×10⁷ < GR_mSc< 4×10⁹ and , 4×10⁹ mSc<10¹¹ The experiments cover the range of mass transfer and heat transfer Grashof numbers 3.64×10⁴ m <3.02×10⁶, 5.67×10⁴ h <6.55×10⁶     

Studies on membrane viscosity stabilized solar pond

In this nonsalt type of solar pond, the nonconvecting layer is composed of a viscous polymer solution partitioned by a number of transparent films. An advantage of partitioning is that a thinner polymer solution can be used and that the light transmittance increases. Results of experimental and theoretical investigations on the performance of this solar pond are summarized as follows:

1. 1. Ionized polyacrylamide solution was chosen as the thickener based on tests about solubility, viscosity, light transmittance and stability.

2. 2. The critical temperature difference for the onset of convection in the polymer layer (ΔT/L)_cr [°C/m] was given by the following formula based on the measurements in various thicknesses of the polymer layers (L) [m] and various concentrations (ζ) [%],

(ΔT/l)_cr=(55−185lnL)exp(4.66L^0.505lnζ

3. 3. An outdoor model pond, 200 × 150 cm surface and 100 cm depth, was constructed in Osaka. Four types of model ponds were tested, and the availability of membrane type with partition films was confirmed.

4. 4. The theoretical temperature rise of the pond using a one-dimensional model was calculated by solving the equations of the heat balance in the pond. As a result, the optimum values of thickness of polymer layer and number of films was determined

     

Three-dimensional driven-cavity flows with a vertical temperature gradient

Numerical studies of three-dimensional flows in a cubical container with a stable vertical temperature stratification are carried out. Flows are driven by the top lid, which slides in its own plane at a constant speed. The top wall is maintained at a higher temperature than the bottom wall. The end walls and the side walls are thermally insulated. Numerical solutions are obtained over a wide range of physical parameters, i.e. 10² ≤ Re ≤ 2 × 10³, 0 ≤ Ri ≤ 10.0 and Pr = 0.71, where the mixed-convection parameter Ri Gr. Re⁻². Systematical comparison of the three-dimensional numerical solutions with the previously reported two-dimensional results illuminates the impact of thermal stratification on the three-dimensional flow characteristics. When Ri < O(1), the effect of the vertical temperature gradient is minor, and the flow structures are similar to those of the non-stratified fluid flows in a conventional lid-driven cavity flow. Fluids in the primary vortex are well mixed, and the temperature is fairly uniform in the main circulating region. When Ri ≥ O(1), the stable temperature distribution tends to suppress the vertical fluid motion. Much of the fluid motion takes place in the vicinity of the top sliding lid and the bulk of the cavity region is nearly stagnant. When Ri > O(1), the fluid motion exhibits vertically layered vortex structures. The Nusselt number is computed at the top and bottom wall, and this also illustrates the varying flow characteristics as Ri encompasses a broad range. Extensive numerical flow visualizations are conducted. Plots demonstrating the primary flows in the (x−y) plane and the secondary flows in the (y−z) plane are presented. These display the influences of Re and Ri on the basic character of the flow and the three-dimensional effects.     

On the factorisation of incidence angle modifiers for CPC collectors

It has been suggested earlier that the incidence angle modifier K_τ for low concentrating collectors with tubular absorbers could be factorised according to K_τ(θ_t,θ_l) ∝ K_τ(θ_t,0)K_τ(0,θ_l, where θ_tand θ_l are the projected incidence angles in the transversal and longtitudinal projection planes, respectively. Ray-tracing calculations on low-concentrating CPC collectors with flat absorbers parallel to the cover show that a K_τ factorisation overestimates the annual delivered energy from the collector by about 4–5%, when compared to calculations using the full incidence angle modifier. Data from outdoor testing has been used for characterization of incidence angle behaviour for a truncated CPC with a concentration of C = 1.56. Multiple linear regression analysis was used. This analysis technique makes feasible the determination of angular dependent incident angle modifiers and is an efficient tool to use for all collectors which cannot be characterised by standard equations of the incidence angle dependence.     

Four-equation turbulence model for prediction of the turbulent boundary layer affected by buoyancy force over a flat plate

Turbulent convective heat transfer with appreciable buoyancy effect over a heated or cooled horizontal flat plate is numerically analyzed by solving four equations for mean square temperature variance , its rate of destruction _θ, turbulent kinetic energy κ and the rate of kinetic energy dissipation . Turbulent time-scale ratio R of temperature fluctuations relative to velocity fluctuations defined by is found to vary widely across the boundary layer. For both highly stable and highly unstable conditions, the ‘four-equation’ model yields better results for mean temperature profile and surface heat flux than the two-equation model. It is also found that the magnitude of thermal von Karman constant κ_θ is not a universal constant but it depends on the thermal stratification of the boundary layer.     

Intensification of turbulent free heat transport in various configurations with adequate binary gas mixtures

The present paper investigates a promising avenue for the intensification of turbulent free convection in various configurations using adequate binary gas mixtures in which helium (He) is the primary gas component and carbon dioxide (CO₂), methane (CH₄), nitrogen (N₂), oxygen (O₂) and xenon (Xe) are the secondary gas components. In the context of binary gas mixtures, the thermo-physical properties: viscosity, thermal conductivity, density and isobaric heat capacity depend on three quantities: temperature, pressure and molar gas composition. Within the platform of turbulent free convection using the five binary gas mixtures for Ra > 10⁹, results are presented for the allied convective coefficient h_mix/B varying with the molar gas composition w in the w-domain [0, 1]. Values of the maximum allied convective coefficients h_mix,max/B attained at the correlative optimal molar gas compositions w_opt are easily extracted from suitable design charts.     

PMMA-assisted synthesis of Li1−xNi0.5Mn1.5O4−δ for high-voltage lithium batteries with expanded rate capability at high cycling temperatures

In this work, poly(methyl methacrylate) (PMMA), a non-surfactant polymer was used to synthesize nonstoichiometric Li_0.82Ni_0.52Mn_1.52O_4−δ (0 ≤ δ ≤ 0.25) spinels. The presence of the polymer was found to be beneficial with a view to facilitating the use of the spinel in electrodes for lithium batteries. Thus, PMMA allowed spinel particles of a high crystallinity and uniform size and shape to be obtained, and particle size to be tailored by using an appropriate calcining temperature and time. By controlling these variables, spinels in nanometric, submicrometric and micrometric particle sizes were prepared and characterized by chemical analysis, X-ray diffraction, electron microscopy, thermogravimetry and nitrogen adsorptions measurements. The spinels were obtained as highly crystalline phases with lithium and oxygen deficiency and some cation disorder as revealed by chemical analysis, thermogravimetric and XRD data. Their electrochemical performance in two-electrode cells was tested at room temperature and 50 °C over a wide range of charge/discharge rates (from C/4 to 4C). Cell performance was found to depend on particle size rather than on structural properties. Thus, the spinel best performing at 50 °C was that consisting of submicrometric particles, which delivered a high capacity and exhibited the best capacity retention and rate capability. Particles of submicronic size share the advantages of nanometric particles (viz. the ability to withstand high charge/discharge rates) and micrometric particles (a high capacity and stability at low rates).     

Conditional probabilities of daily relative sunshine data and the dependence on the weather of the previous day

In this paper, the conditional probabilities p₁₁(m, x) and p₀₁(m, x) of the daily relative sunshine (DRS) are estimated for each month m, using available data for 30 years. p₁₁(m, x) (p₀₁(m, x)) is the probability that the DRS of a day for a certain month is greater than x, (o < x < 1), given that the DRS of the previous day is greater (smaller) than x. The empirical curves for p₁₁(m, x) and p₀₁(m, x) are fitted and the fitting parameters are estimated for each month. The results show a good agreement between the empirical and the calculated values. The vertical distance between the curves p₁₁(m, x) and p₀₁(m, x) shows a strong dependence of the weather on that of the previous day. A method to estimate a sequence of k consecutive days of “good” or “bad” weather is also given.     

Heat transfer enhancement in a tube using circular cross sectional rings separated from wall

A numerical study was undertaken for investigating the heat transfer enhancement in a tube with the circular cross sectional rings. The rings were inserted near the tube wall. Five different spacings between the rings were considered as p = d/2, p = d, p = 3d/2, p = 2d and p = 3d. Uniform heat flux was applied to the external surface of the tube and air was selected as working fluid. Numerical calculations were performed with FLUENT 6.1.22 code, in the range of Reynolds number 4475–43725. The results obtained from a smooth tube were compared with those from the studies in literature in order to validate the numerical method. Consequently, the variation of Nusselt number, friction factor and overall enhancement ratios for the tube with rings were presented and the best overall enhancement of 18% was achieved for Re = 15,600 for which the spacing between the rings is 3d.     

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.