Factored approximations for biaxial incident angle modifiers

Solar collectors using various types of nonimaging concentrators have optical efficiencies which are not symmetrical about the collector normal. To fully specify the optical efficiency for a given sun angle, more details of the collector orientation and incident angle modifier are needed than for flat plate collectors. This could lead to the need for extensive collector test data. Fortunately, for reflecting concentrators, the detailed incident angle modifier, K_ατ(θ_l, θ_t), can be approximated accurately by the product K_ατ(θ_l, 0) K_ατ(0, θ_t), where θ_t and θ_l are projected angles between the sun's position vector and the collector normal. Ray-trace calculations of the various optical effects which result in biaxial incident angle modifiers show the accuracy of the approximation.Since the various optical effects for reflecting concentrators can be represented separately by products of two projected angle factors, extension of the approximation to the general case of low concentration collectors is valid. Measurements and/or calculations need be made only for incident angles in two well-defined orthogonal planes to obtain information sufficient to approximate K_ατ(θ_l, θ_t) for any projected angles of interest for solar collectors.     

Interface characterisation of ZnSe/CuGaSe2 heterojunction

The ZnSe/CuGaSe₂ heterojunctions were fabricated by flash evaporation technique of CuGaSe₂ onto the (110) surface of ZnSe crystals. CuGaSe₂ layers had thickness 2–4 μm and showed a hole concentration up to (1.5–18.0)×10¹⁸ cm⁻³ and mobility μ4–24 cm² V⁻¹ s⁻¹ at 300 K. The charge carrier concentration in ZnSe crystals at 300 K was n=5.6×10¹⁶ cm⁻³ and their mobility μ=300 cm² V⁻¹ s⁻¹. The investigated ZnSe/CuGaSe₂ heterojunctions have at the interface an intermediate layer with a thickness of 450–750 Å and a linear graded band gap as well as an i-ZnSe compensated layer with a thickness of 1–2 μm and resistivity ρ10⁸–10⁹ Ω cm. The i-ZnSe layer is highly compensated due to the presence of Cu acceptor impurities. In this layer the Fermi level position E_c−F₀690 meV and a trap level position E_t−F₀17 meV were determined. The total trap concentration in the i-ZnSe layer is N_t5×10¹⁴ cm⁻³. The mean free path of excited charge carriers in the graded band gap region was calculated as λ55 Å. On the basis of experimental data analysis of electrophysical properties of both ZnSe/CuGaSe₂ heterojunctions and constituent materials the energetic band diagram of the investigated heterostructures is proposed. The current transport mechanism through ZnSe/CuGaSe₂ heterojunctions is consequently elucidated.     

Some aspects of fluctuating vertical wind shears

Fluctuating vertical shears of wind speed have been measured using anemometers on an array of towers. The statistical distributions of these shears are compared with formulas proposed by Fichtl and good agreement is found. A comparison of Fichtl's formula for σ_Δu, the standard deviation of the fluctuating shears, with a more empirical one proposed by Ramsdell shows that the latter is consistent with the former under the proper conditions. The probability of occurrence of extreme shears in speed is discussed. Fluctuating shears two or more times larger than the mean values are shown to occur frequently, and their likelihood increases as the mean measuring height increases if Δz is held fixed. These results are applicable for slightly unstable to neutral conditions over level, homogeneous terrain, and in the surface boundary layers. The normal distribution gives a useful lower bound on shear values. Probabilities of extreme shears as function of are given. σ_Δu is also shown to be affected by τ, the averaging time used for the shear measurements. Increasing τ from 0.2 to 4 sec can decrease σ_Δu by 25 per cent or more. The effects of τ on the probability of extreme events is shown.     

Performance of two equation turbulence models for prediction of flow and heat transfer over a wall mounted cube

This paper deals with the CFD predictions of the three dimensional incompressible flow over a wall mounted cubic obstacle placed in fully developed turbulent flow along with the heat transfer calculations. Reynolds number considered in this study is 1870 based on cube height, h and bulk velocity U_b. Our main objective is to find out the appropriate two equation turbulence model for the complex flow structure which involves recirculation, separation and reattachment. We have used standard k–ε, low-Reynolds number k–ε, non-linear k–ε model, standard k–ω and improved k–ω models to solve the closure problem. The non-linear k–ε model and improved k–ω models along with standard models are validated with bench mark problem – flow through a backward facing step (BFS). Results showed that the improved k–ω model is giving overall better predictions of the flow field especially recirculation zone, mean streamwise velocity, and turbulent characteristics when compared to those by standard eddy viscosity models. The non-linear k–ε model is giving better prediction when compared to standard k–ε and low Reynolds number k–ε models. The complex vortex structure around the cube causes large variation in the local convective heat transfer coefficient. The maximum of the heat transfer coefficient occurred in the proximity of the reattachment points and the minimum is found at the recirculation zone.     

Entropy generation in Poiseuille–Benard channel flow

The issue of entropy generation in Poiseuille–Benard channel flow is analyzed by solving numerically the mass, momentum and energy equations with the use of the classic Boussinesq incompressible approximation. The numerical scheme is based on Control Volume Finite Element Method with the SIMPLER algorithm for pressure–velocity coupling. Results are obtained for Rayleigh numbers Ra and irreversibility φ ranging from 10³ to 5×10⁴ and from 10⁻⁴ to 10 respectively. Variations of entropy generation and the Bejan number as a function of Ra and φ are studied. The limit value φ_l for which entropy generation due to heat transfer is equal to entropy due to fluid friction is evaluated. It has been found that φ_l is a decreasing function of the Rayleigh number Ra. φ_l varies from 0.0015 to 0.096 when Ra decrease from 5×10⁴ to 10³. Stream lines and entropy generation maps are plotted at six times over one period at Ra =10⁴ and φ=10⁻³. It has been found that the maximum entropy generation is localized at areas where heat exchanged between the walls and the flow is maximum. No significant entropy production is seen in the main flow.     

Optical properties of higher and lower refractive index composites in solar selective coatings

The focus of attention in this study was the choice of material for optically solar selective coatings on the basis of their optical constants. A computer programme which calculates the optical constants, solar absorptance at air mass (AM)-2, α, and thermal emittance at 300 K, , of the 200-nm-thick selective coating on the assumption of both the Maxwell Garnett and Bruggeman theories for the metallic volume fraction below and above 0.3 respectively, was used to design the structure of the composite films. Two systems of composite thin films of metal and dielectric were investigated experimentally, fabricated by RF and DC sputter coater and were verified with computer simulations. One system consist of lower refractive index composites such as Ni : SiO₂ and the other of higher refractive index composites such as V : Al₂O₃ in the spectral range of 0.3–20 μm. These films were fabricated on infrared reflective substrates such as nickel plated copper or aluminium. Results of the copper substrates are being presented here. For comparison and verification, tungsten, cobalt and chromium based composites, having different refractive indices, were also investigated which validated the concept of the choice of material in selective coatings. It was observed that high refractive index composites have lower reflective properties by choosing suitable metallic volume fraction in dielectric and antireflection coating. The higher value of the imaginary part of refractive index, k, is responsible for higher absorption by a factor α_λ=4πk/λ. Solar absorptance of 0.98 and 0.96 was achieved by simulation and experimental findings with less than 0.05 thermal emittance for 200 nm thick composites of V : Al₂O₃. It results that higher values of both n and k of the material are more suitable in solar selective coatings.     

Hydrogen desorption kinetics of a LaNi4.7Al0.3 metal hydride electrode using potentiostatic measurements

The reaction kinetics of an activated LaNi_4.7Al_0.3 metal hydride (MH) electrode during the discharge process were studied using charge/discharge and potentiostatic measurements. The electrochemical measurements were conducted at varying applied potentials and temperatures. The potentiostatic measurements show that the reacted fraction α(t) (α(t) is the ratio of the discharge capacity at time, t, to the maximum discharge capacity) of the MH electrode during the discharge process depends on both the applied potential and temperature. Analysis of the kinetic data indicates that the primary rate controlling step for the discharge process of the LaNi_4.7Al_0.3 electrode is the β→α phase transformation process at temperatures in the range 298–328 K and at applied potentials in the range from −0.8 to −0.6 V vs. Hg/HgO. The dependence of reacted fraction α(t) of the MH electrode reaction on time t obeys a nucleation and growth (ng) equation: -ln(1−α(t))=kt^m (k and m are material parameters of the MH electrode during the discharge process; the reaction rate constant K_ng=k^1/m; t is the discharge time (min)). The increase in applied potential leads to a decrease in the hydrogen activity. The nucleation and growth of the α-hydride phase, resulting from the decrease in the hydrogen activity, leads to an increase in the reacted fraction. The reaction rate constant (K_ng) increases with increasing temperature which is in agreement with an Arrhenius-type temperature behavior. The calculated apparent activation energy (E_a) from the Arrhenius equation for the discharge reaction of the MH electrode was 41.1 kJ (mol H)⁻¹ for temperatures ranging from 298 to 328 K.     

The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films

ABSTRACT

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ?T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T_e with a metal lattice temperature T_l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T_e and T_l as well as two different heat-fluxes q _e and q _l related to the gradients of T_e and T_l, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k_e and k_l corresponding to T_e and T_l, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T_e, q _e) and (T_l, q _l), separately. Also, the positive definiteness of k_e and k_l, and of the corresponding heat capacities c_e and c_l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k_l = 0 and q _l =  0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q_e(x, t) has direction that is opposite not only to that of ?T_e(x, t)/?x but also to that of ?T_l(x, t + τ_T)/?x, where τ_T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k_e, k_l, c_e, c_l, and G are positive, an inequality of the second law of thermodynamics type involving a pair (T_e ? T_l, q _e ?  q _l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q _l, q _e) over which uniqueness does not hold true are also revealed.     

An opaque cloud cover model of sky short wavelength radiance

The average angular distribution of short wavelength sky radiance for clear, partly cloudy, and overcast sky conditions has been measured for the range of solar zenith angle 31° to 80°. Detailed analysis of this sky radiance data shows that the normalized sky radiance is given analytically by N(θ, φ) = CN₀(θ, φ) + [1−C]N_C(θ, φ) where N₀(θ, φ) = 0.45 +0.12 θ^* + 0.43 cosθ + 0.72e^−1.88ψ N_c(θ, φ) = [1.63 + 53.7e^−5.49ψ + 2.04 cos² ψ cosθ^*] [1− e^−0.19Secθ][1minus; e^−0.53Secθ], and θ^* is the solar zenith angle (radians), (θ, φ) is the sky radiance direction, Ψ is the scattering angle (radians) between sky and sun directions, and C is the prevailing opaque cloud cover.     

Measured shortwave sky radiance in an urban atmosphere

An extensive data set of measurements of the shortwave sky radiance at Toronto, Canada, was compiled by the authors in 1984. A pyroelectric radiometer with a half-angle field of view of 5 degrees was used to make a total of more than 100,000 sky radiance measurements. This paper presents an analysis of almost 40,000 of these measurements in the form of a set of plots showing means and percentiles of sky radiance as a function of position in the sky; atmospheric clearness index, k_t; diffuse fraction, k; and solar zenith angle, θ_z. The data show (i) that, in the circumsolar region, the highest observed values of sky radiance occur for partly cloudy sky conditions characterized by intermediate values of k and k_t, (ii) that, in the regions of the sky away from the solar position, sky radiance tends to increase monotonically both with increasing k and with increasing k_t, (iii) that there is a progressive transition with increasing k, from the horizon brightening for skies with low diffuse fractions to horizon darkening for skies with diffuse fractions approaching unity, (iv) that the shape of the sky radiance distribution is a strong function of the elevation of the sun in the sky, and (v) that the sky radiance is highly variable, with a positively skewed probability density function.     

Natural convection near 4°C in a water saturated porous layer heated from below

This paper reports a numerical study of two-dimensional natural convection in a horizontal porous layer heated from below and saturated with cold water. The density maximum of water at 3.98°C and atmospheric pressure occurs inside the layer, as the top surface is maintained at 0°C and the bottom surface is varied from 4 to 8°C. Three separate series of numerical simulations document the effect of Rayleigh number, bottom surface temperature, and horizontal length of the porous layer on the overall heat transfer rate vertically through the layer. The range of these numerical experiments is 200 < Ra_p < 10000, 0.167 < H/L < 1 and °C < T_H < 8°C, where Ra_p, H/L and T_H are the Darcy-modified Rayleigh number for a fluid with density maximum, the geometric ratio height/length, and the bottom wall temperature. The numerical results agree with published linear stability results regarding the onset of convection.     

Numerical computation of thermocapillary-driven convection in an open cylindrical cavity with different aspect ratios

The surface tension gradient driven fluid flow that occurs during laser melting has been studied. The steady laminar thermocapillary motion in a cylindrical cavity has been analyzed numerically for 0.01 Pr 20, 50 Re_σ 35000, 0.01 A 10 without the inclusion of buoyancy effects. The study consists of scale analysis and numerical simulations. For a fixed Prandtl number the average free surface Nusselt number, side wall Nusselt number, bottom Nusselt number and maximum stream function are proportional to Re^2/7_σ, Re^4/9_σ, Re^4/9_σ, and Re^−2/7_σ, respectively. The numerical results are qualitatively verified by the scale analysis. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and Marangoni number. In addition, surface deflections are computed using a domain perturbation for small capillary number. It is shown that the degree of the free-surface deformation for the leading-order solution varies strongly with the surface tension Reynolds number.     

Data bank Comparison of monthly mean hourly sunshine fraction estimation techniques from calculated diffuse radiation values

Mean monthly hourly values of global I and diffuse radiation I_d, along with mean monthly daily values of the sunshine fraction σ_d available for four locations in the United Kingdom, are used to develop six models relating I_d/I with the monthly mean hourly clearness index K_t, the estimated monthly mean hourly sunshine fraction σ_h and the monthly mean solar elevation at mid hour α. Two available methods are used to predict the values of σ_h from σ_d and the calculated I_d data are compared. Statistical tests performed for a total of six locations, including those used to develop the models, show that the best results are obtained when σ_h predicted with the method developed by Page is employed in the estimation correlation.     

Effect of spatial variation of incident radiation on spectral response of a large area silicon solar cell and the cell parameters determined from it

Effect of spatial variation of incident monochromatic light on spectral response of an n⁺–p–p⁺ silicon solar cell and determination of diffusion length of minority carriers (L_b) in the base region and the thickness of the apparent dead layer (x_d) in the n⁺ emitter from the spectral response have been investigated. Spectral response of a few 10 cm diameter and 10×10 cm² pseudo-square silicon solar cells was measured with the help of a standard silicon solar cell of 2×2 cm² area in 400–1100 nm wavelength range. Different areas (4, 9, 16, 25 and total area 78.6 or 96 cm²) were exposed. The effect of the radial variation of incident radiation was determined quantitatively by defining a parameter f₁ as the ratio of the average intensity falling on the reference cell to that on the exposed area of the test cell. The value of f₁ varied between 1 and 1.15 (1.25) as the exposed area of the cell varied from 4 cm² to 78.6 (96) cm² indicating that the spatial inhomogeneity of intensity increased with the increase in the exposed cell area. Short-circuit current densities, J_sc, computed from spectral response data for AM1.5 spectrum were less compared to the directly measured values by a factor which was nearly equal to f₁. However, radial variation of intensity does not affect the determination of diffusion length of minority carriers in the base region (by the long wavelength spectral response, LWSR method using the measured spectral response data in 0.85<λ<1.05 μm range) and the thickness of the dead layer (by the method of Singh et al. using the data of 0.45<λ<0.65 μm range) significantly.     

The onset of natural convection in a horizontal fluid layer heated isothermally from below

The onset of buoyancy-driven convection in an initially quiescent fluid layer confined between two horizontal plates is analyzed theoretically. In case of isothermal heating it is well known that convective motion sets in when the Rayleigh number Ra exceeds 1708. For Ra > 1708, there are three characteristic times t_c, t_D and t_u which represent respectively, the critical time to mark the onset of intrinsic instability, the detection time of motion, and the undershoot time in a plot of the heating rate versus time. These characteristic times are analyzed by employing the numerical method under the single mode of instabilities and fitting some experimental t_u-values. The new measures to represent t_c and t_D are suggested, based on the growth rates of fluctuations. It is interesting that t_c is the invariant but the predicted t_D- and t_u-values are dependent upon the magnitude of initial conditions forced. It is shown that for the isothermally heated system of a large Prandtl number the relation of t_u ? 7t_c agrees well with the available experimental t_u-values for Ra > 10⁵ and t_D is located between t_c and t_u. This paper removes the confusion among the characteristic times, t_c, t_D and t_u in the literature on stability. Also the boundary-layer instability model is discussed in order to analyze turbulent thermal convection heat transfer characteristics in the fully developed state, based on the present numerical predictions.     

Design application of the Hottel-Whillier-Bliss equation

A method is presented for experimentally determining the three factors that determine collector efficiency in the Hottel-Whillier-Bliss equation, Q_u = F_RA_c[(τα)_cI - U_L(T_f,i - T_a)]. These factors are: the collector heat removal factor, F_R; the effective transmittance-absorptance product, (τα)_e; and the overall heat loss coefficient, U_L. The method of testing requires: computation of (τα)_e from measurements of cover transmittance and collector reflectance; computation of F_R from a test in which the heat loss term equals zero; and computation of U_L from a test in which insolation equals zero. This method was applied to collectors used on Solar House I at Colorado State University, with experimental and theoretical results being in close agreement. The method can be used to experimentally evaluate collector performance and for optimization of collector design.     

Analysis of the effective thermal conductivity of fractal porous media

Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite volume method (FVM). The influences of the thermal conductivity of solid k_s, the thermal conductivity of fluid k_f, the porosity ε, the size and spatial distribution of pores on the effective thermal conductivity k_e of these structures are analysed in detail. The calculated results indicate that the relation of effective thermal conductivity k_e with thermal conductivity of solid k_s and thermal conductivity of fluid k_f conforms to a power function, and the relation of effective thermal conductivity k_e with porosity ε conforms to an exponential function. The porosity ε is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influence. The numerical results are analysed by comparing with the available empirical formulas from literatures, and provide verification of these empirical formulas.     

Mass transfer effects on MHD flow and heat transfer past a vertical porous plate through a porous medium under oscillatory suction and heat source

This paper considers the effect of mass transfer on free convective flow and heat transfer of a viscous incompressible electrically conducting fluid past a vertical porous plate through a porous medium with time dependant permeability and oscillatory suction in presence of a transverse magnetic field and heat source. The solutions for velocity field, temperature field and concentration distribution are obtained using perturbation technique. The effects of the flow parameters such as magnetic parameter M, Grashof number for heat and mass transfer G_r,G_c, porosity parameter K_p, Prandtl number P_r, Schmidt number S_c, frequency parameter ω and heat source parameter S on the velocity, temperature and concentration distribution of the flow field and the skin friction, heat flux and the rate of mass transfer are studied analytically and presented with the aid of figures and tables. It is observed that the magnetic parameter and the Schmidt number retard the velocity of the flow field while the Grashof number for heat and mass transfer, the porosity parameter and the heat source parameter have accelerating effect on the velocity of the flow field at all points. Further, the Prandtl number reduces the temperature and the Schmidt number diminishes the concentration distribution of the flow field at all points. The skin friction coefficients τ₀ and τ increase due to increase in G_r,G_c and K_p while decrease due to increase in S_c, M, ω and P_r. Further, the rate of mass transfer S_h increases due to increase in S_c while an increase in ω results a decrease in S_h.     

On the calculation of solar radiation in hazy atmospheres and on turbidity in Ibadan

A previous model is examined in greater detail for the harmattan haze periods (November to January) of 1975–1980 at Ibadan, when the atmosphere is often heavily overcast with dust. It is shown that for air mass (m) and turbidity (β) product values of mβ > 4.05 the scattering transmittance τ_scat, for the instantaneous direct solar radiation becomes negative, while for mβ < 0.22 τ_scat changes too rapidly, thus failing to give acceptable values of irradiation for such periods. This problem is overcome by employing the limits 0.22 mβ 3.07 in the calculations, which corresponds to β of 0.40 and 0.22 for “very hazy” and “hazy-hot clear” atmospheres, respectively. The resulting daily and monthly average total insolation are mainly within ± 15% and ± 10%, respectively, of the experimental data provided by the International Institute of Tropical Agriculture (I.I.T.A.), Ibadan.The variation of the turbidity in the city is also studied for all days of the six years. Daily average values 0.10 β 0.175 occur on about 60% of the days, while “clear” (β < 0.125) and “very hazy” (β 0.40) weather days have about 16% and 12.37%, respectively. Some 74.4% of the very hazy days fall within the harmattan period during which the monthly average turbidity is often higher than 0.35.     

Spectrally selective solar absorbers in different non-black colours

Silicon paints were prepared from yellow, ochre, dark ochre, green and blue pigments. To improve the solar absorptance, a_s, of these coatings, an existing black paint was admixed in different ratios. The optical properties of the mixed paints thus formed are expressed in terms of the Kubelka–Munk absorption and scattering coefficients in the spectral region 400–17000 nm. The scattering coefficient obtained for all paints was essentially equal. In the visible region the absorption coefficient follows the spectral characteristics of each respective colour. In the infrared absorption at 9000 nm and above 12000 nm are seen in all cases which result in a thickness-dependent increase of the thermal emittance, e_T, of the coating. The metric chroma (C_ab^*) and lightness (L^*) in CIELAB colour space were calculated for wide-angle observer in average daylight conditions. A range of non-black spectrally selective solar absorber surfaces with a_s>0.8 and e_T<0.3 have been prepared with L^*<45 and C_ab^*<10.