Competitiveness of stationary planar low concentration photovoltaic modules using silicon cells: A focus on concentrating optics

The economical competitiveness of stationary Low Concentration Photovoltaic (LCPV) modules is evaluated, starting from detailed expressions of the Levelized Cost of Energy (LCoE). For trackless LCPV to be competitive with standard modules, the key approach is to maximize the performance of concentrating optics in terms of yearly averaged effective optical power ratio. To express this a novel parameter named P_ro,eff is introduced and its contribution to the expression of LCoE for LCPV modules is discussed. By comparing the LCoEs of standard and LCPV modules, threshold conditions for P_ro,eff and for the relative unitary cost of concentrating optics C_r are found, in dependence on the geometrical concentration gain G and as a function of other sensitive design parameters.Aiming at the maximization of P_ro,eff, the novel design of a modified prism-coupled compound parabolic stationary concentrator is introduced, as a trackless LCPV solution compatible with standard flat panel size, weight and installation infrastructures. It provides geometrical concentration gain G = 5, an acceptance angle of 24° and P_ro,eff = 81%, using a reflective primary concentrator and high refractive index dielectric for the secondary optics. A first experimental validation of the approach is given by a proof-of-concept prototype, implemented in commercially available polymethylmethacrylate, suitable for quasi-stationary installations requiring seasonal adjustment.     

Experimental study of R-134a evaporation heat transfer in a narrow annular duct

An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux G is varied from 300 to 500 kg/m² s, imposed heat flux q from 5 to 15 kW/m², vapor quality x_m from 0.05 to 0.95, and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the gap of 1.0 mm, G is varied from 500 to 700 kg/m² s with the other parameters varied in the same ranges as that for δ = 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher G. Besides, the evaporation heat transfer coefficient also rises substantially at increasing q. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in T_sat, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in h_r. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.     

A generalized self-consistent method for calculation of effective thermal conductivity of composites with interfacial contact conductance

The effective thermal conductivity of composites can be obtained by the generalized self-consistent method (GSCM). The effect of contact conductance that exists at the interface between the matrix and the inclusion, on the effective thermal conductivity is investigated. The particulate composite, transversely isotropic fiber composite, and multi-layered composite are considered in this study. Based on the energy balance, a simple criterion B_eff = 0, yet new and analytical, for determining the effective thermal conductivity of the composite is rigorously derived. The temperature distribution of the matrix and the inclusion can also be obtained by GSCM. This is the by-product of the method, which many other methods do not provide.     

Experimental study of evaporation heat transfer characteristics of refrigerants R-134a and R-407C in horizontal small tubes

An experiment is carried out here to investigate the characteristics of the evaporation heat transfer for refrigerants R-134a and R-407C flowing in horizontal small tubes having the same inside diameter of 0.83 or 2.0 mm. In the experiment for the 2.0-mm tubes, the refrigerant mass flux G is varied from 200 to 400 kg/m² s, imposed heat flux q from 5 to 15 kW/m², inlet vapor quality x_in from 0.2 to 0.8 and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the 0.83-mm tubes, G is varied from 800 to 1500 kg/m² s with the other parameters varied in the same ranges as those for D_i = 2.0 mm. In the study the effects of the refrigerant vapor quality, mass flux, saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. The experimental data clearly show that both the R-134a and R-407C evaporation heat transfer coefficients increase almost linearly and significantly with the vapor quality of the refrigerant, except at low mass flux and high heat flux. Besides, the evaporation heat transfer coefficients also increase substantially with the rises in the imposed heat flux, refrigerant mass flux and saturation temperature. At low R-134a mass flux and high imposed heat flux the evaporation heat transfer coefficient in the smaller tubes (D_i = 0.83 mm) may decline at increasing vapor quality when the quality is high, due to the partial dryout of the refrigerant flow in the smaller tubes at these conditions. We also note that under the same x_in, T_sat, G, q and D_i, refrigerant R-407C has a higher h_r when compared with that for R-134a. Finally, an empirical correlation for the R-134a and R-407C evaporation heat transfer coefficients in the small tubes is proposed.     

Experimental investigation of thermal contact conductance at low temperature based on fractal description

An experimental investigation of thermal contact conductance was conducted with pressed pairs of aluminum alloy 5052 and stainless steel 304 over the low temperature range from 155 to 210 K, with nominal contact pressure from 1 to 7 MPa. The contact surfaces were prepared through bead blasting and characterized with the fractal dimension D and the parameter G of the Weierstrass–Mandelbrot function. The range of fractal dimension is 1.59–1.86 for aluminum and 1.56–1.92 for stainless steel. And the parameter G is in the magnitude of 10⁻⁷ m. From the measured results, thermal contact conductance over this temperature range (155–210 K) is less than that near or above room temperature (T > 300 K). The load sensitivity at low temperature is less than that at room temperature. The smaller fractal dimension D characterizes the rougher surface when G is on the same magnitude and results in the smaller value of the contact conductance and insensitivity to the contact pressure.     

Heat transfer study in a discoidal system: The influence of rotation and space between disks

This article presents an experimental study of the local heat transfer on the rotor surface in a discoidal rotor–stator system air-gap in which an air jet comes through the stator and impinges the rotor. To determine the surface temperatures, measurements were taken on the rotor, using an experimental technique based on infrared thermography. A thermal balance was used to identify the local convective heat transfer coefficient. The influence of the dimensionless spacing interval G between the disks and of the rotational Reynolds number Re was measured and compared with the data available in bibliography. Local convective heat transfer coefficients were obtained for an axial Reynolds number Re_j = 41.6 × 10³, a rotational Reynolds number Re between 0.2 × 10⁵ and 5.16 × 10⁵, and a dimensionless spacing interval G ranging from 0.01 to 0.16.     

Development of heat and mass transfer model for condensation

Divergence and the interfacial temperature deviation are the two main problems in condensation simulation with the Lee model. Based on the heat transfer analysis at the vapor-liquid interface, a correlation is revealed describing the relationship between interfacial temperature deviation and the model parameters, q_i ≈ (T_sat − T_i)(Ak_v)^0.5 where A = h_fgrρ_v / T_sat. With this correlation, the determination of the condensation frequency r is no longer empirical. Furthermore, the correlation indicates that the thermal conductivity of vapor plays an important role. Accordingly, an improved model is proposed amplifying the thermal conductivity of vapor in the phase interaction region. The model is verified with the Nusselt problem and the impacts of the model parameters are discussed and compared with the original Lee model. It is shown that the interfacial temperature deviation is reduced by the amplified thermal conductivity of vapor. The convergence is maintained by increasing both A and k_v synchronously. Verification is also obtained on the forced convection condensation of R134a. The correlation predicts a temperature deviation at 0.1 K and the numerical result successfully reaches 0.12 K.     

0.4% absolute efficiency gain by novel back contact

Replacing the aluminum back contact of screen-printed multicrystalline silicon solar cells by a novel low-temperature layer sequence boosts the absolute power conversion efficiency η by Δη=0.4%. The optimized hydrogenated amorphous silicon (a-Si:H)-based back side junction provides efficient back side passivation and contacting at the same time. The improved passivation quality reduces the effective surface recombination velocity S_eff to S_eff<20 cm s^?1. Due to the optimized back side layer sequence, the open circuit voltage V_OC rises by ΔV_OC=15 mV up to V_OC=622 mV and the short circuit current increases by ΔJ_SC=0.8 mA cm^?2.     

Laminar natural convection in an air-filled square cavity with partitions on the top wall

The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr_H of approximately 1.3 × 10⁸) and non-dimensional top wall temperatures θ_T of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height H_P/H of 0.0625 and 0.125 attached to the top wall at x/H = 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and θ_T. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and Nu near the corner region was affected by the partition height due to the change in the recirculating flow and due to the thermal effect on the rear surface of the partition.     

Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 ⩽ Re ⩽ 40), power-law index (0.6 ⩽ n ⩽ 2) and Prandtl number (1 ⩽ Pr ⩽ 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented.     

Synthesis,structural and electrochemical properties of pulsed laser deposited Li(Ni,Co)O2 films

We report the epitaxial growth of the LiNi_1−yM_yO₂ films (M = Co, Co–Al) on heated nickel foil using pulsed laser deposition in oxygen environment from lithium-rich targets. The structure and morphology was characterized by X-ray diffractometry, electron scanning microscopy and Raman spectroscopy. Data reveal that the formation of oriented films is dependent on two important parameters: the substrate temperature and the gas pressure during ablation. The charge–discharge process conducted in Li-microcells demonstrates that effective high specific capacities can be obtained with films 1.35 μm thick. Stable capacities of 83 and 92 μAh cm⁻² μm are available in the potential range 4.2–2.5 V for LiNi_0.8Co_0.2O₂ and LiNi_0.8Co_0.15Al_0.05O₂ films, respectively. The self-diffusion coefficient of Li ions determined from galvanostatic intermittent titration experiments is found to be 4 × 10⁻¹² cm² s⁻¹.     

Heat transfer on a power law stretching sheet subjected to free stream pressure gradient

The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations, irrespective of the condition whether U_w > U_∞ or U_w < U_∞, containing three parameters: β measuring the stretch rate of the moving boundary, ε is the ratio of free stream velocity to composite reference velocity and Pr is the Prandtl number of the ambient fluid. The numerical solutions of the thermal boundary layer equations are obtained for three Prandtl numbers 0.7, 1.0 and 10 for 0 ? ε ? 1 and for 0 ? β ? 2. The heat transfer coefficient show appreciable dependence on the ratio of free stream velocity to union of velocities of the stretching surface boundary and free stream.     

Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a thermally non-equilibrium porous layer is considered for investigation numerically with the presence of a cross flow. The mathematical model is derived for steady, two-dimensional laminar flow based on Darcy model and two-energy equation for fluid and solid phases. A parametric study is carried out by varying the following parameters: cross flow to jet flow velocity ratio parameter (0 ⩽ M ⩽ 1); porosity scaled thermal conductivity ratio parameter (0.1 ⩽ K_r ⩽ 1000); heat transfer coefficient parameter (0.1 ⩽ H ⩽ 1000); Péclet number (1 ⩽ Pe ⩽ 1000) and Rayleigh number (10 ⩽ Ra ⩽ 100). The total average Nusselt number is defined based on the overall thermal conductivity, which is assumed to be the arithmetic mean of the porosity scaled thermal conductivity of the fluid and solid phases. The total average Nusselt number as well as the average Nusselt number for both fluid and solid phases is presented for different governing parameters. It is found that the presence of a weak cross flow in a jet impinging jet may degrade the heat transfer. The results show that the average Nusselt number calculated from the thermal equilibrium model are the maximum possible values and these values can be reproduced by large values of H × K_r.     

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Direct numerical simulation is employed to investigate the two-dimensional boundary layer instability of a natural convection flow on a uniformly heated vertical plate submerged in a homogeneous quiescent environment. A Boussinesq fluid with Prandtl numbers of Pr = 0.733 (air) and 6.7 (water), in the local Rayleigh number range 0 ? Ra_x ? 2.4 × 10¹⁰, is studied. Controlled low amplitude numerical disturbances introduced into the base flow excite unstable travelling waves, with the resulting waves tracked and analyzed as they travel up the boundary layer. The numerical simulation readily reproduced what is predicted by the parallel linear stability theory for the two dimensional mode relatively short wave spectrum, but not for some parts of the long wave spectrum. Critical Rayleigh numbers have been obtained separately for both the temperature and velocity signals using the numerical results, and shown to be in good agreement with each other provided the data is renormalized using the boundary layer scalings of Sparrow and Greg [1]. It has been shown that the disturbance behavior depends on the Prandtl and Rayleigh numbers, the excitation frequency and to a lesser extent the prescribed thermal coupling at the plate.     

The effect of porous media particle size on forced convection from a circular cylinder without assuming local thermal equilibrium between phases

A detail numerical analysis of the effect of particle diameter of a packed bed of spherical particles on forced convection about an embedded circular cylinder is presented. This parametric study focusses on the two-phase energy (LTNE—local thermal non-equilibrium) model, which does not assume local thermal equilibrium (LTE) between the solid medium and the fluid. The investigation is performed for a cylinder-to-particle diameter ratio D_cy/d_p = 10–100, at a wide ranges of Reynolds number Re_D = 1–250 and solid-to-fluid thermal conductivity ratio k_r = 0.01–1000. A comparison of predictions from the LTNE and LTE energy models is also made. This paper quantifies the influence of the key non-dimensional parameters on the heat transfer rate. It is also shown that although the presence of the porous materials around the heated cylinder enhances the overall heat transfer and increases the pressure drop in the bed compared to an empty channel, using a porous medium with large particle diameters increases considerably this enhancement in heat transfer and decreases significantly the unfavorable pressure drop.     

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets

A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets is suggested and tested in Diesel engine-like conditions. The model is based on the assumption that properties of components are weak functions of the number of carbon atoms in the components (n). The components with relatively close n are replaced by the quasi-components with properties calculated as average properties of the a priori defined groups of actual components. Thus the analysis of heating and evaporation of droplets consisting of many components is replaced by the analysis of heating and evaporation of droplets consisting of relatively few quasi-components. In contrast to previously suggested approaches to modelling the heating and evaporation of droplets consisting of many components, the effects of temperature gradient and quasi-component diffusion inside droplets are taken into account. The model is applied to Diesel fuel droplets, approximated as a mixture of 21 components C_nH_2n+2 for 5 ? n ? 25, which correspond to a maximum of 20 quasi-components with average properties for n = n_j and n = n_j+1, where j varies from 5 to 24. It is pointed out that droplet surface temperatures and radii, predicted by a rigorous model taking into account the effect of all 20 quasi-components, are very close to those predicted by the model, using just five quasi-components. Errors due to the assumptions that the droplet thermal conductivity and species diffusivities are infinitely large cannot be ignored in the general case.     

Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions with the limitation of the Darcy model. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 1.0), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The correlation for Nu_avg in the forced convection regime is suggested. It is shown that mixed convection mode can cause minimum average Nusselt number unfavorably due to counteraction of jet flow against buoyancy driven flow. Hence, careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

Experimental study on spreading and evaporation of inkjet printed pico-liter droplet on a heated substrate

In this work, the spreading and evaporation of 2–70 pL droplet (17–50 μm diameter) of water and ethylene glycol jetted by drop-on-demand piezo-driven jetting head on the heated substrate are studied. According to the experimental results, the interfacial oscillation phenomena of water droplet whose Ohnesorge number (Oh) is about 10^?2 is similar to that in inviscid impact driven region, while that of ethylene glycol droplet (Oh ≈10^?1) is similar to that in highly viscous impact driven region followed by capillary driven extra spreading. In addition, various time scales used for nano/micro-liter droplets agree well with the times for interfacial oscillation, viscous damping, extra wetting, and evaporation in pico-liter droplets. In the case of water droplet, the spreading processes end before the evaporation becomes significant. However, in the case of highly viscous ethylene glycol droplet, the extra wetting overlaps the evaporation at high temperature.     

The particle thermal conductivity influence of nanofluids on thermal performance of the microtubes

The paper presents the numerical analysis on microchannel laminar heat transfer and fluid flow of nanofluids in order to evaluate the suitable thermal conductivity of the nanoparticles that results in superior thermal performances compared to the base fluid. The diameter ratio of the micro-tube was D_i/D_o = 0.3/0.5 mm with a tube length L = 100 mm in order to avoid the heat dissipation effect. The heat transfer rate was fixed to Q = 2 W. The water based Al₂O₃, TiO₂ and Cu nanofluids were considered with various volume concentrations ϕ = 1,3 and 5% and two diameters of the particles d_p = 13 nm and 36 nm. The analysis is based on a fixed Re and pumping power Π, in terms of average heat transfer coefficient and maximum temperature of the substrate. The results reveal that only the nanofluids with particles having very high thermal conductivity (λ_Cu = 401 W/m K) are justified for using in microcooling systems. Moreover, the analysis is sensitive to both the comparison criteria (Re or Π) and heat transfer parameters (h_ave or t_max).     

Effects of particle volume fraction on spray heat transfer performance of Al2O3–water nanofluid

An experimental investigation is conducted into the effects of the particle volume fraction on the spray heat transfer performance of a nanofluid comprising de-ionized water and Al₂O₃ particles with a diameter of 35 nm. The tests are performed with a flat, horizontal heated surface using a nozzle with an orifice diameter of 0.7 mm and a nozzle-to-heated surface distance of 17 mm. The spray mass flux is varied in the range of 26.433–176.751 kg/m² s, while the particle volume fraction is specified as 0%, 0.001%, 0.025%, or 0.05%. It is found that the optimal heat transfer performance is obtained using a particle volume fraction of 0.001%. The surface compositions of the sprayed samples are observed using scanning electron microscopy. The results show that the surfaces sprayed with a nanofluid containing 0.025 Vol% or 0.05 Vol% of nanoparticles contain a small amount of Al. However, those cooled using a nanofluid with a particle volume fraction of 0% or 0.001% show no traces of Al.