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The high efficiency of concentrated solar power (CSP) in energy conversion makes it a very attractive device for using solar energy as a substitute of nonrenewable energy sources. The open volumetric receiver plays an important role in the performance of a CSP. The optimized design of solar receiver implies the thorough knowledge of the heat transfer between the air and the foam and of the temperature distribution in the receiver. Heat transfer in the cylindrical SiC porous volumetric receiver of a solar tower, undergoing the impact of concentrated solar radiation, is investigated numerically in this paper. Governing equations are written with the volume averaging technique. A two-equation model for the energy equation, under the local thermal nonequilibrium assumption, is used. Numerical simulations are carried out through the commercial code COMSOL Multiphysics. The solid and fluid temperatures, the fluid velocity and the pressure drop, for various boundary and morphological conditions, are predicted and discussed. The receiver efficiency is finally maximized carrying out an extended parametric analysis of process parameters.

Predicting heat transfer is a primary task in the design of open-cell foams. When a Local Thermal Non Equilibrium (LTNE) model is employed, convection heat transfer between the solid and fluid phases is considered, and a volumetric heat transfer coefficient needs to be defined. Some recent studies pointed out that the effects of developing convection heat transfer between the fluid and the solid in a foam are to be taken into account. The developing thermal flow of air through an open-cell foam, with a uniform heat flux solid/fluid boundary condition, is investigated numerically in this paper. The geometry is modeled with reference to Kelvin's tetrakaidecahedron foam model. A correlation among the porosity, the cell diameter and the ratio of heat transfer surface to volume is derived. Three regions are identified along the flow direction: an impingement region, a thermally developing region and a thermally developed region. Dimensional and dimensionless convection heat transfer coefficients have been predicted numerically as a function of the axial coordinate of the foam, for different values of the Reynolds number and the porosity. A correlation is presented among the predicted values of the volumetric Nusselt number, the porosity, and the Reynolds number in the thermally developed region, which is in good agreement with experimental data and numerical predictions by other authors. Finally, the analysis of the convection heat transfer through a single foam cell, at a local pore-scale, is presented.

Transport phenomena through open-cell foams are strongly affected by their complex microstructure. Morphological parameters, such as the diameter of pores and cells, the strut thickness, and the specific surface area, play key roles. Due to the intricate nature of an open-cell foam, its morphological models are very useful in engineering applications. We first review correlations in the literature of the morphological parameters that affect transport phenomena in foams. Then, with reference to the Kelvin's foam model, we present a unique model for the characterization of morphological parameters of open-cell foams, accounting for different strut shapes. New correlations among morphological parameters are proposed. There is good agreement between the correlations obtained with the proposed model and the experimental results from the literature. The model, accounting for any shape of the struts cross section, predicts values of foam morphological parameters generally closer to those predicted by available models not valid for all strut shapes.

It is well known that the manufacturing process of open-cell foams slightly elongates their struts in one direction, thus making them anisotropic; in turn, anisotropy affects foam characteristics. Furthermore, actual foams can be characterized with reference to a Representative Volume Element (RVE), defined as the cubic sub-volume having the same characteristics as those of the whole foam. An appropriately chosen RVE is very helpful to pass simulation data from a micro-to a macro-scale. The important role played by RVE in characterizing foams performance suggests further research in its determination, in order to reduce computational power and to allow to apply the volume-averaging technique to open-cell foams. In this paper, anisotropy and RVE for the effective thermal conductivity of open-cell metal foams are numerically analyzed. After scanning with Computed Tomography (CT) and postprocessing four open-cell aluminum foams with different porosities and the same Pores Per Inch (PPI) value, their morphologies are investigated in order to evaluate the effects of porosity on cells anisotropy. Foam cell elongation is quantified by an anisotropy ratio. Simulations are performed on CT data with a finite-element method to compute the effective thermal conductivities along three orthogonal directions, and results are compared with data published in the literature. A new correlation between effective thermal conductivity, porosity and direction is presented. The dependence of effective thermal conductivity on cells elongation is also pointed out. RVE sizes for different porosities, directions and inaccuracy thresholds are then investigated. Finally, an existing analytical model is suitably adapted to reliably predict the RVE size with a new correlations which accounts for the directionally-averaged effective thermal conductivity.

Open-cell metal foams are promising materials for heat transfer augmentation, due to their tortuosity and high specific surface area. The volume-averaging technique under the assumption of local thermal non-equilibrium between the solid and fluid phases is often used to model devices equipped with open-cell foams; it requires an accurate knowledge of the interfacial convective heat transfer coefficient. Its dependence on the anisotropy of elongated foam cells is investigated numerically in the present work. Four aluminum foam samples with different porosities and equal PPIs are considered; their geometry is reconstructed by means of x-ray computed tomography. Mass, momentum and energy equations for the fluid phase (air) are solved, while the solid phase is accounted for with a uniform heat flux boundary condition. Interfacial convective heat transfer coefficients and Nusselt numbers are predicted. The dependence of the interfacial heat transfer coefficient in the elongation direction on the effective porosity and fluid inlet velocity is pointed out. The comparison of predicted values with those given by correlations from the open literature shows a good agreement. Finally, correlations for the prediction of Nusselt numbers, accounting for the foam anisotropy, are proposed, which can be useful in the study of metal foams.

An analytical solution to the three-dimensional quasi-stationary problem in a finite depth and width solid with a circular Gaussian moving heat source at the body surface is developed and analyzed. The temperature distribution and the axial coordinate at which the maximum midplane temperature is achieved are presented as a function of Peclet number, solid thickness and width. The dependence of the maximum midplane temperature on the process parameters is highlighted. Combinations of process parameters for which the solution to the three-dimensional problem can be approximated by those to simpler models are pointed out.

Simplified thermal models in laser and electron beam surface hardening can be very useful to industrial users. Hardening depth as a function of austenitization temperature and Peclet number is evaluated for one-dimensional stationary and two-dimensional uniform strip moving heat source problems without melting. Reliable correlations for predicting both hardening depths and maximum temperatures are given in terms of dimensionless meaningful parameters. Calculated values are also compared with experimental results reported by other authors.

Natural convection in a convergent channel with finite-thickness principal walls at uniform heat flux is investigated numerically. Heat conduction in the walls and the effects of walls emissivity are taken into account. Laminar two-dimensional steady-state conditions are assumed. Results in terms of wall dimensionless temperature profiles as a function of convergence angle, channel spacing, and heat flux are given for various values of wall emissivity. Wall temperatures decrease significantly, passing from delta = 0 degrees to 2 degrees at the lowest channel spacing. Streamlines and temperature fields show a recirculating region in the channel for large values of L-w/b(min) and for delta equal to 5 degrees and 10 degrees. Correlations between Nusselt numbers and Rayleigh numbers are proposed. Dimensionless parameters are in the following ranges: 4.4

Air natural convection in an asymmetrically heated channel with unheated extensions has been investigated experimentally. Local and maximum wall temperatures and heat transfer coefficients are presented, for different values of the process parameters. Optimal configurations in terms of the minimum values of maximum wall temperatures are obtained. Average Nusselt numbers and maximum dimensionless wall temperatures are correlated to the Rayleigh number and to the geometrical dimensionless parameters in the 10–1.5×10 5 range of the Rayleigh number times the expansion ratio. The addition of downstream unheated extensions improves the thermal performance of the channel for some configurations, the longer the extension and the lower the aspect ratio the lower the wall temperature in the channel.

The ease of thermal control by means of air natural convection stimulates the investigation of configurations with the aim at improving the thermal performance. The effect of adding adiabatic extensions downstream of a vertical isoflux symmetrically heated channel has been experimentally analyzed. Optimal configurations have been identified through the measured wall temperature profiles, with reference to the extension and expansion ratios ( L / L h and B / b ) of the insulated extensions. Conspicuous maximum wall temperature reductions have been achieved by means of these optimal configurations. In details, percent increases of the heat transfer rate (i.e., average channel Nusselt number) were of order 10–20% depending on the channel aspect ratio, L h / b , and imposed wall heat flux. In any case, quite large extensions should be added to enhance the heat transfer rate, i.e. about 3.0 times the height of the channel, while the optimal expansion ratio was nearly 2.0 for all the configurations. Composite correlations between the average Nusselt number and the maximum dimensionless wall temperatures and Ra * , the Rayleigh channel number, B / b and L / L h parameters, in the 1.5⩽ L / L h ⩽4.0,1.0⩽ B / b ⩽4.0 and 10 2 ⩽ Ra * B / b ⩽5.0×10 6 ranges, have been evaluated.

The numerical and experimental analysis of laser back-scribing fabrication of a-Si photovoltaic cells, made out of a multilayer thin film on a glass substrate, is carried out. The numerical study is performed by means of a rather simple combined optical and thermal model. Experiments are carried out throughout the three phases of the manufacturing process. The successive targets of the selective cut are a transparent conductive oxide thin film (TCO), a TCO⧹a-Si double layer and a TCO⧹a-Si⧹Al multilayer. Experimental results and predictions from the numerical model are compared in terms of the cut energy flux values. In the numerical study the cut energy flux is assumed to be the one which determines the melting of the material. The predicted cut energy fluxes are in good agreement with experimental results.

An experimental study on air natural convection on an inclined discretely heated plate with a parallel shroud below was carried out. Three heated strips were located in different positions on the upper wall. The distance between the walls, b, was changed in the range 7.0–40.0 mm and two values of the heat flux dissipated by the heaters were taken into account. Several inclination angles between the vertical and the horizontal were tested. The wall temperature distribution as a function of the channel spacing and the inclination angle, the source heat flux, the number and the arrangement of the heat sources are presented. The analysis shows that, for angles not greater than 85 deg, increasing the distance between walls does not reduce the wall temperatures, whereas at greater tilting angles (>85 deg) there is an opposite tendency. This is confirmed by flow visualization at angles equal to 85 deg and 90 deg and b=20.0 and 32.3 mm. Dimensionless maximum wall temperatures are correlated to the process parameters in the ranges 1.2s˙104⩽Ral cos θ⩽8.6s˙105; 0 deg⩽θ⩽88 deg; 0.48⩽l/b⩽1.6 and 10⩽L/b⩽32.6 with 1.0⩽d/l⩽3.0; the agreement with experimental data is good. The spacing which yields the best thermal performance of the channel is given. Local Nusselt numbers are evaluated and correlated to the local Rayleigh numbers and the tilting angles in the ranges 20⩽Rax′⩽8.0s˙105 and 0 deg⩽θ⩽88 deg. The exponent of monomial correlations between local Nusselt and Rayleigh numbers are in the 0.23–0.26 range. Comparisons with data from the literature, in terms of Nusselt number, exhibited minor discrepancies, mainly because of some difference in test conditions and of heat conduction in the channel walls.

The thermal field in a solid subjected to a periodic heat flux at the surface is compared to that induced by a constant heat flux, for the same temperature attained at the same depth. The depth at which the peak to peak amplitude of the temperature oscillation lays within a chosen approximation is derived. The fraction of the heat flux that in a continuous or single on-off heating induces the same temperature attained in a periodic on-off heating is evaluated, at given depths after the same time. Surface maximum temperature values are correlated to relevant parameters.

In laser and electron beam surface processing the knowledge of the thermal field and, particularly, of the maximum temperatures attained is a very important issue. The two-dimensional solution for a uniform strip heat source moving at a constant velocity along the surface of a semi-infinite body is analysed. A comparison between the approximate one-dimensional and the two-dimensional models is presented. The ratio between the maximum temperature values is given by the two models and the time at which they are reached are reported. Guidelines for estimating the range of variables within which the results of the two models are in a reasonable agreement are given.