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Open-cell foams are promising to enhance heat transfer in many applications, such as electronics cooling. Though heat transfer coefficients are low, natural convection in open-cell foams is used in low-end applications, as consumer electronics or switching devices. In this paper air natural convection in a vertical channel equipped with an open-cell foam, with a symmetric uniform heat flux boundary condition at the vertical sides, is investigated numerically. The foam is modeled as a continuous porous medium under the assumption of Local Thermal Non-Equilibrium (LTNE) between solid and fluid phases. Mass, momentum and energy equations are solved numerically under the appropriate boundary conditions by employing a commercial finite element code. The velocity of the fluid and the temperature of the solid as well as the global heat transfer coefficient, for different thermo-physical properties and morphologies of the foam, and for various channel aspect ratios, are predicted.

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.

Their relatively high thermal conductivity makes metal open-cell foams promising heat transfer enhancers for lightweight applications. Conduction occurs through both solid and fluid phases, depending on the material and the microstructure. The effective conductivity of a foam is predicted by means of analytical and numerical methods, based on both idealized and realistic foam geometries, as well as by empirical correlations based on experiments. In this paper, a new model for the prediction of the effective thermal conductivity of foams is proposed. The proposed Three-Dimensional Thermal Fin (TTF) theory is based on the Electrochemical Fin (ECF) theory previously applied to the analysis of ion and electron transport through nanoporous materials. It has computational time two - three times shorter than those of current numerical techniques, such as finite-element methods. Starting from a tomography-reconstructed metallic open cell foam, the 3-D structure is modeled as a network. Conventional fin heat transfer scaled equations, applied to each part of the network, allow for the evaluation of the temperature distribution and heat rates. The effective thermal conductivity of the metal foam is then derived. The proposed model is validated by comparison with experimental results as well as with predictive models from the open literature and a finite-element based model.

Research on natural convection in open channels is very extensive due to its role in many engineering applications such as thermal control of electronic systems. In this paper, a parametric analysis is carried out in order to add knowledge of heat transfer in air natural convection for a symmetrically heated vertical parallel plate channel with a central auxiliary heated or adiabatic plate. The two‐dimensional steady‐state problem is solved by means of the stream function–vorticity approach and the numerical solution is carried out by means of the control volume method. Results are obtained for both a heated and unheated auxiliary plate, for a Rayleigh number in the range 103–106, for a ratio of the auxiliary plate height to the channel plate height equal to 0, 0.5 and 1 and for a ratio of the channel length to the channel gap in the range 5–15. Correlations for maximum wall temperatures and average channel Nusselt numbers are proposed.

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

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.

The aim of this work is the evaluation of the radiation contribution to the steady-state heat transfer in metallic foams by means of the radiative conductivity model. Because of the complexity of the structure, reference is made to a simplified physical radiative model, where the elementary cell of the foams is treated as a cubic cell. The contribution of the radiation heat transfer is investigated on a local basis. The local radiative conductivity has been used to evaluate the influence of radiative heat transfer in a two dimensional conductive-convective-radiative problem involving a forced fluid flow within a heated channel filled with a metallic foam. The effect of the solid emissivity and the foam porosity is pointed out for different foams.

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

In this study a numerical investigation of mixed convection in air in horizontal parallel walled channels with moving lower plate is carried out. The moving lower plate has a constant velocity and it is adiabatic, whereas the upper one is heated at uniform heat flux. The effects of horizontal channel height, heat flux and moving plate velocity are analyzed. Results in terms of temperature and stream function fields are given and the mass flow rate per unit of length and divided by the dynamic viscosity is reported as a function of Reynolds number based on the moving plate velocity. For stationary condition of lower plate, a typical C–loop inside the horizontal channel is detected. Different flow motions are observed in the channel and the two reservoirs, depending on the heat flux values and the distance between the heated upper stationary plate and lower adiabatic moving plate. The dimensionless induced mass flow rate presents different increase between the Reynolds number lower or greater than 1000.Copyright © 2005 by ASME

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 effect of heat conduction on air natural convection in a vertical channel, symmetrically heated, with flush-mounted strips at the walls, was numerically analyzed. Reference was made to laminar two-dimensional steady-state flow and to full elliptic Navier-Stokes equations on a I-shaped computational domain. Solutions were carried out by means of the FLUENT code. Results are presented in terms of wall temperature profiles, air velocity and temperature profiles in the channel. The wall temperature is affected by the location of the strip on the channel wall and maximum wall temperature is far larger when the heater is located in the upper region of the channel. Heat conduction in the channel wall lowers maximum wall temperature below the heater and the thicker the wall the larger the temperature reduction.Copyright © 2002 by ASME

Air natural convection in a vertical channel-chimney system with the channel walls symmetrically heated at a uniform heat flux has been experimentally investigated. Flow visualization photographs and average air temperatures are presented. Some profiles of air temperature fluctuations are reported, which point out the fluid flow interactions in the chinmey. The flow visualization showed that the cold air inflow penetrating into the chimney affects the thermal performance of the channel. The improvement in the thermal performance of the channel determined by the chimney effect, for various values of the process parameters, has also been pointed out. In all investigated configurations and ranges of the process parameters the air flow in the channel was laminar. The flow in the chimney is strongly affected by the aspect ratio. Moreover, at the lower values of the expansion ratio the flow was laminar in the chimney and in its lower corner a stable vortex was noticed whereas at larger values of the expansion ratio a cold ambient air downflow worsened the thermal performance of the system. Interactions between the thermal plume arising from the channel, the vortex in the comer in the inlet chimney region and the cold air inflow yield fluctuations in the air temperature in the system. The distribution of time averaged air temperature in the cross sections validates indications given by the flow visualization in the chimney.Copyright © 2002 by ASME

A simplified one-dimensional analytical model of radiative heat transfer in foams is presented, based on the idea of dividing the porous material into layers at the pore level and then modeling each layer of the porous material as an equivalent semi-transparent, absorbing and reflecting plane. Compared to existing models, the model proposed in this paper has the advantage of explicitly accounting for the geometry of the foam and the radiative energy fluxes, at the same time ensuring self-consistency and offering the computational lightness of analytical models, without sacrificing the mathematical simplicity of the formulation. Using a regular cubic lattice representation and assuming diffuse radiation, straightforward analytical correlations are derived to evaluate the characteristics both of single layers of foam and of finite thickness samples, accounting for various boundary conditions. The predictions of the model are in good agreement with experimental data taken from the literature.

Air natural convection on a vertical isoflux plate with a downstream unheated extension and a facing parallel shroud has been experimentally investigated, for different values of the wall heat flux and of the geometrical parameters. In most configurations the adiabatic extension improves the thermal performance of the channel. For the larger values of the channel aspect ratio (Lh/b = 10) the system with a geometrically asymmetric chimney performs better than that with a geometrically symmetric chimney. Maximum wall temperatures and average Nusselt numbers are correlated to the thermal and geometrical process parameters, in the ranges Ra* B/b = 3.102 − 105 and L/Lh = 1.5–4.0.

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.

Nowadays trends in natural convection heat transfer are oriented toward either the seeking of new configurations to enhance the heat transfer parameters or the optimization of standard configurations. An experimental investigation on air natural convection in divergent channels with uniform heat flux at both the principal walls is presented in this paper to analyze the effect of radiative heat transfer. Results in terms of wall temperature profiles as a function of the walls diverging angle, the interwall spacing, the heat flux are given for two value of the wall emissivity. Flow visualization is carried out in order to show the peculiar pattern of the flow between the plates in several configurations. Nusselt numbers are then evaluated and correlated to the Rayleigh number. The investigated Rayleigh number ranges from 7.0 × 102 to 4.5 × 108 . The maximum wall temperature decreases at increasing divergence angles. This effect is more evident when the minimum channel spacing decrease. A significant decrease in the maximum wall temperature occurs passing from e = 0.10 to e = 0.90, except in the inlet region. Flow visualization shows a separation of the fluid flow for bmin = 40 mm and θ = 10°. Correlations between Nusselt and Rayleigh numbers show that data are better correlated when the maximum channel spacing is chosen as the characteristic length.Copyright © 2003 by ASME