arXiv subjects

A. Barletta

Publications and source records attributed to A. Barletta.

15 recordsLinked to original sources

arXiv2026

The Wooding problem revisited

The threshold conditions to convective instability in a semi-infinite porous layer saturated by a fluid are determined. The classical setup for this problem in geothermal fluid dynamics was originally modelled by Wooding in 1960. Its formulation is here reconsidered to allow for an imperfect heat transfer across the boundary, parametrised through the Biot number. The temperature boundary condition considered by Wooding is here recovered as the limit of an infinite Biot number. The linear stability analysis of the stationary boundary layer which establishes in the porous medium when a boundary steady suction occurs is carried out. Two different versions of the Rayleigh number are considered, namely, a temperature-difference-based version and a heat-flux-based version. While the former is the classical Rayleigh number for flow in porous media, the latter is a variant definition which displays a finite limit at neutral stability in both the opposite limiting cases of an infinite or of a zero Biot number.

physics.flu-dyn↗

arXiv2025

On Prats' problem with anomalous diffusion

The classical Prats' problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This study, however, substitutes thermal diffusion with mass diffusion. Furthermore, the usual scheme of mass diffusion is extended to comprehend also the anomalous phenomena of superdiffusion or subdiffusion. Such phenomena are modelled via a time-dependent mass diffusivity which yields a significant change in the formulation of the stability eigenvalue problem. In particular, the ordinary differential equations governing the time evolution of the perturbations acting on the base throughflow become non-autonomous. This makes a significant difference in the discussion of the conditions leading to instability, with a marked effect of the anomaly in the mass diffusion process. The transition from convective to absolute instability for subdiffusion processes is also addressed.

physics.flu-dyn↗

arXiv2025

Status of the Trinity PeV Neutrino Observatory

The Trinity Neutrino Observatory aims to detect tau neutrinos in the energy range of 1 PeV to 10 EeV. We are developing the observatory in three stages. The first stage, known as the Trinity Demonstrator, was deployed in Fall 2023. The Demonstrator serves as a pathfinder for the full observatory and will inform the design of the first Trinity Telescope. We discuss the status and initial results of the Trinity Demonstrator. In 346 hours of observations with the Demonstrator, we do not identify a neutrino candidate event.

astro-ph.IM↗

arXiv2025

Mixed convection and onset of instability due to asymmetric wall heat fluxes in a porous channel

The problem of convective instability onset in a horizontal porous channel is explored. The channel's impermeable walls are heated with asymmetric thermal conditions modelled through unequal, but uniform, wall heat fluxes. A stationary solution describing the mixed convection flow is obtained from the governing local balance equations. Then, the linear instability of this flow is analysed by formulating an eigenvalue problem with normal modes. The research specifically highlights the role of the flow rate regime, parametrised through the P\'eclet number, where the Rayleigh number and the heat flux asymmetry ratio are key to defining when instability occurs. The numerical solution of the stability eigenvalue problem is achieved by employing the shooting method. Analytical results are also obtained by employing large-wavelength asymptotic expansions. A numerical analysis is performed to discuss the neutral stability curves and the critical values of the Rayleigh number under different flow and asymmetry conditions.

physics.flu-dyn↗

arXiv2025

Wall roughness and viscous dissipation effects in microchannel heat sinks with semicircular cross-section

A statistical analysis of the wall roughness effect is carried out to determine the impact of the shape uncertainty on the Poiseuille number and Nusselt number of laminar forced convection. The focus is on the fully developed regime in a semicircular microchannel where the heat transfer occurs from the diametrical plane boundary, modelled as a perfectly smooth surface. On the other hand, the curved semicircular boundary is devised as rough and with a negligible wall heat flux. Three types of thermal boundary conditions are implemented: the T condition, the H1 condition and the H2 condition. The T condition serves to model a case where the fluid temperature does not undergo any change in the streamwise direction, while the H1 and H2 conditions are employed to describe a net heating of the fluid. A statistical sample of several different rough microchannels is used to detect the actual effects of roughness on the Poiseuille number and on the Nusselt number, through the evaluation of their average values and standard deviations. The governing local momentum and energy balance equations are solved numerically by a finite element method taking into account the viscous dissipation contribution to the local energy balance.

physics.flu-dyn↗

arXiv2024

Shape uncertainty analysis of laminar forced convection in a round microchannel with viscous dissipation

The shape of a microchannel is usually affected by a significant uncertainty due to the small size of the cross-section, comparable with the typical wall-roughness length scale. Such an uncertainty is present at any scale, but it is definitely amplified and, hence, significantly important when the hydraulic diameter becomes smaller than some tenth micrometers. The focus of this paper is on the numerical analysis of the sensitivity to shape random modification, within a prefixed maximum extent, of the main flow and heat transfer characteristics of fully-developed forced convection. The numerical solutions are carried out by employing a finite-element solver repeated over a statistical sample of randomly generated perimetral profiles that simulate the wall roughness. The study includes the evaluation of the Fanning friction factor and of the Nusselt number for the T, H1 and H2 thermal boundary conditions.

physics.flu-dyn↗

arXiv2024

Anomalous mass diffusion in a binary mixture and Rayleigh-Benard instability

The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion phenomenology emerging when the mean squared displacement of molecules in the diffusive random walk is not proportional to time, as in the usual Fick's diffusion, but it is proportional to a power of time. The power-law model of anomalous diffusion identifies subdiffusion when the power-law index is smaller than unity, while it describes superdiffusion when the power-law index is larger than unity. This study reconsiders the stability analysis of the Rayleigh-Benard problem by extending the governing equations to include the anomalous diffusion.

physics.flu-dyn↗

arXiv2024

Laminar forced convection characteristics in a round microchannel with shape uncertainty: effect of wall slip

The shape of a microchannel cross-section is usually affected by a significant uncertainty due to the small hydraulic diameter. Such an uncertainty is indeed present at any scale, but is amplified in smaller scales, becoming significantly important when the hydraulic diameter is smaller than some tenth micrometers. In this scenario, this paper is focused on analyzing the sensitivity of the heat and fluid flow characteristics with respect to the channel shape, considering a random modifications in the channel cross section. Forced convection in a fully developed regime with a wall slip is considered, and the analysis includes the evaluation of the Fanning friction factor and of the Nusselt number for the H1 thermal boundary condition, considering different slip-flow configurations, as dictated by the slip-length parameter. The heat and fluid flow problem is solved for one thousand randomly generated channel geometries, based on a circular microchannel which is allowed to have its boundary points move within 10\% of its nominal diameter. The calculated data for $f \Re$ and $\Nu$ are then analyzed, and compared with the nominal values (obtained for smooth channels). The results show that, on an average basis, the roughness effect has a tendency to reduce the Nusselt number while increasing the friction factor, however, with a small number of exceptions.

physics.flu-dyn↗

arXiv2023

Dissipation instability of Couette-like adiabatic flows in a plane channel

The mixed convection flow in a plane channel with adiabatic boundaries is examined. The boundaries have an externally prescribed relative velocity defining a Couette-like setup for the flow. A stationary flow regime is maintained with a constant velocity difference between the boundaries, considered as thermally insulated. The effect of viscous dissipation induces a heat source in the flow domain and, hence, a temperature gradient. The nonuniform temperature distribution causes, in turn, a buoyancy force and a combined forced and free flow regime. Dual mixed convection flows occur for a given velocity difference. Their structure is analysed where, in general, only one branch of the dual flows is compatible with the Oberbeck-Boussinesq approximation, for realistic values of the Gebhart number. A linear stability analysis of the basic stationary flows with viscous dissipation is carried out. The stability eigenvalue problem is solved numerically, leading to the determination of the neutral stability curves and the critical values of the Péclet number, for different Gebhart numbers. An analytical asymptotic solution in the special case of perturbations with infinite wavelength is also developed.

physics.flu-dyn↗

arXiv2023

Viscous heating and instability of the adiabatic buoyant flows in a horizontal channel

The stability of buoyant flows occurring in the mixed convection regime for a viscous fluid in a horizontal plane-parallel channel with adiabatic walls is investigated. The basic flow features a parallel velocity field under stationary state conditions. There exists a duality of flows, for every prescribed value of the mass flow rate across the channel cross-section, caused by the combined actions of viscous dissipation and of the buoyancy force. As pointed out in a previous study, only the primary branch of the dual solutions is compatible with the Oberbeck-Boussinesq approximation. Thus, the stability analysis will be focussed on the stability of such flows. The onset of the thermal instability with small-amplitude perturbations of the basic flow is investigated by assuming a very large Prandtl number, which is equivalent to a creeping flow regime. The neutral stability curves and the critical parametric conditions for the onset of instability are determined numerically.

physics.flu-dyn↗

arXiv2022

On the use and misuse of the Oberbeck-Boussinesq approximation

The Oberbeck-Boussinesq approximation is the most widely employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this note, the basic features of the Oberbeck-Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck-Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented.

physics.flu-dyn↗

arXiv2021

Thermal instability of the buoyant flow in a vertical cylindrical porous layer with a uniform internal heat source

The buoyancy-induced parallel flow in a vertical cylindrical porous layer is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as isothermal and permeable to an external fluid reservoir. The onset of the convective instability is analysed by linearising the governing equations for the perturbations. The governing parameters driving the instability are the heat-source Rayleigh number and the ratio between the internal radius and the external radius. Neutral stability curves and the critical values of the Rayleigh number, the perturbation wave number and the angular frequency are computed numerically. It is shown that axisymmetric modes form the most dangerous mode of instability.

physics.flu-dyn↗

arXiv2020

On the stability of parallel flow in a vertical porous layer with annular cross-section

The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable. The emergence of linear instability by convection cells is excluded on the basis of a numerical solution of the linearised governing equations. This result extends to the annular geometry the well-known Gill's theorem regarding the impossibility of convective instability in a vertical porous plane slab whose boundaries are impermeable and isothermal with different temperatures. The extension of Gill's theorem to the annular domain is approached numerically by evaluating the growth rate of normal mode perturbations and showing that its sign is negative, which means asymptotic stability of the basic flow. A concurring argument supporting the absence of linear instability arises from the investigation of cases where the impermeability condition at the vertical boundaries is relaxed and a partial permeability is modelled through Robin boundary conditions for the pressure. With partially permeable boundaries, an instability emerges which takes the form of axisymmetric normal modes.

physics.flu-dyn↗

arXiv2020

Buoyant flow and instability in a vertical cylindrical porous slab with permeable boundaries

The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid reservoirs. There exists a stationary parallel velocity field with a zero flow rate and pure conduction heat transfer. Its linear stability is analysed with normal mode perturbations of the pressure and temperature fields. The transition to convective instability is caused by the basic horizontal temperature gradient. Hence, its nature differs from that of the usual Rayleigh-Bénard instability. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem, solved numerically. Its solution provides the neutral stability curve at each fixed aspect ratio between the external radius and the internal radius. The critical Rayleigh number triggering the instability is evaluated for different aspect ratios. It is shown that the system becomes more an more unstable as the aspect ratio increases, with the critical Rayleigh number dropping to zero when the aspect ratio tends to infinity.

physics.flu-dyn↗

arXiv2009

Local energy balance, specific heats and the Oberbeck-Boussinesq approximation

A thermodynamic argument is proposed in order to discuss the most appropriate form of the local energy balance equation within the Oberbeck-Boussinesq approximation. The study is devoted to establish the correct thermodynamic property to be used in order to express the relationship between the change of internal energy and the temperature change. It is noted that, if the fluid is a perfect gas, this property must be identified with the specific heat at constant volume. If the fluid is a liquid, a definitely reliable approximation identifies this thermodynamic property with the specific heat at constant pressure. No explicit pressure work term must be present in the energy balance. The reasoning is extended to the case of fluid saturated porous media.

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