Transport Phenomena in Porous Media: from Open-Cell Foams to Biological Systems

The complex geometry of a porous medium makes challenging the study of transport phenomena through it. Investigations are carried out treating the whole macroscopic porous medium as an equivalent homogeneous medium, whose governing equations are averaged over a Representative Elementary Volume (REV). Governing equations are coupled with the microscopic problem scales by means of the so-called closing coefficients. Results of the study of transport phenomena in two classes of porous media: open-cell foams and biological systems, also with reference to human arteries are presented in this thesis. For open-cell foams, analysis of microscales pressure drop and convective heat transfer were carried out with both experimental and numerical techniques. Experiments were carried out for various open-cell aluminum foam samples with different porosities and PPI in order to study pressure drop. Local convection heat transfer in one foam sample, for different inlet velocities of the fluid, was analyzed. Numerical predictions were obtained by using a finite element scheme. The geometry for the numerical models was reconstructed by means of two techniques. In the first, tomographic scans on three open-cell aluminum foam samples with different porosities were carried out to obtain a real foam; in the second the geometry was computationally reconstructed with reference to Kelvin’s foam model, obtaining an ideal foam. The ideal foam geometry was further modified in order to analyze thermally developing effects and strut shape effects on pressure drop and convection heat transfer. Nusselt number was correlated to process parameters, for thermally developed flow, and it was shown that the accuracy of the ideal model improves when the strut shape is well-modeled. By using the macroscopic porous medium approach, two industrial applications of open-cell foams were studied with a numerical approach. The first application is a volumetric solar receiver, where an open-cell ceramic foam is employed as the porous absorber; the second one was an aluminum foam-based heat sink. In both cases, results are presented for different foam morphologies and thermo-fluid-dynamic conditions. Low density lipoprotein (LDL) deposition through the walls of human arteries was studied by using a macroscopic porous medium approach. Different arteries were analyzed: a straight artery, a stenosed artery and the aorta-iliac bifurcation. Governing equations, with the appropriate boundary conditions, were solved by using both a numerical approach and an analytical approach. For the straight artery, Numerical modeling allowed to analyze the non-Newtonian fluid effects on the prediction of LDL deposition in different size straight artery. The above effects were studied by comparing various non-Newtonian fluid models and showed that a Newtonian fluid assumption can be used without introducing remarkable differences. An analytical approach was used to investigate LDL deposition in an arterial wall under hyperthermia and hypertension, obtaining a simplified analytical solution. Energy and species equations were coupled by means of the Ludwig-Soret effect. LDL accumulation under hyperthermia in a stenosed artery modeled with a cosinusoidal function was numerically analyzed. In all cases, hyperthermia and hypertension increase LDL accumulation. For the aorta-iliac bifurcation, a numerical 2-D study of non-Newtonian effects on LDL mass transport showed that the Newtonian fluid assumption is weak in presence of recirculation zones

Pennes' bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation

[EN] The objective of this study was to compare three different heat transfer models for radiofrequency ablation of in vivo liver tissue using a cooled electrode and three different voltage levels. The comparison was between the simplest but less realistic Pennes' equation and two porous media-based models, i.e. the Local Thermal Non-Equilibrium (LTNE) equations and Local Thermal Equilibrium (LTE) equation, both modified to take into account two-phase water vaporization (tissue and blood). Different blood volume fractions in liver were considered and the blood velocity was modeled to simulate a vascular network. Governing equations with the appropriate boundary conditions were solved with Comsol Multiphysics finite-element code. The results in terms of coagulation transverse diameters and temperature distributions at the end of the application showed significant differences, especially between Pennes and the modified LTNE and LTE models. The new modified porous media-based models covered the ranges found in the few in vivo experimental studies in the literature and they were closer to the published results with similar in vivo protocol. The outcomes highlight the importance of considering the three models in the future in order to improve thermal ablation protocols and devices and adapt the model to different organs and patient profiles.This work was supported by the Spanish Ministerio de Economia, Industria y Competitividad under "Plan Estatal de Investigacion, Desarrollo e Innovacion Orientada a los Retos de la Sociedad", Grant No "RTI2018-094357-B-C21" and by the Italian Government MIUR Grant No "PRIN-2017F7KZWS".Tucci, C.; Trujillo Guillen, M.; Berjano, E.; Iasiello, M.; Andreozzi, A.; Vanoli, GP. (2021). Pennes' bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation. Scientific Reports. 11(1):1-13. https://doi.org/10.1038/s41598-021-84546-6S113111Chu, K. F. & Dupuy, D. E. 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Effects of Pulsed Radiofrequency Source on Cardiac Ablation.

Heart arrhythmia is caused by abnormal electrical conduction through the myocardium, which in some cases, can be treated with heat. One of the challenges is to reduce temperature peaks—by still guaranteeing an efficient treatment where desired—to avoid any healthy tissue damage or any electrical issues within the device employed. A solution might be employing pulsed heat, in which thermal dose is given to the tissue with a variation in time. In this work, pulsed heat is used to modulate induced temperature fields during radiofrequency cardiac ablation. A three-dimensional model of the myocardium, catheter and blood flow is developed. Porous media, heat conduction and Navier–Stokes equations are, respectively, employed for each of the investigated domains. For the electric field, solved via Laplace equation, it is assumed that the electrode is at a fixed voltage. Pulsed heating effects are considered with a cosine time-variable pulsed function for the fixed voltage by constraining the product between this variable and time. Different dimensionless frequencies are considered and applied for different blood flow velocity and sustained voltages. Results are presented for different pulsed conditions to establish if a reasonable ablation zone, known from the obtained temperature profiles, can be obtained without any undesired temperature peaks

A heat transfer analysis of axial and radial functionally-graded ceramic foams solar air receivers

Volumetric solar receiver are promising as heat transfer devices in concentrated solar power applications because they allow to reduce heat losses at the receiver entrance when compared to more conventional tubular receivers. Among various porous materials, ceramic foams have been shown to be promising because of their extended heat transfer area and effective thermal conductivity, especially when they are manufactured by considering variable morphologies thanks to modern techniques like additive manufacturing. In this contribution, porous media numerical simulations are presented for fluid flow and heat transfer in ceramic foams receiver with different porosity functions on either axial or radial directions, and also when porosity varies on both directions. Such simulations are performed by employing Beer-Lambert law to model radiative heat transfer, and a Gaussian distribution for the incoming radiation. Results are obtained by constraining the average porosity for the different cases, showing that graded foams allow to obtain more or less similar outflow temperatures, but with reduced heat losses at the receiver entrance and also with less uniform velocity profiles to promote heat convection in some critical points of the receive

Numerical Investigation of a Phase Change Material Including Natural Convection Effects

Nowadays, Organic Rankine Cycle (ORC) is one of the most promising technologies analyzed for electrical power generation from low-temperature heat such as renewable energy sources (RES), especially solar energy. Because of the solar source variation throughout the day, additional Thermal Energy Storage (TES) systems can be employed to store the energy surplus saved during the daytime, in order to use it at nighttime or when meteorological conditions are adverse. In this context, latent heat stored in phase-change transition by Phase Change Materials (PCM) allows them to stock larger amounts of energy because of the larger latent energy values as compared to the specific heat capacity. In this study, a thermal analysis of a square PCM for a solar ORC is carried out, considering four different boundary conditions that refer to different situations. Furthermore, differences in including or not natural convection effects in the model are shown. Governing equations for the PCM are written with references to the heat capacity method and solved with a finite element scheme. Experimental data from literature are employed to simulate the solar source using a time-variable temperature boundary condition. Results are presented in terms of temperature profiles, stored energy, velocity fields and melting fraction, showing that natural convection effects are remarkable on the temperature values and consequently on the stored energy achieved

The effects of exterior boundary conditions on a internally heated tumor tissue with a thermoporoelastic model

Modeling flow field in tumor regions interstitial space is of primary importance, because of the importance of advection in macromolecule drug delivery. Its deformation has also to be taken into account because of the forces caused by the fluid; if the tumor region is not isothermal, this deformation can be also strongly affected by temperature fields. In this paper, the effects of thermal boundary conditions on a tumor region periphery with an internal heat source are investigated. The tumor region is modeled as a deformable sphere, in which two phases can be distinguished. The fluid phase is the interstitial fluid, while the rest of the tumor is modeled as the solid phase, including also capillaries and tissues. Transient-state governing equations for mass, momentum and energy are written for both phases, by also considering tumor deformation under the linear elastic material assumption. A situation of Tumor Blood Flow (TBF) rapid decay, in which vascular pressure rapidly approaches to zero, is considered, while the heat source is modeled as a fourth-grade radial-decay function. Boundary conditions for the energy equation are varied on the external surface of the sphere, in order to appreciate the effects of the surrounding on flow and temperature fields inside the tumor. After scaling equations, a finite-element scheme is employed for the numerical solution. Comparisons with analytical solutions from literature show a good agreement. Results are shown for different dimensionless parameters that are referred to temperature, volumetric strain, pressure and velocity, showing in which case external boundary conditions strongly affect tumor region flow fields and a third-kind boundary condition is needed

Hyperthermia effects on macroscopic fluid transport in tumors

Combining the effects of transvascular and interstitial fluid movement with the structural mechanics of a tissue is important to accurately describe processes such as nutrient transport in a tumor cell. Further, hyperthermia can have a role; for example, temperature variations can be induced in order to treat some kinds of tumors, like liver tumor. Recently, the study of the effects of hyperthermia on fluid flow and mass transport in biological systems by considering the fluid-structure interaction has gained researchers attention. In the present paper, fluid flow in a tumor mass is analyzed at a macroscopic scale by considering the effects of both solid tissue deformation and hyperthermia. Governing equations are averaged over a Representative Elementary Volume (REV) of the living tissue, and written by means of the thermo-poroelasticity theory. Darcy's law is used to describe fluid flow through the interstitial space, while transvascular transport is described with a generalized Starling's law. The effects of hyperthermia on the living tissue are included with a source term in the tissue momentum equation that considers the thermal expansion. Governing equations with the appropriate boundary conditions are solved with the finite commercial code COMSOL Multiphysics in steady state regime. The numerical model is validated with analytical results from Netti et al. [1997] for an isothermal case. Results are presented in terms of pressure, velocity and temperature fields, for various thermal loads and it is analyzed the effect of hyperthermia on various physical parameters