Heat Transport Model Research Articles

The Contamination of Groundwater Model for Heat and Concentration Transport within Porous Media Under Electromagnetic Fields

The Contamination of Groundwater Model for Heat and Concentration Transport within Porous Media Under Electromagnetic Fields

Mathematical models of heat transport in film apparatus with intensifiers for gas cooling and water heating

In connection with the increased requirements for the efficiency of processes in industrial apparatus of the fuel and energy complex, the design or modernization of scrubbers for cooling the flue and process gases is an urgent task. An effective tool for solving this problem is the mathematical modeling of transport phenomena in two-phase media. Empirical, semi-empirical and numerical models are used, each of which has its own advantages and disadvantages. When developing new designs of contact devices of apparatus, it is more expedient to use software programs, and in solving problems of designing or modernizing apparatus using known types of contact devices, it is better to use semi-empirical methods. This article shows the application of mathematical models of the flow structure of the cell model and of complete displacement, which are relatively easy to solve on a computer, and hydraulic resistance is the main empirical information about the applied contact devices. In this case, the timeline and costs of design works can be reduced.

A modified hypothesis of Reynolds stress tensor modeling for mixed turbulent convection in crystal growth

Within implicit large eddy simulation, we have provided unsteady 3D numerical study of turbulent melt convection during 100 mm diameter Si Cz growth, using refined time step and material properties. Comparison of calculated and measured time-averaged temperature profiles along the melt/crucible interface has demonstrated advantages of using updated material properties. Reference data on the spatial distributions of the turbulent stress tensor and heat fluxes in the melt have been obtained and used for validation of the conventional and modified hypothesis of Reynolds stress tensor modeling. Contrary to the conventional Boussinesq assumption of isotropic turbulent viscosity, our modified hypothesis has reproduced qualitative and quantitative details of reference Reynolds stress tensor distributions, including the boundary layer anisotropy due to the wall and free surface effects, mean velocity shear effect, and the buoyancy contribution to enhance vertical velocity fluctuations. Using our modified hypothesis and generalized Reynolds analogy for turbulent heat transport modeling, it become feasible to reproduce quantitatively the distributions of the turbulent heat flux, shear and buoyancy production terms of the kinetic energy transport equation, which is the necessary basis for further turbulence model development.

Climate and Seasonal Temperature Controls on Biogeochemical Transformations in Unconfined Coastal Aquifers

AbstractCoastal aquifers are host to a range of biogeochemical reactions that alter groundwater‐derived nutrient, metal, and other chemical loads to coastal ecosystems. Temperature is a strong control on microbially mediated reactions; thus, chemical reactivity in coastal aquifers may vary spatially and temporally with changes to groundwater temperature. In this study, we investigated the influence of global groundwater and sea surface temperature controls and seasonal temperature variability on biogeochemical processing in coastal aquifers using variable‐density groundwater flow, heat transport, and reactive transport models. The coupled models showed that nitrate removal efficiency in coastal aquifers increased from 5% to 88% as fresh groundwater temperature increased from 5°C to 35°C, while ocean temperature had a negligible effect on removal efficiency. Transient simulations based on monthly groundwater and ocean temperature measurements showed that denitrification and ammonification hotspots migrated seaward seasonally within warm fresh groundwater masses. The reaction hotspots were separated by colder groundwater emplaced during winter months. The reaction hotspots and nitrate plumes oscillated vertically along horizontal flow paths due to buoyancy effects between warm and cold groundwater. Comparison between transient and temperature‐equivalent steady‐state models suggests that steady‐state models adequately capture mean annual NO3− removal, but neglect local reactive transience and changes to plume geometry. The sensitivity analysis provides a first‐order estimate of the reactive potential of coastal aquifers considering globally diverse thermal regimes. The findings have implications for regional‐scale estimates of groundwater nutrient fluxes and for predicting coastal aquifer reactivity in a warming climate.

Numerical Modelling of Heat Transport in Freezing Mortars with an External Liquid Reservoir

Abstract Several studies indicate that the temperature distribution in concrete may affect the extent of frost scaling. This study presents a numerical model that describes the thermal response of freezing mortars in the presence of an external liquid reservoir, where the external liquid is either pure water or 3% sodium chloride solution. The phase transformation of supercooled external liquid is modelled in two stages: quick freezing, when the supercooled liquid starts to form crystals and slow freezing. The model is developed in two parts. In part I, the focus is the modelling of external liquid, and therefore a non-porous body with an external liquid reservoir is modelled and validated. In part II, the model developed in part I is developed further for a porous body containing different phases, i.e., unfrozen liquid and ice, in the pores. A comparison of simulated and experimentally measured temperature distributions shows a good agreement.

Salinity and temperature profiling for the submarine groundwater discharge simulations: Quantification through heat and solute transport model

Developed coastal regions are the hotspots for contaminated groundwater discharge, affecting sensitive marine ecosystems. The present study aims to identify submarine groundwater discharge (SGD) locations and quantify the contaminant load reaching to the western coast of India (Gujarat coast) using stable isotopes, seepage meter, heat and solute transport model. The coastal aquifers are highly enriched in trace metals due to various active natural processes and anthropogenic activities across the coast. Terrestrial and recirculated SGD was a significant contributor to flow and metal load, which ranged from 1.04 to 181.1 m3.year−1 and 0–77.41 kg.year-1, respectively. The highest estimated SGD in the Gujarat coast was relatively less than the SGD reported in the Bay of Bengal and comparable to the South Chennai coast. The order of metal flux found in the study was Zn > Fe > Cr > Pb > Ni > Cu > Mn, whereas the highest flux of Zn (77.41 kg. year−1) was reported at Fansa beach, which was 7x Fe-flux and 45 x Cr-flux, respectively. Higher micronutrients (Fe and Zn) load in the southern coast leads to increased vulnerability of eutrophication, algal blooms and biotic ligand formation in aquatic species. This enrichment of micronutrients in the coastal ecosystem was evident by the growth of seaweeds on the seabed at SGD identified locations.

Assessment of the high-temperature aquifer thermal energy storage (HT-ATES) potential in naturally fractured geothermal reservoirs with a stochastic discrete fracture network model

High-temperature aquifer thermal energy storage (HT-ATES) is a cost-effective and suitable technology to store large amounts of energy. HT-ATES has been demonstrated to be an efficient and stable tool to buffer seasonal imbalances and significantly reduce greenhouse gas emissions. Fractured reservoirs are widespread in sedimentary basins worldwide. However, naturally fractured reservoirs have received little attention as potential formations for HT-ATES. The main concern regarding thermal energy storage in naturally fractured formations is the high fracture permeability, which may result in fast fluid flow and an increase in thermal losses. Therefore, quantification of the effects of fracture flow is essential to HT-ATES site verification.An HT-ATES system in a generic fractured reservoir is simulated with a 3D stochastically generated discrete fracture network (DFN) model combined with a fluid flow and heat transport model. The pressure and temperature evolutions at the well are analyzed, and the total extracted energy and thermal recovery efficiency are evaluated. The results confirm that the presence of the DFNs enhances thermal loss and thereby results in a lower thermal recovery efficiency compared with those of an unfractured reservoir. Such a decrease can reach 20%. However, simulations show that naturally fractured reservoirs might be potential candidates for HT-ATES due to a larger injectivity. A further discussion is conducted to characterize the relative importance of the hydrogeological properties of the fractures and fracture network structure on the thermal behavior of the HT-ATES system.This study provides preliminary insights into the impacts of complex natural DFN on the thermal performance of HT-ATES in fractured reservoirs.

The effect of thermal conductivity on the outgassing and local gas dynamics from cometary nuclei

Aims.The aim of this work is to investigate the parameters influencing the generation of the inner comae of a comet with a spherical nucleus and to model the gas activity distribution around its nuclei. Here, we investigate the influence of thermal conductivity combined with sub-surface H2O and CO2-ice sources on insolation-driven sublimation and the resulting gas flow field. In the process, we adopted some of the rotational and surface properties of the target of the Rosetta mission, comet 67P/Churyumov-Gerasimenko (67P/CG).Methods.We used a simplified model of heat transport through the surface layer to establish sublimation rates from a H2O- and CO2-ice sub-surface into a vacuum. We then applied the 3D Direct Simulation Monte Carlo method to model the coma as a sublimation-driven flow. The free parameters of the model were used to test the range of effects arising from thermal inertia and the depth of the source on the gas outflow.Results.Thermal inertia and the depth of the sublimation front can have a strong effect on the emission distribution of the flow at the surface. In models with a thermal inertia up to 80 TIU (thermal inertia units: J m−2K−1s−1∕2), the H2O distribution can be rotated about the rotation axis by about 20° relative to models with no thermal lag. For CO2, the maximum activity can be shifted towards the sunset terminator with activity going far into the nightside for cases with low thermal diffusivity. The presence of a small amount of CO2can reduce the presence of H2O by at least an order of magnitude on the nightside by blocking H2O flow. In addition, CO2can also decrease the speed of the mixed flow in the same region up to 200 m s−1, compared to cases with no CO2activity.Conclusions.Even low values of the thermal inertia can substantially modify the gas flow field. Including CO2leads to strong variations in the local CO2/H2O density ratio between the dayside and nightside. CO2can dominate the gas composition above the nightside and can also act to modify the H2O flow field close to the terminator.

Modeling of heat transport phenomena using the equations of mathematical physics

The study of physical phenomena that include conservative principles is part of the research field of the equations of mathematical physics. To deepen in methods to solve the equations of mathematical physics is a contribution in understanding the modeling of applications in different areas. This research studies the physical phenomenon of heat transport with convection from the viewpoint of modeling with differential equations. The advantage of working with equations is to apply the techniques of mathematical analysis and numerical methods to obtain the temperature function. In the research, the solution of the heat transport model is computed according to the analytical method of separable variables in order to represent the temperature function as a trigonometric series. With the help of a simple numerical method, it is possible to derive a scheme of calculation of the temperature function. By performing a case study, the methods are compared, and their fit is verified by simulation.

Groundwater heat transfer and thermal outflow plume modelling in the Alps

Thermal water discharge within the gravity-driven groundwater flow system in the Alps and other similar areas around the world may be hidden in Quaternary deposits which, in these regions, often cover the regional aquifer. When thermal water drains into Quaternary deposits, the mixing of the deep thermal component and the cold shallow groundwater forms a thermal plume that extends parallel to the main groundwater flow in shallow system. In the Bled case study in Slovenia, the thermal water discharges from carbonate rocks into Quaternary glaciofluvial sediments, and as the Toplice spring at a rate of 5 l/s at an average temperature of 21.5 °C. Knowing the spatial extent and intensity of thermal outflow is essential to decision making related to the development and protection of this renewable resource. By approximating the thermal water outflow from a discharge zone as a planar source, a planar advective heat transport model can be used to evaluate its geometry and quantify rates. An analytical procedure follows rough assumptions leading to conservative results. Moreover, a numerical model using the FEFLOW code was applied for comparison with the simulations of the analytical model. The heat transport model was based on measured hydraulic parameters (e.g. groundwater levels) and borehole temperatures as well as on-site and international literature (e.g. dispersivity, thermal conductivity). Nine scenarios were applied accounting for different dimensions of the heat source and compared to the results of numerical simulations. Each scenario was verified by calculating the relative error between the analytical models and the measured borehole temperatures. The results confirm that the main outflow of thermal water can be determined using planar geometry, and is 200–300 m wide. The height of the thermal outflow zone is approximately 25 m, corresponding to the expected thickness of the direct contact between the fractured dolomite and the shallower Quaternary aquifer. Using the proposed widths and depths, the hidden natural thermal outflow rates are estimated at 57–86 l/s.

Quasilinear turbulent particle and heat transport modelling with a neural-network-based approach founded on gyrokinetic calculations and experimental data

A novel quasilinear turbulent transport model DeKANIS has been constructed founded on the gyrokinetic analysis of JT-60U plasmas. DeKANIS predicts particle and heat fluxes fast with a neural network (NN) based approach and distinguishes diffusive and non-diffusive transport processes. The original model only considered particle transport, but its capability has been extended to cover multi-channel turbulent transport. To solve a set of particle and heat transport equations stably in integrated codes with DeKANIS, the NN model embedded in DeKANIS has been modified. DeKANIS originally determined turbulent saturation levels semi-empirically based on JT-60U experimental data, but now it can also estimate them using a theory-based saturation rule. The new saturation model is still partly connected to experimental data, but it offers the potential for applying DeKANIS independently of the device.

Simulation of Heat and Water Transport on Different Tree Canopies: A Finite Element Approach

Heat and water transport modeling is a widely explored topic in micro-meteorology, agriculture, and forestry. One of the most popular models is the Simultaneous Heat and Water (SHAW) model, which includes partial differential equations (PDEs) for air-soil temperature and humidity, but with a priori discretized PDE for the foliage temperature in each canopy layer; it is solved using the finite difference method and the canopy shape is defined as a simple rule of proportionality of total quantities such as the total leaf area index. This work proposes a novel canopy shape characterization based on Weibull distribution, providing a continuous vertical shape function capable of fitting any tree species. This allows formulating a fully continuous SHAW-derived model, which is numerically solved by a finite element approach of P1 Lagrange type. For this novel approach, several numerical experiments were carried out to understand how the shape of well distinguishable canopies influences heat and water transport.

On the modelling of heat and fluid transport in fibrous porous media: Analytical fractal models for permeability and thermal conductivity

Building upon fractal theory and relying exclusively on analytical models, we develop models for predicting the permeability and effective thermal conductivity of two-directional (2-D) fibrous porous materials. In contrast to previous permeability and conductivity models, two hypothetical parameters (β and ζ) with physical meaning are introduced to consider the contact thermal resistance at the fiber interfaces, and analytical models for both in-plane and out-of-plane directions are developed. Relevant geometrical and physical parameters, including porosity, average tortuosity, and thermal resistance, are obtained by modeling the representative structure (RS) of the fibrous porous material. Good agreement with existing experimental data for fibrous materials over a wide range of porosity (from 0.50 to 0.99) validates the developed models, for both the permeability and effective thermal conductivity. It is demonstrated that, compared with previous models based on simplified geometries relying on periodic distribution assumptions, the current fractal model can better characterize the randomness of pore size and distribution commonly found in commercial fibrous materials.

Modeling heat transport processes in enhanced geothermal systems: A validation study from EGS Collab Experiment 1

Heat recovery from an enhanced geothermal system (EGS) is a complex process involving heat transport in both fracture networks and rock formations. A comprehensive understanding of and the ability to model the underlying heat transport mechanisms is important for the success of EGS commercialization but remains challenging in practice due to the generally insufficient characterization of EGS reservoirs. In the present study, we analyze an extensively monitored intermediate-scale EGS field experiment performed in a well-characterized testbed. The high-resolution, high-quality measurements from the field experiment enable the development of a high-fidelity model incorporating a well-constrained fracture network. Based on the field experiment, we investigate the complex heat transport processes in an EGS-relevant environment and validate the capability of a numerical approach in simulating these inherently coupled heat transport processes. A series of numerical simulations were performed to study the effects of different heat transport mechanisms, including thermal convection with fracture flow, thermal conduction in rock formations, and the Joule-Thomson effect. The agreement of thermal responses between field measurements and simulation results indicates that our numerical approach can appropriately model the heat transport processes pertaining to heat recovery from EGS reservoirs.

Heat transport by flow through rough rock fractures: a numerical investigation

Fracture surface topography exhibits long-range spatial correlations resulting in a heterogeneous aperture field. This leads to the formation, within fracture planes, of preferential flow channels controlling flow and transport processes. By means of a 3-D heat transport model coupled with a 2-D fracture flow model based on the lubrification approximation (i.e., local cubic law), we investigate how the statistical parameters determining spatial aperture variations in individual fractures control the heat exchange at the fluid/rock interface and heat transport by flow. Ensemble statistics over fracture realizations provide insights into the main hydraulic and geometrical parameters controlling the hydraulic and thermal behaviour of rough fractures. Similarly to the rough fracture’s hydraulic behaviour, we find that its heat transport behaviour deviates from the conventional parallel plate fracture model with increasing fracture closure and/or decreasing correlation length. We demonstrate that the advancement of the thermal front is typically slower in rough fractures compared to smooth fractures having the same mechanical aperture. In contrast with previous studies that neglect temporal and spatial temperature variations in the rock matrix, we find that the thermal behavior of a rough-walled fracture can, under field-relevant conditions, be predicted from a parallel plate model with an aperture equal to the rough fracture’s effective hydraulic aperture. This greatly simplifies the prediction of possible reservoir thermal behavior when using field measurable quantities and hydrological modeling.

Framing a novel approach for pseudo continuous modeling using Direct Numerical Simulations (DNS): Fluid dynamics in a packed bed reactor

This research frames a novel approach to develop a pseudo-continuous model for describing the dynamics of a Newtonian fluid in an industrial-scale packed-bed reactor presenting a low tube to particle diameter ratio (dt/dp = 3.048) at particle Reynolds numbers ranging from 750 to 1750. The model accounts for the effect of compressional work on the pressure drop and the velocity field. The development of the pseudo-continuous model uses pseudo-steady-state local information obtained from Direct Numerical Simulations (DNS) to determine the so-called fluid dynamic descriptors. The suitability of the geometry configuration, determined from rigid body dynamic calculations, and particle-resolved simulations (PRS) is assessed by describing pressure drop observations and analyzing void fraction and velocity predictions. Local information related to the apparent permeability allows the development of a modified correlation to quantify solid–fluid frictional mechanisms. The pseudo-continuous model, developed by quantifying solid–fluid interactions with the use of either local information or the modified correlation, is able to describe properly velocity profiles obtained out of PRS. Velocity profiles predicted by the pseudo-continuous model are in agreement with those simulated by the Navier–Stokes-Darcy-Forchheimer equations. The density field and the divergence of the velocity field elucidate how fluid dynamics, along with the pressure drop, is affected by the fluid compressibility. The approach described here can be extended to complex pellet shapes, including the development of pseudo-continuous models for heat and mass transport, paving the way for the design of more efficient industrial-scale packed-bed reactors.

Disentangling phonon channels in nanoscale heat transport

Phonon surface scattering has been at the core of heat transport engineering in nanoscale structures and devices. Herein, we demonstrate that this phonon pathway can be the sole mechanism only below a characteristic, size-dependent temperature. Above this temperature, the lattice phonon scattering co-exist along with surface effects. By artificially controlling mass disorder and lattice dynamics at the atomic-level in nanowires without affecting morphology, crystallinity, chemical composition, and electronic properties, the temperature-thermal conductivity-diameter triple parameter space is mapped, and the main phonon scattering mechanisms are disentangled. This led to the identification of the critical temperature at which the effect of lattice mass-disorder on thermal conductivity is suppressed to an extent that phonon transport becomes governed entirely by the surface. This behavior is discussed based on Landauer-Dutta-Lundstrom near-equilibrium transport model. The established framework provides the necessary input to further advance the design and modelling of phonon and heat transport in semiconductor nanoscale systems.

A 2D Model for Heat Transport in a Hele–Shaw Geometry

A 2D Model for Heat Transport in a Hele–Shaw Geometry

Transport of Heat by Hydrothermal Circulation in a Young Rift Setting: Observations From the Auka and JaichMaa Ja'ag' Vent Field in the Pescadero Basin, Southern Gulf of California

AbstractHeat flow measurements collected throughout the Auka and JaichMaa Ja'ag' hydrothermal vent fields in the central graben of the Southern Pescadero Basin, southern Gulf of California, indicate upflow of hydrothermal fluids associated with rifting dissipate heat in excess of 10 W/m2 around faults that have a few kilometers in length. Paradoxically, longer faults do not show signs of venting. Heat flow anomalies slowly decay to background values of ∼2 W/m2 at distances of ∼1 km from these faults following an inverse square‐root distance law. We develop a near‐fault model of heat transport in steady state for the Auka vent field based on the fundamental Green's function solution of the heat equation. The model includes the effects of circulation in fracture networks, and the lateral seepage of geothermal brines to surrounding hemipelagic sediments. We use an optimal fitting method to estimate the reservoir depth, permeability, and circulation rate. Independently derived constraints for the model, indicate the heat source is at a depth of ∼5.7 km; from the model, permeability and flow rates in the fracture system are ∼10−14 m2 and 10−6 m/s, respectively, and ∼10−16 m2 and 10−8 m/s in the basin aquitards, respectively. Model results point to the importance of fault scaling laws in controlling sediment‐hosted vent fields and slow circulation throughout low permeability sediments in controlling the brine's chemistry. Although the fault model seems appropriate and straightforward for the Pescadero vents, it does seem to be the exception to the other known sediment‐hosted vent fields in the Pacific.

Lattice Boltzmann scheme for hydrodynamic equation of phonon transport

In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann equation with the resistive scattering term as an equivalent source term, we recover a phonon hydrodynamic equation which is reduced to the Guyer-Krumhansl heat transport equation and the Fourier's law in the limit of dominant normal scattering and dominant resistive scattering respectively. The transition of heat transport from diffusive regime to hydrodynamic regime is modeled extensively by the present numerical scheme, which produces results in good agreement with the benchmark solutions and experimental measurement. Two well-known phonon hydrodynamic phenomena including the phonon Poiseuille flow and second sound propagation are well captured by the lattice Boltzmann scheme. This work will promote the numerical modeling and deeper understanding of the non-Fourier heat transport induced by phonon normal scattering.