Heat Transport Model Research Articles

Decarbonization of existing heating networks through optimal producer retrofit and low-temperature operation

District heating networks are considered crucial for enabling emission-free heat supply, yet many existing networks still rely heavily on fossil fuels. With network pipes often lasting over 30 years, retrofitting heat producers in existing networks offers significant potential for decarbonization. This paper presents an automated design approach, to decarbonize existing heating networks through optimal producer retrofit and ultimately enabling 4th generation operation. Using multi-objective, mathematical optimization, it balances CO2 emissions and costs by assessing different CO2 prices. The optimization selects producer types, capacities, and for each period their heat supply and supply temperature. The considered heat producers are a natural gas boiler, an air-source heat pump, a solar thermal collector, and an electric boiler. A non-linear heat transport model ensures accurate accounting of heat and momentum losses throughout the network, and operational feasibility. The multi-period formulation incorporates temporal changes in heat demand and environmental conditions throughout the year. By formulating a continuous problem and using adjoint-based optimization, the automated approach remains scalable towards large scale applications. The design approach was assessed on a medium-sized 3rd generation district heating network case and was able to optimally retrofit the heat producers. The retrofit study highlights a strong influence of the CO2 price on the optimal heat producer design and operation. Increasing CO2 prices shift the design towards a heat supply dominated by an energy-efficient and low-emission heat pump. Furthermore, it was observed that even for the highest explored CO2 price of 0.3€kg−1, the low-emission heat pump, electric boiler and solar thermal collector cannot fully replace the natural gas boiler in an economic way.

Using Rainfall‐Induced Groundwater Temperature Response to Estimate Lateral Flow Velocity

AbstractThis study introduces a novel heat tracing method for estimating lateral groundwater flow velocity induced and sustained by heavy rainfall events in lowland areas, leveraging the distinct temperature difference between rainfall and groundwater. The method is motivated by the observation that the rainfall‐induced groundwater temperature signal dissipates along the flow path. To explain the observed temperature anomaly and then estimate the lateral flow velocity, we develop a semi‐analytical model for heat transport in the aquifer, accounting for conduction losses to adjacent layers. Our findings reveal that interactions between the aquifer, vadose zone, and bedrock significantly influence the temperature signal, thereby affecting velocity estimation. Inaccuracies in measured aquifer properties, such as thickness, porosity, and thermal conductivity of surrounding layers, increase the uncertainty of velocity estimates. However, variations in aquifer thermal conductivity have a minimal effect on the method's overall accuracy. When estimating multiple parameters, velocity estimates tend to be less reliable, especially if aquifer porosity remains uncertain. This is due to the challenges of simultaneously inverting both velocity and porosity. Overall, this work underscores the potential of using heat as a tracer for assessing lateral groundwater flow following rainfall, offering a practical, low‐cost solution applicable in a wide range of settings.

Solar convective velocities: Updated helioseismic constraints

Modeling heat transport by convection is one of the most challenging aspects of solar and stellar physics. The literature currently provides apparently inconsistent observational estimates of the strength of large-scale convective flows in the upper layers of the solar convection zone. In addition, the large-scale convective flows predicted from numerical simulations are substantially stronger than some of the observational inferences in the literature. The current work aims to provide a consistent presentation of some of the main results in the literature both from observations and simulations. To achieve this aim, we carry out an analysis of published estimates of the strength of solar convection at different spatial scales. In particular, we employ a consistent set of conventions to compute the kinetic energy density in the east-west flows. This establishes a clear baseline for future work. The main conclusion is that there are inconsistencies between different observational results and also differences between observations and simulations. This conclusion is important as it demonstrates a need to determine the sources of the inconsistencies between different observational inferences and also to determine the missing ingredients in simulations of solar subsurface convection.

A conceptual and numerical model of fluid flow and heat transport in the Topusko hydrothermal system

Comprehensive understanding of hydrothermal systems is often obtained through the integration of conceptual and numerical modelling. This integrated approach provides a structured framework for the reconstruction and quantification of fluid dynamics in the reservoir, thereby facilitating informed decision-making for sustainable utilisation and environmental protection of the hydrothermal system. In this study, an updated conceptual model of the Topusko hydrothermal system (THS; central Croatia) is proposed based on structural, geochemical, and hydrogeological analyses. The stratigraphic sequence and the structural framework of the THS were defined based on geological maps and field investigations. As depicted by hydrochemical and isotope analyses, thermal waters in Topusko (temperatures of up to 65 °C) are of meteoric origin and circulate in a carbonate aquifer. The THS receives diffuse recharge approximately 13 km S from Topusko, where Triassic carbonates crop out. Gravity-driven regional groundwater circulation is favoured by regional thrusts that tectonically uplifted Palaeozoic low permeable rocks. These structures confine the fluid flow in the permeable, fractured and karstified, Triassic carbonates favouring the northward circulation of the water. A regional anticline lifts the aquifer closer to the surface in Topusko. Open fractures in the anticline hinge zone increase the fracturing and permeability field of the aquifer promoting the quick upwelling of the thermal water resulting in the Topusko thermal springs. Numerical simulations of fluid flow and heat transport corroborate the proposed conceptual model. In particular, a thermal anomaly was modelled in the Topusko subsurface with temperature values of 31.3 °C and 59.5 °C at the surface and at the base of the thermal aquifer, respectively, approaching the field observations. These findings showed that the circulation of Topusko thermal water is influenced by regional and local geological structures suggesting that the enhanced permeability field in the discharge area enables the formation of the natural thermal springs.

Transported Entropy of Ions and Peltier Coefficients in 8YSZ and 10Sc1CeSZ Electrolytes for Solid Oxide Cells.

In this study, the transported entropy of ions for 8YSZ and 10Sc1CeSZ electrolytes was experimentally determined to enable precise modeling of heat transport in solid oxide cells (SOCs). The Peltier coefficient, crucial for thermal management, was directly calculated, highlighting reversible heat transport effects in the cell. While data for 8YSZ are available in the literature, providing a basis for comparison, the results for 10Sc1CeSZ show slightly smaller Seebeck coefficients but higher transported ion entropies. Specifically, at 700°C and an oxygen partial pressure of pO2=0.21 bar, values of SO2-*=52±10 J/K·F for 10Sc1CeSZ and SO2-*=48±9 J/K·F for 8YSZ were obtained. The transported entropy was also validated through theoretical calculations and showed minimal deviations when comparing different cell operation modes (O2||O2-||O2 and H2, H2O||O2-||O2). The influence of the transported entropy of the ions on the total heat generation and the partial heat generation at the electrodes is shown. The temperature has the greatest influence on heat generation, whereby the ion entropy also plays a role. Finally, the Peltier coefficients of 8YSZ for all homogeneous phases agree with the literature values.

Random Walk Modeling of Conductive Heat Transport in Discontinuous Media

We consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion appears to be unaffected by the value of Δt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta t$$\\end{document}. The GUM algorithm presents an optimal trade-off between accuracy and computational time.

Longitudinal dispersivity estimation according to heat and mass groundwater transport model calibration for Baikalsk paper and mill site

The paper presents the results of the numerical three-dimensional model of groundwater heat and mass transfer in the territory of Baikalsk paper and mill site calibration based on the materials of groundwater composition and properties twenty-year monitoring, which showed that the longitudinal dispersion at heat transfer is an order of magnitude greater than at mass transfer.

Coupled field modelling of thermomechanical response in materials using peridynamic heat transport model and non-ordinary state-based peridynamics

Predicting the mechanical response of materials subjected to transient heat processes is crucial in various engineering applications. This paper introduces a novel peridynamic (PD) coupled field model formulated within the framework of Non-Ordinary State-Based Peridynamics (NOSBPD). This model offers the capability to simulate the coupled thermo-mechanical behavior of materials by incorporating both thermal transport and mechanical deformation analyses. To verify the model’s accuracy, a benchmark problem involving a steel plate undergoing transient thermal expansion is investigated. This model presents a valuable tool for various engineering applications involving coupled thermo-mechanical processes.

High-resolution numerical modelling of seasonal volume, freshwater, and heat transport along the Indian coast

Abstract. Seasonal reversal of winds and equatorial remote forcing influences the circulation of the Arabian Sea (AS) and Bay of Bengal (BoB) basins in the northern Indian Ocean. In this study, we numerically modelled the physical characteristics of the AS and BoB, using the Massachusetts Institute of Technology general circulation model (MITgcm) at a high spatial resolution of 1/20° forced with climatological initial and boundary conditions. The simulated temperature, salinity, and flow fields were validated with satellite and in situ datasets. We then studied the exchange of coastal waters by evaluating transports computed from the model simulations. The alongshore volume transport on the eastern coast is stronger with high seasonal variability due to the poleward-flowing western boundary current and equatorward-flowing East Indian Coastal Current. West coast transport is influenced by large intraseasonal oscillations. The alongshore freshwater transport is an order less than the alongshore volume transport. Out of the net volume transport, freshwater accounts for a maximum of 6.03 % during the southwestern monsoon season, followed by 4.85 % in the post-monsoon season. We observe an inverse relationship between alongshore freshwater and volume transport on the western coast and a direct relationship on the eastern coast. The contribution of eddy-induced heat and freshwater transport was also examined. The relation between net heat transport and net heat flux illustrates the role of coastal currents and equatorial forcing in dissipating heat within the coastal waters. We observed that meridional heat transport over the AS is stronger than over the BoB. Both basins act as a heat source during the summer monsoon and heat sink during the winter. This high-resolution model setup simulates all the important physical climatological patterns, leading to a better understanding of the state of the northern Indian Ocean.

Multiscale modeling of heat and mass transfer in dry snow: influence of the condensation coefficient and comparison with experiments

Abstract. Temperature gradient metamorphism in dry snow is driven by heat and water vapor transfer through snow, which includes conduction/diffusion processes in both air and ice phases, as well as sublimation and deposition at the ice–air interface. The latter processes are driven by the condensation coefficient α, a poorly constrained parameter in the literature. In the present paper, we use an upscaling method to derive heat and mass transfer models at the snow layer scale for values of α in the range 10−10 to 1. A transition α value arises, of the order of 10−4, for typical snow microstructures (characteristic length ∼ 0.5 mm), such that the vapor transport is limited by sublimation–deposition below that value and by diffusion above it. Accordingly, different macroscopic models with specific domains of validity with respect to α values are derived. A comprehensive evaluation of the models is presented by comparison with three experimental datasets, as well as with pore-scale simulations using a simplified microstructure. The models reproduce the two main features of the experiments: the non-linear temperature profiles, with enhanced values in the center of the snow layer, and the mass transfer, with an abrupt basal mass loss. However, both features are underestimated overall by the models when compared to the experimental data. We investigate possible causes of these discrepancies and suggest potential improvements for the modeling of heat and mass transport in dry snow.

Theory and Measurement of Heat Transport in Solids: How Rigidity and Spectral Properties Govern Behavior.

Models of heat transport in solids, being based on idealized elastic collisions of gas molecules, are flawed because heat and mass diffuse independently in solids but together in gas. To better understand heat transfer, an analytical, theoretical approach is combined with data from laser flash analysis, which is the most accurate method available. Dimensional analysis of Fourier's heat equation shows that thermal diffusivity (D) depends on length-scale, which has been confirmed experimentally for metallic, semiconducting, and electrically insulating solids. A radiative diffusion model reproduces measured thermal conductivity (K = DρcP = D × density × specific heat) for thick solids from ~0 to >1200 K using idealized spectra represented by 2-4 parameters. Heat diffusion at laboratory temperatures (conduction) proceeds by absorption and re-emission of infrared light, which explains why heat flows into, through, and out of a material. Because heat added to matter performs work, thermal expansivity is proportional to ρcP/Young's modulus (i.e., rigidity or strength), which is confirmed experimentally over wide temperature ranges. Greater uptake of applied heat (e.g., cP generally increasing with T or at certain phase transitions) reduces the amount of heat that can flow through the solid, but because K = DρcP, the rate (D) must decrease to compensate. Laser flash analysis data confirm this proposal. Transport properties thus depend on heat uptake, which is controlled by the interaction of light with the material under the conditions of interest. This new finding supports a radiative diffusion mechanism for heat transport and explains behavior from ~0 K to above melting.

Development of novel osteochondral scaffolds and related in vitro environment with the aid of chemical engineering principles

In tissue engineering, collaboration among experts from different fields is needed to design appropriate cell scaffolds and the required three-dimensional environment. Osteochondral tissue engineering is particularly challenging due to the need to provide scaffolds that imitate structural and compositional differences between two neighboring tissues, articular cartilage and bone, and the required complex biophysical environments for cultivating such scaffolds. This work focuses on two key objectives: first, to develop bilayered osteochondral scaffolds based on gellan gum and bioactive glass and, second, to create a biomimetic environment for scaffold characterization by designing and utilizing novel dual-medium cultivation bioreactor chambers. Basic chemical engineering principles were utilized to help achieve both aims. First, a simple heat transport model based on one-dimensional conduction was applied as a guideline for bilayer scaffold preparation, leading to the formation of a gelatinous upper part and a macroporous lower part with a thin, well-integrated interfacial zone. Second, a novel cultivation chamber was developed to be used in a dynamic compression bioreactor to provide possibilities for flow of two different media, such as chondrogenic and osteogenic. These chambers were utilized for characterization of the novel scaffolds with regard to bioactivity and stability under dynamic compression and fluid perfusion over 14 d, while flow distribution under different conditions was analyzed by a tracer method and residence time distribution analysis.

Impact of ocean heat transport on sea ice captured by a simple energy balance model

Future projections of Arctic and Antarctic sea ice suffer from uncertainties largely associated with inter-model spread. Ocean heat transport has been hypothesised as a source of this uncertainty, based on correlations with sea ice extent across climate models. However, a physical explanation of what sets the sea ice sensitivity to ocean heat transport remains to be uncovered. Here, we derive a simple equation using an idealised energy-balance model that captures the emergent relationship between ocean heat transport and sea ice in climate models. Inter-model spread of Arctic sea ice loss depends strongly on the spread in ocean heat transport, with a sensitivity set by compensation of atmospheric heat transport and radiative feedbacks. Southern Ocean heat transport exhibits a comparatively weak relationship with Antarctic sea ice and plays a passive role secondary to atmospheric heat transport. Our results suggest that addressing ocean model biases will substantially reduce uncertainty in projections of Arctic sea ice.

Fracture modes and grain growth of tungsten during extreme cyclic heating

To investigate the fracture mechanisms resulting from the thermomechanical loading in fusion reactors, cyclic heating experiments were carried out on tungsten discs (W). These experiments involved subjecting the samples to an arc-jet plasma gun, which can deliver a heat flux exceeding 20 MW m−2. The W discs had varying thicknesses and pulse durations. To gain a better understanding of the thermal environment, finite element (FE) simulations were performed to model heat transport through exposed specimens and the cooling assembly, and these were compared with experimental measurements. The temperature at the edge of the sample was found to reach a maximum of 1500 °C, and the temperature at the center of the upper surface of the disc fluctuated between a maximum of over 2800 °C and a minimum of 500 °C, depending on the thickness of the disc and the thermal contact between the sample and the cooling structures. Cracks were found to propagate through different modal regimes, starting with ductile growth, followed by a combination of ductile/intergranular growth, intergranular growth, and finally brittle transgranular fracture (cleavage fracture). Steep temperature gradients (∼1.6 × 106 °C/m) were found to induce grain growth, with a grain boundary mobility of 7.5 eV under moderate thermal stresses. Alternatively, crack formation and growth can occur due to residual stresses. Cumulative residual stress has been shown to correlate with the duration of exposure to elevated temperatures, leading to increased hardening, although with noticeable grain growth. Consequently, the strength of the sample is primarily driven by thermal stress rather than grain growth.

Two-phase numerical simulation of thermal and solutal transport of zero mass flux conditions over a porous deformable disc: The extension of Jeffrey-Hamel model

In recent times, numerous assertions on the thermophysical properties of nanoliquids in various flow regimes, particularly the laminar flow regimes have been documented in the literature. With this focus, this theoretical investigation is to explore multiple solutions of the laminar two-dimensional Jeffrey fluid describing the Buongiorno nanofluid model and features of heat transport near a stagnation point across a movable radial disc. Also, the study seeks to explore the effects of zero mass flux and velocity of mass transpiration embedded within a Jeffrey fluid. With the help of the ansatz similarity transformations, the study simplifies complex partial differential equations into a set of ordinary differential equations, facilitating numerical dual solutions employing the bvp4c solver. The multiple solutions become apparent in a specific range of the shrinkable parameter. The results of the present study show that the suction parameter intensifies the phenomena of friction factor in the upper solution, whereas an annulment trend is observed in the lower solution. In addition, the shear stress and heat transfer rate decline with higher impacts of the Deborah number for the first solution while a monotonical behaviour is seen for the second solution. Besides, the absolute critical value decreases owing to the change value of the Deborah number, as a result, the separation of the boundary layer accelerates. Moreover, the heat transfer rate declined by about 0.29%, 0.37%, and 0.28% for the FBS and 0.30%, 0.32%, and 0.28% for the SBS with larger values of Nta, Nba and Sca, respectively. Lastly, the outcomes of the present examination with existing data are an excellent match for the limiting cases.

Modeling of heat and solute transport in a fracture-matrix mine thermal energy storage system and energy storage performance evaluation

Repurposing groundwater-filled mine cavities for thermal energy storage has demonstrated promising potential to buffer the imbalance of energy supply and demand. Fractured formations are widespread in old mines due to previous excavation activities, which dominates the performance and efficiency of the mine thermal energy storage (MTES) system. Therefore, understanding the mechanisms of fluid flow, heat, and solute transport in fractured reservoirs in the MTES system is essential for its application and the assessment of environmental impact. In this study, fluid flow, heat, and solute transport in a 3D fracture-matrix MTES system are modeled simultaneously based on site-specific data in Freiberg, Germany. The simulations are conducted with a coupled Hydro-Thermo-Component process newly developed in the open-source software OpenGeoSys (OGS). To stabilize the simulation in the fracture-matrix hybrid system, a flux-corrected transport scheme is specifically implemented and applied in the model. Thus, heat and mass exchange between the embedded fractures and the matrix in the formation of MTES can be accurately simulated on the basis of the conforming mesh. In a hypothetical short-term scenario of a 15-day heating and cooling cycle of the MTES operation, the solute is transported faster than the heat in the fractured formation, indicating that disturbance of mineral compositions in the original mine water can affect a larger region than heat. The embedded fracture network in the surrounding formation is also found to increase the thermal energy storage capacity by 44%, while decreasing the recovery ratio by 14% compared to those of the unfractured formation. More energy will be transported and stored in the more fractured formation from heated mine water, but less energy can be recovered. The behavior of the MTES system strongly depends on local geology and hydraulic conditions and therefore needs to be evaluated in a site- and application-specific manner. This study provides preliminary insights into the performance and efficiency, as well as the environmental impact of the MTES operation in the short term.

Modeling of heat conduction through rate equations

AbstractStarting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following a variant of the Coleman-Noll procedure where the entropy production too is given by a non-negative constitutive equation. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive function for the heat flux that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to providing already known models (e.g., Maxwell-Cattaneo-Vernotte’s and Jeffreys-like heat conductors), this scheme allows the formulation of new models of heat transport that are likely to apply also in nanosystems. This is consistent with the fact that higher-order time derivatives of the heat flux are in order when high-rate regimes occur.

Exact solution of Maxwell–Cattaneo–Vernotte model: Diffusion versus second sound

In this work we study the Maxwell–Cattaneo–Vernotte model for heat transport by conduction. We present a methodology to find the exact solution of the model without decoupling the system, so we do not need the restriction (∂T/∂t)(x,0)=0. Furthermore, we found a critical value for the thermal relaxation time depending on the physical constants of the system, which allows us to classify heat transport as diffusion or second sound. Finally, we conducted computer simulations and demonstrated that the relaxation time may not be as small as expected for certain initial conditions.

Sea and brackish water desalination through a novel PVDF-PTFE composite hydrophobic membrane by vacuum membrane distillation

The present study aims to evaluate the performance of porous hydrophobic Polyvinylidene fluoride − Polytetrafluoroethylene (PVDF-PTFE) composite membranes for desalination by vacuum membrane distillation (VMD) technique. The effect of operating parameters such as feed NaCl concentration (10,000 to 40,000 mg/L), feed temperature (50 °C to 80 °C), and downstream pressure (80 to 120 mmHg) on water permeation rate was studied. The increase in feed temperature enhanced the water permeation rate due to a rise in driving force across the membrane. For a constant downstream pressure of 80 mmHg, feed temperature of 80 °C and feed flow rate of 80 L/h, the membrane exhibited a maximum water flux of 3 kg/m2h with 99.86% salt rejection when aqueous NaCl concentration of 10,000 mg/L was charged as feed. Membrane characterization was performed using various analytical tools to determine physico-chemical properties such as pore size, structural elucidation, thermal stability, crystallinity, and hydrophobicity of the membrane material. Further, a temperature and concentration polarization coefficient-based analysis was performed by solving the mass and heat transport model equations using MATLAB software. The proposed research study promotes the application of VMD for recovering potable water from highly saline sea/brackish water and alleviates brine disposal issues.

Simulation of Groundwater Quality in Xi 'an,Shaanxi Province Based on Visual Modflow

The so-called groundwater quality simulation is to study the spatial and temporal variation law of the concentration of a certain soluble substance (element or other component) when it is dispersed and transported by simulation method, to predict the instantaneous dynamics and expansion range of polluted groundwater, and to provide scientific basis for formulating reasonable and effective prevention measures. In recent years, the environmental hydrogeology survey results of some provinces, cities and regions in China show that the groundwater in most cities in China has been polluted to varying degrees. This situation directly affects industrial and agricultural production and people's health. However, in the past, environmental hydrogeology work was mostly limited to surface investigation, lacking quantitative and predictive evaluation research. Monitoring groundwater quality dynamics and forecasting the development trend of groundwater pollution is one of the main tasks of groundwater pollution investigation and research. Relevant information shows that some countries in the world have already carried out this research and established a predictive groundwater quality model. Among them, the United States has established 22 material transport models and 5 heat transport models; France has established 5 models of material transport and 4 models of heat transport. The following countries have only established material transport models: 7 in Israel; 2 in the UK; 2 in Canada; 1 in West Germany and 1 in Japan. Therefore, we believe that the study of groundwater quality simulation experiment, which is still blank in China's scientific field, has become an important subject that needs to be carried out urgently to ensure the four modernizations and people's health. The hydrogeological conditions and dynamic characteristics of groundwater resources have been comprehensively analyzed and studied. It points out that the continuous exploitation of groundwater resources in 2018 has led to the deterioration of groundwater quality, land degradation, underground, cracks and depletion of groundwater resources, and puts forward some preventive measures.