Thermal Dispersion Coefficient Research Articles

INVESTIGATION OF THERMAL DISPERSION FOR STEADY AND PULSATING WATER FLOW IN METAL FOAM

The dispersion coefficient in metal foam is critical for analysis and design using the volume-averaged equations. This coefficient is hardly investigated for steady flow, and has not been reported for non-steady flows in metal foam. This paper presents experimental and numerical investigations on the thermal dispersion coefficient in a metal-foam rectangular channel for steady and pulsating water flow. The foam channel was asymmetrically heated from one side representing a heat sink. The heating was accomplished by applying a constant heat flux. For the steady-state investigation, Reynolds number based on the hydraulic diameter of the channel ranged from 365 to 1164. For this range, the experimental thermal dispersion was obtained and given in the form of a correlation. For the pulsating flow investigation, the flow frequency ranged from 0.07 to 0.17 Hz with a maximum velocity amplitude of 0.07 m/s. The thermal dispersion coefficient was obtained experimentally for the pulsating flow in metal foam, most likely for the first time. Results have shown that the velocity amplitude has a significant effect on the thermal dispersion coefficient, whereas the frequency has a limited effect. The dispersion coefficient for pulsating flow was significantly higher than that for steady-state flow, and the difference between the two increased with Reynolds number. This increase in dispersion for pulsating flow is responsible in part for the increased heat transfer.

Effects of non-Darcy mixed convection over a horizontal cone with different convective boundary conditions incorporating gyrotactic microorganisms on dispersion

This paper investigates the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium. Multiple convective boundary conditions are applied to address the heat, mass and motile microorganism transfer phenomena. This paper incorporates the dispersion effect for gyrotactic microorganisms due to biological and environmental applications. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations & then solved using the MATLAB BVP4C function. The computation of grid independence test is analyzed for different flow profiles to show the precision of the points. In a few instances, our present numerical data is compared with previously published works, leading to excellent agreement. The non-Darcy effect, as well as mixed convection values from 0.1 to 0.9 and buoyancy parameters from 0.2 to 0.8, all significantly affects the velocity profile. The reduction in the microorganism profile is brought on by the increase in the bioconvection Lewis parameter and bio convection peclet number between 0.3 and 1. In the absence of dispersion, the variation of Biot numbers between 0.5 and 2, favor heat, mass, and motile microorganism transfer the most in the range of mixed convection parameter 0.5 to pure forced convection 1. Thermal, solutal and microorganism dispersion coefficients a, b, c that lie between frac{1}{7} and frac{1}{3} and higher values of modified peclet number ranges from 2 to 10 cause increased dispersion effects which lower flow transfer rates mostly in forced convection regime.

A Novel Slug Heat Test Theoretical and Indoor Model Research for Determining Thermal Property Parameters of Aquifers and Rock-Soil Skeletons

As important parameters for characterizing heat transfer, thermal property parameters of aquifers and rock-soil skeletons have important research significance in the development and utilization of geothermal resources. The slug heat test is inspired by the slug test, and the heat is instantaneously excited in the test well so as to change the temperature of test section in the test well instantaneously. Based on the thermal radial convection-dispersion theory and the principle of heat conservation, the theoretical model of the slug heat test is established, and the model is solved by Laplace transform and inverse transform to obtain multiple sets of standard curves under different conditions. The slug heat tests were conducted in the indoor model, the slug heat test data under different hydrodynamic conditions were fitted with the standard curves and the thermal property parameters, including effective thermal conductivity, stagnant thermal conductivity, thermal mechanical dispersion coefficient, thermal dispersive degree, thermal diffusivity, heat capacity of aquifer, heat capacity and thermal conductivity of rock-soil skeletons, were accurately obtained. The test results are in good agreement with the empirical values. Meanwhile, the effective thermal conductivity of the aquifer also clearly increases with the increase of flow rate. The excitation temperature difference had little effect on the effective thermal conductivity of the aquifer. At the same time, numerical simulation methods are used to establish a numerical model consistent with the indoor test model, and the numerical model is assigned with the thermal property parameters obtained from the indoor slug heat test, and the measured values of temperature changes in the test well during the slug heat test under different hydrodynamic and excitation strength conditions are compared with the simulated values for verification. The research results show that the slug heat test has the characteristics of high applicability, simple operation and rapid testing, and can effectively determine the thermal properties parameters of aquifers and rock-soil skeletons.

Experimental evidence for local thermal non-equilibrium during heat transport in sand representative of natural conditions

When modelling heat transport in hydrogeological systems, a standard assumption is local thermal equilibrium (LTE), which implies that the porous medium temperature at the interface between the solid and fluid instantaneously reaches equilibrium. Few studies have investigated the validity of the LTE assumption and its violation, also known as local thermal non-equilibrium (LTNE), as well as its impact on the accuracy of heat transport models. While the theoretical conditions under which LTNE occurs in natural groundwater flow have recently been revealed, these have not yet been experimentally verified. We examined the applicability of the LTE assumption by conducting systematic laboratory experiments using eight distinct flow velocities (Reynolds number, Re < 0.37) through sand (0.76 mm grain size), injecting both heat and solute as tracers and observing the response at multiple points downstream. Theoretical heat transport parameters were calculated from solute tracer experiments by applying a retardation factor, and the results were subsequently compared to the actual parameters estimated from heat tracing. Our experimental results confirm that the LTE assumption can be violated under natural groundwater flow conditions, and that LTNE impacts thermal dispersion coefficients more significantly than thermal front velocities. The largest differences between the predicted and estimated thermal transport parameters were 112% and 13% for the dispersion coefficients and velocities, respectively. Our results demonstrate that LTNE effects need to be considered in heat transport modelling especially when analyzing thermal dispersion coefficients.

A Fractal Model for Thermal Dispersion Coefficients of Porous Media

The thermal dispersion coefficient is an important parameter to characterize heat and mass transfer in porous media, which is related to the physical properties of fluid and the structure of porous media. The pore-throat structure model for fractal porous media was established, and the local head loss and the velocity dispersion effect were studied for the fluid changing from the turbulent state to the laminar state around the pore-throat structure. The thermal dispersion coefficient formula was derived under the influences of the micropore-throat structure and the velocity dispersion effect. The results show that, the thermal dispersion coefficient is directly proportional to the pore-throat ratio, the number of pore-throat structures and the tortuous fractal dimension, and is inversely proportional to the porosity and the area fractal dimension. Furthermore, in the range of 1~150, the pore-throat ratio has a significant influence on the velocity dispersion effect, and the fluid has a local head loss around the pore-throat structure, which leads to an enhancement of the velocity dispersion effect and an increase of the thermal dispersion coefficient.

Transient heat transfer processes in a single rock fracture at high flow rates

Understanding the process of heat transfer in fractures and the influence of fracture surface morphology is crucial for optimized heat mining. In this work, we investigated transient heat transfer behavior at high flow rates, ranging from 80 to 350 mm/s, at various inflow temperatures. A split sandstone core was installed in an experimental setup that allowed the fluid to be circulated, cooled and reheated. Water was circulated through the fracture and a temperature step was induced with the help of a heat exchanger upstream to the core. Thermocouples before and after the core enabled the measurement and evaluation of transient cooling and heating curves. The thermal breakthrough curves reveal the capacity of the rock to maintain maximum outflow temperature for a substantial amount of time. Thermal and mass dispersion coefficients are comparable but analytical solutions for heat transport can only be used with strong limitations. Heat transfer coefficients were determined using the stationary state. The evaluation of the surface roughness identifies its substantial influence on the heat transfer coefficient. Our experiments show that flow velocities beyond 200 mm/s lead to cold outflow temperatures, causing undesired cooling and prolonged heat transfer processes in the reservoir. These effects should not be underestimated in terms of the efficiency of geothermal energy generation.

Large-scale laboratory study on the evolution law of temperature fields in the context of underground coal gasification

This article presents the evolution law of temperature fields in a large-scale laboratory Underground Coal Gasification reactions using Ulanqab lignite under actual conditions. The results show that in the cultivation stage of oxidation zone, the main direction of the temperature field expansion is consistent with the crack direction of the coal seam. In the gasification stabilization stage, the main direction of the temperature field expansion is along the channel. The temperature of the coal seam and the overlying rock mass at its interface with the furnace directly above the gasification channel is equivalent to that of the coal seam temperature, and this temperature is much greater than the temperatures observed near both side walls of the gasification channel at the interface. However, temperatures perpendicular to the axis of the gasification channel are similar at a vertical distance of 40 cm away from the interface. The temperature distributions indicate that the transmission of heat through the overlying rock mass is more rapid in the vertical direction than in the horizontal direction. Moreover, some degree of thermal dispersion is observed in the vertical direction near the outlet. The thermal dispersion coefficient is 0.72 and dispersion angle γ is 78.7°.

Double dispersed bioconvective Casson nanofluid fluid flow over a nonlinear convective stretching sheet in suspension of gyrotactic microorganism

AbstractMicroorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.

Pore-scale modeling of coupled thermal and solutal dispersion in double diffusive-advective flows through porous media

In double diffusive-advective flows through porous media, the combined effects of fluid and solid properties, pore space geometry, and flow conditions on the transport rates and distribution of the thermal and solutal fronts can be characterized by dispersion coefficients. In this study, conjugate heat and solute transport in the process of miscible displacement through porous media is studied through pore-scale numerical simulations in 2D and 3D digital representations of the unconsolidated sandpacks. The temperature and solute concentration distributions during both viscously stable and unstable displacements are obtained by solving the point equations of flow and transport on the discretized computational domains. Next, the longitudinal components of the solute and thermal dispersion coefficients are determined by fitting the effluent profiles to the analytical solutions of the advection-diffusion equations for the transport of mass and heat, respectively. The length scales of the solutal and thermal transition zones are also measured along the principal direction of the flow and then correlated with the displacement time. In stable displacements, different dispersion regimes are identified based on the magnitude of the solutal and thermal Peclet numbers. It is observed that the onset of convective spreading is different in the 2D and 3D simulation runs. In unstable displacements, the results indicate that solutal dispersion is more affected by thermo-solutal viscous fingering compared to thermal dispersion. Moreover, as the viscosity contrast across the thermal and solutal fronts increases, the dynamics of the mixing length growth gradually changes from dispersion-dominated toward fingering-dominated. Finally, the results show that two-dimensional simulation runs may not completely characterize the dispersion-related phenomena that occurs during heat and solute transfer in a real porous medium. Therefore, it is essential to conduct three-dimensional runs to capture all the underlying mechanisms contributing to the mixing and dispersion in porous media. The outcomes of this study can pave the way for an optimal design and implementation of an efficient non-isothermal miscible displacement in porous media.

Study of the Effect of Thermal Dispersion on Internal Natural Convection in Porous Media Using Fourier Series

Natural convection in a porous enclosure in the presence of thermal dispersion is investigated. The Fourier–Galerkin (FG) spectral element method is adapted to solve the coupled equations of Darcy’s flow and heat transfer with a full velocity-dependent dispersion tensor, employing the stream function formulation. A sound implementation of the FG method is developed to obtain accurate solutions within affordable computational costs. In the spectral space, the stream function is expressed analytically in terms of temperature, and the spectral system is solved using temperature as the primary unknown. The FG method is compared to finite element solutions obtained using an in-house code (TRACES), OpenGeoSys and COMSOL Multiphysics®. These comparisons show the high accuracy of the FG solution which avoids numerical artifacts related to time and spatial discretization. Several examples having different dispersion coefficients and Rayleigh numbers are tested to analyze the solution behavior and to gain physical insight into the thermal dispersion processes. The effect of thermal dispersion coefficients on heat transfer and convective flow in a porous square cavity has not been investigated previously. Here, taking advantage of the developed FG solution, a detailed parameter sensitivity analysis is carried out to address this gap. In the presence of thermal dispersion, the Rayleigh number mainly affects the convective velocity and the heat flux to the domain. At high Rayleigh numbers, the temperature distribution is mainly controlled by the longitudinal dispersion coefficient. Longitudinal dispersion flux is important along the adiabatic walls while transverse dispersion dominates the heat flux toward the isothermal walls. Correlations between the average Nusselt number and dispersion coefficients are derived for three Rayleigh number regimes.

Determination of Heat Transfer Coefficient and Thermal Dispersion of a Representative Porous Structure Based on Pore Level Simulations

In the present work, pore level simulations were performed to calculate heat transfer coefficient and thermal dispersion coefficient of a consolidated porous structure. A three-dimensional cubic unit cell structure, made up of six cuboid struts was selected to represent the idealized porous structure. To analyze fluid flow and heat transfer through the porous structure, governing fluid flow and energy equations were solved using the finite-volume method. A parametric study was carried out to investigate the effects of Reynolds number, Prandtl number, and porosity on heat transfer coefficient of the considered structure. A separate parametric study explored the variation of stream-wise dispersion coefficient with Reynolds number, Prandtl number, thermal conductivity ratio of the solid and the fluid phase, and porosity. Finally, generalized correlations for both non-dimensional heat transfer coefficient and stream-wise dispersion coefficients were proposed. It is observed that the obtained heat transfer coefficient follows two distinct trend lines for both porosities considered in the present investigation. For the considered operating conditions, the stream-wise dispersion coefficient is found to be proportional to square of Peclet number.

Experimental comparison of thermal and solute dispersion under one‐dimensional water flow in saturated soils

Thermal dispersion, which is similar to solute dispersion, results mainly from microscopic differences in pore‐scale water velocities in porous media. In this study, heat and Cl− were used as tracers to perform a systematic and quantitative comparison of the characteristics of coupled heat and solute dispersion through three types of saturated packed media (a sand, silt loam and sandy clay loam soil). An inverse model was used to calculate the thermal dispersion coefficient (Dh) and solute dispersion coefficient (Ds) by fitting a heat and solute transport model to the measured temperature and solute breakthrough curves obtained using the thermo–time domain reflectometry (thermo–TDR) technique under the same experimental conditions. Results showed that Ds and Dh were both described by a power function of water flux. Most importantly, heat and solute dispersivities had the same dimensions of length , the magnitudes of which were maintained almost unchanged with water flux densities and depended considerably on soil texture. Fine‐textured soil had a greater dispersivity than did coarse‐textured soil, and solute dispersivity was 220% greater than heat dispersivity in sandy clay loam, about 92% greater in silt loam soil and 36% greater in sand. We suggest that the magnitude and dimension of heat dispersion were essentially comparable to those of solute dispersion, which provides a better understanding of the relation between heat and solute dispersion. It has also been shown to be advantageous in practice for using heat dispersion to quantify easily solute dispersion approximately (or vice versa).Highlights Thermal and solute dispersion coefficients were power functions of water fluxes. Heat and solute dispersivities had the same length and order of magnitude. Thermal dispersion was experimentally comparable to solute dispersion. Solute dispersion may be predicted quantitatively by heat dispersion values (or vice versa).

Pore-level modeling of effective longitudinal thermal dispersion in non-isothermal flows through granular porous media

In non-isothermal flows through porous media, the rate of heat transport across the domain and the distribution of temperature profile are strongly affected by the thermal properties of the fluid and solid phases, flow conditions, and the topological geometry of the pore structure. The combined effect of these parameters on the dynamics of heat transfer is generally characterized by the thermal dispersion coefficient. In this study, we model thermal dispersion in granular porous media using pore-scale numerical simulations. The flow and heat transport equation are solved in a porous domain at the pore-level to obtain the distribution of temperature inside the fluid phase and solid grains. The effluent temperature profile at the outlet is then fitted to the analytical solution of the macroscale heat advection-dispersion equation to determine the longitudinal component of the effective thermal dispersion tensor. Several simulation runs are carried out to investigate the effect of Peclet number, fluid to solid thermal conductivity and heat capacity ratios, and the temperature-dependent viscosity on the variation of the longitudinal thermal dispersion coefficient. The results indicate the existence of different thermal dispersion regimes separated by a threshold Peclet number. Below the threshold, thermal dispersion is dominated by conduction and longitudinal dispersion coefficient is equal to the effective thermal conductivity of the porous medium. Above the threshold, there is a transition region in which both conduction and advection are responsible for the heat ttansport. At higher Peclet numbers, dispersion regime is advection-dominated and normalized dispersion coefficient increases with the Peclet number and thermal conductivity ratio whereas it decreases with the heat capacity ratio. In this regime, the relationship between dispersion coefficient and Peclet number follows a power-law functionality with the exponent decreasing with the heat capacity ratio. To summarize the results, a characterization diagram is constructed for thermal dispersion regime based on the values of Peclet number and thermal conductivity ratio. Finally, the presence of viscous fingering due to the monotonically increasing viscosity along the flow is observed to further increase the longitudinal thermal dispersion. The outcomes of this study are of great importance in the design, implementation, and performance optimization of thermal processes in granular porous media.

Revealing the Behavior of Photons in a Birefringent Interferometer.

The interferometer is one of the most important devices for revealing the nature of light and for precision optical metrology. Although many experiments were performed for probing photon behavior in various configurations, a complete study of photon behavior in a birefringent interferometer has not been performed, to our knowledge. By using an environmental turbulence immune Mach-Zehnder interferometer, we observe tunable photonic beatings by rotating a birefringent crystal versus the temperature of the crystal for both the single photon and two photons. Furthermore, the two-photon interference fringes beat 2 times faster than the single-photon interference fringes. This beating effect is used to determine the thermal dispersion coefficients of the two principal refractive axes with a single measurement: the two-photon interference shows superresolution and high sensitivity. Obvious differences between two-photon and single-photon interference are also revealed in unbalanced situations. In addition, the influence of the photon bandwidth on the beating behaviors that come from polarization-dependent decoherence is also investigated. Our findings will be important for better understanding the behavior of two-photon interference in a birefringent interferometer and for precision optical metrology with quantum enhancement.

Experimental investigation of the thermal dispersion coefficient under forced groundwater flow for designing an optimal groundwater heat pump (GWHP) system

Mechanical thermal dispersion has often been neglected or underestimated in the simulation of heat transport in porous media, e.g., by using zero or the default value in simulators, or by using the scaling law for solute dispersivity as a thermal dispersivity value. However, large amounts of water usually injected in groundwater heat pump (GWHP) systems may increase the groundwater flow velocity much faster than natural flow and thus change the importance of mechanical dispersion in heat transport. In this study, to investigate the effects of water injection on the flow field, thermal dispersion coefficient, and associated heat transport process, a laboratory experiment using two different heat sources as tracers was performed at various background flow velocities (Re < 0.52). The analysis results from analytical and numerical models indicate that injected water increases both flow velocities and thermal dispersion coefficients, especially near the injection well, and thus makes the effect of mechanical dispersion on heat transport very important even at low background flow velocity. This result was also found in the field-based modeling results, but the radius of hydraulic and thermal effects was larger. In particular, thermal dispersivity on a field scale is known to increase depending on the scale of measurement and the degree of aquifer heterogeneity. Therefore, to ensure the efficiency and sustainability in field applications such as GWHP systems, it is necessary to evaluate site-specific thermal dispersivity through field experiments.

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In non-isothermal flows through porous media, the rate of heat transport across the domain and the distribution of temperature profile are strongly affected by the thermal properties of the fluid and solid phases, flow conditions, and the topological geometry of the pore structure. The combined effect of these parameters on the dynamics of heat transfer is generally characterized by the thermal dispersion coefficient. In this study, we model thermal dispersion in granular porous media using pore-scale numerical simulations. The flow and heat transport equation are solved in a porous domain at the pore-level to obtain the distribution of temperature inside the fluid phase and solid grains. The effluent temperature profile at the outlet is then fitted to the analytical solution of the macroscale heat advection-dispersion equation to determine the longitudinal component of the effective thermal dispersion tensor. Several simulation runs are carried out to investigate the effect of Peclet number, fluid to solid thermal conductivity and heat capacity ratios, and the temperature-dependent viscosity on the variation of the longitudinal thermal dispersion coefficient. The results indicate the existence of different thermal dispersion regimes separated by a threshold Peclet number. Below the threshold, thermal dispersion is dominated by conduction and longitudinal dispersion coefficient is equal to the effective thermal conductivity of the porous medium. Above the threshold, there is a transition region in which both conduction and advection are responsible for the heat ttansport. At higher Peclet numbers, dispersion regime is advection-dominated and normalized dispersion coefficient increases with the Peclet number and thermal conductivity ratio whereas it decreases with the heat capacity ratio. In this regime, the relationship between dispersion coefficient and Peclet number follows a power-law functionality with the exponent decreasing with the heat capacity ratio. To summarize the results, a characterization diagram is constructed for thermal dispersion regime based on the values of Peclet number and thermal conductivity ratio. Finally, the presence of viscous fingering due to the monotonically increasing viscosity along the flow is observed to further increase the longitudinal thermal dispersion. The outcomes of this study are of great importance in the design, implementation, and performance optimization of thermal processes in granular porous media.

The effect of particle size on thermal and solute dispersion in saturated porous media

Thermal dispersion, caused by fluid velocity and temperature fluctuations in the pore space and the effects of hydrodynamic mixing on the temperature field, controls convective heat transport in saturated porous media. While the thermal dispersion coefficient, a governing parameter in the thermal equilibrium model (TEM), has been investigated for natural systems, the dependence of the thermal dispersion coefficient on particle size remains undetermined. Previous research found that the relationship between the thermal dispersion coefficient and flow velocity follows a power law and that there may be a temperature difference between the solid and fluid phase (thermal non-equilibrium). However, experiments are limited to discrete particle sizes and comparison of the dispersion-velocity relationship is impeded by different experimental approaches. We conducted a series of separate heat and solute transport experiments in a column filled with uniform porous media consisting of different sized glass spheres for a range of flow velocities. The thermal and solute dispersion coefficients obtained from experimental measurements were correlated with flow velocities through the thermal or solute Péclet number. Our results demonstrate that, while solute dispersion is independent of particle size, the dependence of the TEM based thermal dispersion coefficient on flow rates is influenced by the particle size. This is caused by the fact that, unlike solute transport, heat exchanges between fluid and particles and that this induces thermal non-equilibrium between both phases. The results have significant implications for quantifying forced convective heat transport in natural porous media because thermal non-equilibrium between the phases is not considered. The porous media particle size must be considered when selecting appropriate values for the thermal dispersion coefficient.

Analyzing natural convection in porous enclosure with polynomial chaos expansions: Effect of thermal dispersion, anisotropic permeability and heterogeneity

In this paper, global sensitivity analysis (GSA) and uncertainty quantification (UQ) have been applied to the problem of natural convection (NC) in a porous square cavity. This problem is widely used to provide physical insights into the processes of fluid flow and heat transfer in porous media. It introduces however several parameters whose values are usually uncertain. We herein explore the effect of the imperfect knowledge of the system parameters and their variability on the model quantities of interest (QoIs) characterizing the NC mechanisms. To this end, we use GSA in conjunction with the polynomial chaos expansion (PCE) methodology. In particular, GSA is performed using Sobol’ sensitivity indices. Moreover, the probability distributions of the QoIs assessing the flow and heat transfer are obtained by performing UQ using PCE as a surrogate of the original computational model. The results demonstrate that the temperature distribution is mainly controlled by the longitudinal thermal dispersion coefficient. The variability of the average Nusselt number is controlled by the Rayleigh number and transverse dispersion coefficient. The velocity field is mainly sensitive to the Rayleigh number and permeability anisotropy ratio. The heterogeneity slightly affects the heat transfer in the cavity and has a major effect on the flow patterns. The methodology presented in this work allows performing in-depth analyses in order to provide relevant information for the interpretation of a NC problem in porous media at low computational costs.

Effect of pore to throat size ratio on thermal dispersion in porous media

In this study, the effects of pore to throat size ratio on thermal dispersion of periodic porous media consisting of inline array of rectangular rods are investigated, numerically. The continuity, momentum and energy equations are solved for representative elementary volumes (REVs) of the porous media to obtain microscopic velocities in the voids between the rods and temperature distribution for entire of the REVs. Volume averaging method is employed to compute the macroscopic velocity and temperature values. There are velocity and temperature deviations between the macroscopic and microscopic values. These deviations are computed numerically and thermal dispersion coefficients of the porous media are determined. The aim of this study is to analyze the effects of pore to throat size ratio on the longitudinal and transverse thermal dispersion in the porous media. The study is performed for pore to throat size ratios between 1.63 and 7.46, porosities from 0.7 to 0.9, and pore level Reynolds numbers between 1 and 100. It is found that in addition to the porosity and Reynolds number, the parameter of pore to throat size ratio plays an important role on thermal dispersion in a porous medium. It is found that there is an optimum value of pore to throat size ratio for maximum longitudinal thermal dispersion coefficient; however, the transverse thermal dispersion increases with the increasing of values of pore to throat size ratio.

多孔質体内熱流動のモデリングの進展

Recent advances in mathematical modeling of heat and fluid flow in porous media were discussed starting from an introduction of volume averaging theory and leading to various engineering applications. Mathematical interpretations of tortuosity, thermal dispersion and interstitial heat transfer are provided with their models based on solvable volume averaged quantities. A useful concept “effective porosity” was introduced to account for the tortuosity. Moreover, an inverse relationship between the interstitial heat transfer coefficient and thermal dispersion coefficient was explained, which enables us to estimate the thermal dispersion simply by measuring the interstitial heat transfer using a single blow method. Engineering applications based on the local space sharing concept will be discussed ranging from bioheat transfer to ion transport through a membrane.