Search Results (71)

Managing groundwater flow in crystalline basement aquifers (CBAs) remains challenging due to their dependence on secondary permeability fields characterized by high spatial variability. This study combines pumping and tracer tests to estimate the hydraulic properties and connectivity in four bedrock wells within a CBA in Southwestern Nigeria. The pumping tests caused drawdowns up to 4.13 m and 12.60 m in observation and pumping wells, with significant drawdowns only in three of four wells, revealing poor connection with the fourth well. The time-drawdown plots confirm double porosity effects suggesting fracture and matrix flow and release of water from a fractured dyke. Fracture and matrix hydraulic conductivities exceeded 7.9 × 10⁻⁷ m/s and 1.00 × 10⁻¹⁰ m/s, while the aquifer yield ranged from 0.08 to 0.34%. Groundwater flow velocity and dispersivity of 5.80 × 10⁻⁴ m/s and 2.60 m were estimated from the tracer test, while a Peclet number of 3.25 suggests dominant advective flow. Calculated sustainable yield shows that each well could provide water for up to 1600 people under controlled low pumping at 0.50 l/s with higher rates possible using larger diameter wells. These results confirm high variability in groundwater flow within CBAs, justifying the need to characterize them effectively. Full article

The Fokker–Planck (FP) equation represents the drift and diffusive processes in kinetic models. It can also be regarded as a model for the collision integral of the Boltzmann-type equation to represent thermo-hydrodynamic processes in fluids. The lattice Boltzmann method (LBM) is a drastically simplified discretization of the Boltzmann equation for simulating complex fluid motions and beyond. We construct new two FP-based LBMs, one for recovering the Navier–Stokes equations for fluid dynamics and the other for simulating the energy equation, where, in each case, the effect of collisions is represented as relaxations of different central moments to their respective attractors. Such attractors are obtained by matching the changes in various discrete central moments due to collision with the continuous central moments prescribed by the FP model. As such, the resulting central moment attractors depend on the lower-order moments and the diffusion tensor parameters, and significantly differ from those based on the Maxwell distribution. The diffusion tensor parameters for evolving higher moments in simulating fluid motions at relatively low viscosities are chosen based on a renormalization principle. Moreover, since the number of collision invariants of the FP-based LBMs for fluid motions and energy transport are different, the forms of the respective attractors are quite distinct. The use of such central moment formulations in modeling the collision step offers significant improvements in numerical stability, especially for simulations of thermal convective flows under a wide range of variations in the transport coefficients of the fluid. We develop new FP central moment LBMs for thermo-hydrodynamics in both two and three dimensions, and demonstrate the ability of our approach to simulate various cases involving thermal convective buoyancy-driven flows especially at high Rayleigh numbers with good quantitative accuracy. Moreover, we show significant improvements in the numerical stability of our FP central moment LBMs when compared to other existing central moment LBMs using the Maxwell distribution in achieving high Peclet numbers for mixed convection flows involving shear effects. Full article

To uncover the critical mechanisms responsible for mesoscopic level development during flow-mediated crystal growth, we develop a semi-two-way hydrodynamic coupled structural phase-field crystal formalism (HXPFC-s2). The new formalism, inspired by previous attempts at coupling hydrodynamic and phase-field crystal (PFC) equations, allows for studying mesoscopic flow-mediated crystallization at diffusive timescales pertinent to industrial applications. Unlike previous efforts, the devised coupling to the structural PFC (XPFC) equations allows generalization to more complex crystal structures through explicit parameterization of the direct correlation function (DCF). Utilizing the HXPFC-s2 formalism, we seek to uncover the determinant physical mechanisms in crystallization under simple shear flows by comparing temperature-driven crystallization to flow-mediated crystallization under varying flow-strengths. Parallels and deviations of under-cooling and flow-strength effects on crystal growth are drawn using the crystal cluster-size and system ordering time evolutions. In doing so, we identify scaling behaviors with a Peclet-like number, $\stackrel{\sim }{\mathrm{Pe}}$, a critical Peclet-like number, ${\stackrel{\sim }{\mathrm{Pe}}}^{*}$, and flow-field-crystal plane-dependent interactions. Our findings may be relevant for controlling crystal growth and phase behaviors in flow applications. Full article

Understanding the behavior of fluid flow and solute transport in fractured rock is of great significance to geoscience and engineering. The discrete fracture network is the predominate channel for fluid flow through fractured rock as the permeability of fracture is several magnitudes higher than that of the rock matrix. As the basic components of the fracture network, investigating the fluid flow in crossed fractures is the prerequisite of understanding the fluid flow in fractured rock. First, a program based on the successive random addition algorithm was developed to generate rough fracture surfaces. Next, a series of fracture models considering shear effects and different surface roughness were constructed. Finally, fluid dynamic analyses were performed to understand the role of flowrate and surface roughness in the evolution of flow field, concentration field, solute breakthrough, and solute mixing inside the crossed fractures. Results indicated that the channeling flow at the fracture intersection became more pronounced with the increasing Péclet number (Pe) and Joint Roughness Coefficient (JRC), the evolution of the concentration field was influenced by Pe and the distribution of the concentration field was influenced by JRC. For Pe < 10, the solute transport process was dominated by molecular diffusion. For 100 > Pe > 10, the solute transport process was in the complete mixing mode. In addition, for Pe > 100, the solute transport process was in the streamline routing mode. The concentration distribution was affected by the local aperture at the fracture intersection corresponding to different surface roughness. Meanwhile, the solute mixing equation was improved based on this result. The research results are beneficial for further revealing the mechanism of fluid flow and solute transport phenomenon in fractured rock. Full article

Bioconvection phenomena play a pivotal role in diverse applications, including the synthesis of biological polymers and advancements in renewable energy technologies. This study develops a comprehensive mathematical model to examine the effects of key parameters, such as the Lewis number (Lb), Peclet number (Pe), volume fraction ($\phi$), and angle of inclination $\left(\alpha \right)$, on the flow and heat transfer characteristics of a nanofluid over an inclined cylinder embedded in a non-Darcy porous medium. The investigated nanofluid comprises nano-encapsulated phase-change materials (NEPCMs) dispersed in water, offering enhanced thermal performance. The governing non-linear partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations and solved numerically via the Network Simulation Method (NSM) and an implicit Runge–Kutta method implemented through the bvp4c routine in MATLAB R2021a. Validation against the existing literature confirms the accuracy and reliability of the numerical approach, with strong convergence observed. Quantitative analysis reveals that an increase in the Peclet number reduces the shear stress at the cylinder wall by up to 18% while simultaneously enhancing heat transfer by approximately 12%. Similarly, the angle of inclination ($\alpha$) significantly boosts heat transmission rates. Additionally, higher Peclet and Lewis numbers, along with greater nanoparticle volume fractions, amplify the density gradient of microorganisms, intensifying the bioconvection process by nearly 15%. These findings underscore the critical interplay between bioconvection and transport phenomena, providing a framework for optimizing bioconvection-driven heat and mass transfer systems. The insights from this investigation hold substantial implications for industrial processes and renewable energy technologies, paving the way for improved efficiency in applications such as thermal energy storage and advanced cooling systems. Full article

This study presents a comprehensive 3D numerical analysis of thermal stratification, fluid dynamics, and heat transfer efficiency across six hot water storage tank configurations, identified as Tank-1 through Tank-6. The objective is to determine the most effective design for achieving uniform temperature distribution, stable stratification, and efficient heat retention in sensible heat storage systems, with potential for integration with phase change materials (PCMs). Using COMSOL Multiphysics 5.6, simulations were conducted to evaluate key performance indicators, including the Richardson number, capacity ratio, and exergy efficiency. Among the tanks, Tank-1 demonstrated the highest efficiency, with a capacity ratio of 84.6% and an exergy efficiency of 72.5%, while Tank-3, which achieved a capacity ratio of 70.2% and exergy efficiency of 50.5%, was identified as the most practical for real-world applications due to its balanced heat distribution and feasibility for PCM integration. Calculated dimensionless numbers (Reynolds number: 635, Prandtl number: 4.5, and Peclet number: 2858) indicated laminar flow and dominant convective heat transfer across all the configurations. These findings provide valuable insights into the design of efficient thermal storage systems, with Tank-3’s configuration offering a practical balance of thermal performance and operational feasibility. Future work will explore the inclusion of PCM containers within Tank-3, as well as applications for heat pump and solar water heaters, and high-temperature heat storage with various working fluids. Full article

The purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and losses in a sequence of bets) and reframes it as a CDE in the limit of many bets. The use of the CDE clarifies the role of steady growth (characterized by a velocity U) and random fluctuations (characterized by a diffusion coefficient D) to predict a probability distribution for the remaining bankroll as a function of time. Whereas the Kelly Criterion selects the investment fraction that maximizes the median bankroll (0.50 quantile), we show that the CDE formulation can readily find an optimum betting fraction f for any quantile. We also consider the effects of “ruin” using an absorbing boundary condition, which describes the termination of the betting sequence when the bankroll becomes too small. We show that the probability of ruin can be expressed by a dimensionless Péclet number characterizing the relative rates of convection and diffusion. Finally, the fractional Kelly heuristic is analyzed to show how it impacts returns and ruin. The reframing of the Kelly approach with the CDE opens new possibilities to use known results from the chemico-physical literature to address sequential betting problems. Full article

The transition from batch to continuous production in the catalytic hydrogenation of nitrile butadiene rubber (NBR) into hydrogenated NBR (HNBR) marks a significant advance for applications under demanding conditions. This study introduces a continuous process utilizing a static mixer (SM) reactor, which notably achieves a hydrogenation conversion rate exceeding 97%. We thoroughly review a mechanistic model of the SM reactor to elucidate the internal dynamics governing the hydrogenation process and address the inherent uncertainties in key parameters such as the Peclet number (Pe), dimensionless time (θτ), reaction coefficient (R), and flow rate coefficient (q). A comprehensive dataset generated from varied parameter values serves as the basis for training an artificial neural network (ANN), which is then compared against traditional models including linear regression, decision tree, and random forest in terms of efficacy. Our results clearly demonstrate the ANN’s superiority in predicting the degree of hydrogenation, achieving the lowest root mean squared error (RMSE) of 3.69 compared to 21.90 for linear regression, 4.94 for decision tree, and 7.51 for random forest. The ANN’s robust capability for modeling complex nonlinear relationships and dynamics significantly enhances decision-making, planning, and optimization of the reactor, reducing computational demands and operational costs. In other words, this approach allows users to rely on a single ML-based model instead of multiple mechanistic models for reflecting the effects of possible uncertainties. Additionally, a feature importance study validates the critical impact of time and element number on the hydrogenation process, further supporting the ANN’s predictive accuracy. These findings underscore the potential of ML-based models in streamlining and enhancing the efficiency of chemical production processes. Full article

Many biotechnology sectors that depend on fluids and their physical characteristics, including the phenomenon of bioconvection, have generated a great deal of discussion. The term “bioconvection” describes the organized movement of microorganisms, such as bacteria or algae. Microorganisms that participate in bioconvection display directed movement, frequently in the form of upward or downward streaming, which can lead to the production of distinctive patterns. The interaction between the microbes’ swimming behavior and the physical forces acting on them, such as buoyancy and fluid flow, is what drives these patterns. This work considers the laminar-mixed convection incompressible flow at the stagnation point with viscous and gyrotactic microorganisms in an unsteady electrically conducting hybrid nanofluid (Fe₃O₄-Cu/water). In addition, hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, can be used in biological domains, including drug delivery and microcirculatory system flow dynamics. The governing system has been reduced to a set of ordinary differential equations (ODEs) through the use of the group technique. The current research was inspired by an examination of the impacts of multiple parameters, including Prandtl number, $Pr$, magnetic diffusivity, ${\eta }_0$, shape factor$, n$, microorganism diffusion coefficient, $D_n$, Brownian motion coefficient, $D_B$, thermophoresis diffusion coefficient, $D_T$, bioconvection Peclet number, $Pe$, temperature difference, $\delta t$, and concentration difference, $\delta c$. The results show that as $Pr$ rises, temperature, heat flux, and nanoparticles all decrease. In contrast, when the ${\eta }_0$ value increases, the magnetic field and velocity decrease. Heat flow, bacterial density, and temperature decrease as the $D_B$ value rises, yet the number of nanoparticles increases. As the $D_T$ value increases, the temperature, heat flow, and concentration of nanoparticles all rise while the density of bacteria decreases. Even though temperature, heat flux, nanoparticles, and bacterial density all decrease as $\delta c$ values climb, bacterial density rises as $D_n$ values do although bacterial density falls with increasing, $\delta t$ and $Pe$ values; on the other hand, when n values increase, temperature and heat flow increase but the density of bacteria and nanoparticle decrease. The physical importance and behavior of the present parameters were illustrated graphically. Full article

This research study investigated the transient behavior of the convection–diffusion model for the infiltration heat recovery (IHR) and the influence of the building envelope heat capacity, along with other factors. A transient numerical model was developed and validated to analyze the IHR under various conditions. The results highlight the role of heat capacity, thermal conductivity, wall thickness, airflow rate, airflow direction, and wall porosity on the temperature distribution and the heat recovery factor within the wall. Higher-heat-capacity walls displayed a delayed temperature rise, while low-thermal-conductivity walls reduced the conduction heat transfer and increased the IHR factor. The impact of heat capacity diminished with very low thermal conductivity walls but became evident for high-thermal-conductivity walls, particularly at higher Peclet numbers. Thicker walls enhanced the heat retention and improved the IHR, with a reduced influence of airflow rate. Higher IHR factors were associated with thicker walls, lower Peclet numbers, and higher heat capacities. The analysis also showed that the wall porosity affected the IHR with less significance than the other factors. Incorporating these findings into building energy modeling tools could improve the prediction accuracy of the thermal behavior of buildings. Accordingly, this study contributes to building physics by understanding IHR dynamics and thermal mass interactions, as well as improving building energy modeling accuracy for performance prediction. Future research can explore the impacts of additional factors on IHR and investigate the effect of IHR on the overall energy consumption of buildings. Full article

Recently, researchers have developed new heat transfer fluids that have high thermal conductivity, heat capacity, and low viscosity for food applications. Because the thermal conductivity of nanoparticles is higher than base fluids (water, ethylene glycol, and so on), nanofluids (NFs) are characterized by high performance in heat transfer operations. In this study, the aim was to determine the effect of NFs used in heat transfer equipment on the heat transfer coefficient using Analysis of Covariance (ANCOVA), which is an optimization test. For heat transfer modeling of tomato juice, the effect of alumina content in NFs on Reynolds Number (Re) and overall heat transfer coefficient was evaluated. For heat transfer modeling of milk, the effect of carbon nanotube content in NFs on Peclet Number (Pe) and convective heat transfer coefficient was assessed. As a result, it was determined that Re and alumina content to be crucial in the heat transfer of tomato juice within their p-values. However, in milk production heat transfer, carbon nanotubes had no crucial importance. Full article

Limiting casting expression speed was obtained and the flow redistribution and thermal history in a horizontal direct-chill (HDC) casting was predicted using the numerical modeling approach. The governing solidification equations were non-dimensionalized to understand the relevant contribution of each term in the solidification processes in the HDC system. The effect of an increase in the casting speed on the flow characteristics and sump length was represented by the Péclet number Pe. Details of the simulation reveal that at a low Pe, the natural convective flow creates minor counter-clockwise recirculating cells in the lower half of the HDC domain. However, at a Pe above 82.75, the minor recirculating cells disappear due to the strong forced convective flow from the upstream. Additionally, an increase in the Pe increases the sump length, strength, and spread of the turbulence field within and beyond the mold region. The limiting casting conditions are computed by predicting the sump length over which the alloy temperature is above the solidus temperature. This gives a simple relation for the casting speed as a function of the geometrical data and the alloy properties. The current work is useful to casting engineers who always rely on trial and error in choosing a new casting speed whenever a new alloy is to be produced. Hence, with the new information and the casting speed relations, it is possible and easy to predict the operating window over which melt break-out can occur during HDC. Full article

We theoretically considered two-dimensional flow in a vertically aligned thick molten liquid film to investigate the competition between cooling and gravity-driven draining, which is relevant in the formation of metallic foams. Molten liquid in films cools as it drains, losing its heat to the surrounding colder air and substrate. We extended our previous model to include non-isothermal effects, resulting in coupled non-linear evolution equations for the film’s thickness, extensional flow speed and temperature. The coupling between the flow and cooling effect was via a constitutive relationship for temperature-dependent viscosity and surface tension. This model was parameterized by the heat transfer coefficients at the film–air free surface and film–substrate interface, the Péclet number, the viscosity–temperature coupling parameter and the slope of the linear surface tension–temperature relationship. A systematic exploration of the parameter space revealed that at low Péclet numbers, increasing the heat transfer coefficient and gradually reducing the viscosity with temperature was conducive to cooling and could slow down the draining and thinning of the film. The effect of increasing the slope of the surface tension–temperature relationship on the draining and thinning of the film was observed to be more effective at lower Péclet numbers, where surface tension gradients in the lamella region opposed the gravity-driven flow. At higher Péclet numbers, though, the surface tension gradients tended to enhance the draining flow in the lamella region, resulting in the dramatic thinning of the film in the later stages. Full article

This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs. Full article

This article examines the effects of entropy generation, heat transmission, and mass transfer on the flow of Jeffrey fluid under the influence of solar radiation in the presence of copper nanoparticles and gyrotactic microorganisms, with polyvinyl alcohol–water serving as the base fluid. The impact of source terms such as Joule heating, viscous dissipation, and the exponential heat source is analyzed via a nonlinear elongating surface of nonuniform thickness. The development of an efficient numerical model describing the flow and thermal characteristics of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in various devices continues to increase. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting higher-order coupled ODEs are converted into a system of first-order ODEs and then solved using the RK 4th-order method with shooting technique. The remarkable impacts of pertinent parameters such as Deborah number, magnetic field parameter, electric field parameter, Grashof number, solutal Grashof number, Prandtl number, Eckert number, exponential heat source parameter, Lewis number, chemical reaction parameter, bioconvection Lewis number, and Peclet number associated with the flow properties are discussed graphically. The increase in the radiation parameter and volume fraction of the nanoparticles enhances the temperature profile. The Bejan number and entropy generation rate increase with the rise in diffusion parameter and bioconvection diffusion parameter. The novelty of the present work is analyzing the entropy generation and solar radiation effects in the presence of motile gyrotactic microorganisms and copper nanoparticles with polyvinyl alcohol–water as the base fluid under the influence of the source terms, such as viscous dissipation, Ohmic heating, exponential heat source, and chemical reaction of the electromagnetohydrodynamic (EMHD) Jeffrey fluid flow. The non-Newtonian nanofluids have proven their great potential for heat transfer processes, which have various applications in cooling microchips, solar energy systems, and thermal energy technologies. Full article