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In this study, laser Directed Energy Deposition technology is employed to fabricate internal structures within the hollow interiors of rotating parts such as tubes and cylinders. A three-dimensional transient multiphysics model for C276 material was developed, which anticipated the impact of angular velocity from tube rotation on various aspects. This model, validated by experiments, focused on the melt pool morphology, Marangoni convection, oriented crystal microevolution, and deposited material microhardness. It was found that at 150 ms deposition, the dimensions of the melt pool stabilized. With an increase in the Peclet number, heat transfer within the melt pool transitioned from conduction to convection. A rise in angular velocity reduced the melt pool deposition height, limited by the volume of the deposited material. Additionally, this angular velocity generated tangential forces, leading to an asymmetric melt distribution in the longitudinal section of the melt pool and a movement of the melt toward the melting front. At the bottom of the melt pool, the growth of C276 columnar crystals was notably inclined toward the center of Marangoni convection. The microhardness of the deposited material showed a stable distribution along the inclined crystal direction, whereas significant fluctuations were observed perpendicular to the cylinder substrate. These findings highlighted the considerable effect of Marangoni convection on microstructural evolution. [ABSTRACT FROM AUTHOR]

Pumpkin seeds swagger a wealthy vitamin and mineral composition. They contain vitamins (A, B, C, K, D, E), minerals (calcium, selenium, zinc, magnesium, copper, potassium, press, manganese and phosphorus), a few amino acids such as glutamic, linolenic and arginine, and greasy plant acids. The Peclet number includes the peripheral rotation speed of the RTS condenser tube. In our case, the Peclet number reflects how the heat transfer to the grain layer due to convection, when the RTS capacitor rotates, relates to the heat transfer due to the thermal conductivity of the grain layer. Thus, in the first drying period, the determining factors for mass transfer will be the conditions at the phase boundary – the mode of air movement outside the grain, the area of the grain, the surface temperature of the RTS condenser. In total, pumpkin seeds contain 12 essential and eight nonessential amino acids. [ABSTRACT FROM AUTHOR]

The laminar burning velocity (LBV) and cellular instability of ammonia/syngas/air were investigated using the spherically expanding flame method at an initial pressure of 3 atm and temperatures of 298–448 K. The impacts of equivalence ratio, temperature, and hydrogen ratio on LBV were scrutinized. The results demonstrate that the LBV varies non-monotonically with the equivalence ratio and increases with increasing temperature and hydrogen ratio. Flame instability was analyzed using flame uplift rate, Lewis number, thermal expansion ratio, flame thickness, critical radius, critical Peclet number and logarithmic growth rate of perturbation in combination with the schlieren images. Of these, the flame uplift rate is used to quantify buoyancy instability, a flame instability that has received little attention. At high pressures, lower LBV makes the flame susceptible to buoyancy instability. The flame uplift rate increases with increasing flame radius, suggesting that the buoyancy instability becomes increasingly significant as the spherical flame expands. The diffusional-thermal instability is weaker at the fuel-rich side and enhanced at the leaner side. As the hydrogen ratio increases, the flame instability increases. Hydrodynamic instability is not susceptible to temperature, which is only slightly weakened with increasing temperature. Additionally, the phenomenon of superadiabatic flame temperature (SAFT) in ammonia/syngas/air flames was first found and analyzed its temperature dependence. Increasing the initial temperature suppresses SAFT occurrence. [Display omitted] • LBVs of ammonia/syngas/air mixtures were measured at 298–448 K and 3 atm. • The buoyancy instability was studied in detail using flame uplift rates. • The effect of initial temperature on the flame instability was analyzed in detail. • The phenomenon of SAFT in ammonia/syngas/air flames was first found. [ABSTRACT FROM AUTHOR]

This research investigates the infiltration patterns of a bentonite-sand slurry into saturated sand. Bentonite-sand slurry is formed when excavated sand mixes with bentonite slurry inside the excavation chamber, a common phenomenon during slurry shield tunneling. Employing a normal laboratory setup designed to emulate field conditions, the study elucidates the impacts of varying bentonite and sand concentrations, as well as the pressure applied, on the infiltration process. The findings highlight that low-permeability zone invariably form on the sand layer's surface, with their formation rate and pressure transfer efficiency being negatively influenced by the sand particle accumulation from the slurry. The infiltration process, as dictated by changes in the Peclet number (Pe), can be effectively categorized into three distinct stages: mud spurt, internal filter cake formation, and surface filtration. The correlation between the duration of the first two stages and the sand content can be described by a linear function. It was observed that low-permeability zone formation can be expedited, and slurry pressure transfer can be enhanced, by increasing the concentration of bentonite. The manipulation of excess slurry pressure, however, produced inconsistent outcomes, as increased applied pressure was found to lower pressure transmission efficiency. Mechanisms of bentonite-sand-slurry infiltration are discussed, and implications for field applications are described. [ABSTRACT FROM AUTHOR]

Solid cancer remains a serious threat to global health despite decades of progress. Traditional chemotherapy treatment has been used to curb the disease despite its inability to reach cancer cells at high enough quantities leading to adverse toxicity on healthy cells, producing severe side effects, and exacerbating patient suffering. Active targeted nano-drugs (ATNDs) acting as transporter systems have become a viable solution to this shortcoming, offering the possibility of more precise cancer targeting. Therefore, in the present study, we develop a numerical model of capturing ATNDs, incorporating movements within and outside the tumor spheroid and the magnetic forces guiding the nanoparticles. By combining a model of ATNDs transport with a tumor-effector dynamic model based on porous media phenomena, we demonstrate how the models may be combined to model drug-loaded nanoparticle transport in an external magnetic field. We analyze the controlled drug delivery against traditional chemotherapy based on the combined effect of immunotherapy and chemotherapy with the dispersion of nano-drugs to lead a solute cloud toward the tumor. We found that the amalgamation of immune and chemotherapy delivered by ATNDs enhances cancer therapy efficacy compared with conventional chemotherapy. Increased drug convection toward the tumor region presented by ascending values of the Peclet number inhibits the growth of tumor cells and prolongs progression-free survival. Increases in source term and vessel permeability also increase the likelihood of tumor suppression, while raising the hematocrit and magnetic number results in reduced tumor cell killing. Sensitivity analysis of the dynamic model parameters has been discussed. This work demonstrates that ATND-delivery systems can improve therapeutic agent delivery to the tumor tissue, and promote tumor cell killing. • Analyze the impact of drug dispersion on the dynamical systems of tumor-effectors with conventional and targeted therapy. • Incorporate drug dispersion phenomena to describing targeted nano-drugs delivery with hematocrit and drug source term. • Numerical and sensitivity simulation shows the impact of the flow and dynamical control parameters on therapy treatment. • Targeted nano-drug delivery shows more prominent in drug accumulation in the tumor than the conventional treatment. • Outcomes demonstrate the effectiveness of targeted drug delivery to the tumor tissue and enhance tumor cell kill. [ABSTRACT FROM AUTHOR]

An analytical solution for the diffusive wave model with a concentrated lateral inflow for a finite channel is presented. Flow depth and flow discharge are taken as the upstream boundary, whereas the downstream end is subjected to a stage–discharge relationship. The focus is on analyzing the impact of the lateral inflow concentrated at different locations on the flow discharge and flow depth. Unit-step responses for all the impulse responses for the lateral inflow are also presented and compared with the corresponding results of a semi-infinite channel where the downstream boundary is ignored. For higher Peclet numbers, the semi-infinite channel responses are found to be a satisfactory substitute for the finite channel responses to predict flow discharge, when a flow discharge is imposed at the upstream boundary, and a steady uniform condition is applied at the downstream boundary. However, for lower values of Peclet number, the same is not replicated. Furthermore, for the flow depth responses, the semi-infinite channel results are not appropriate approximations for finite length channel responses since the flow depth is observed to be sensitive to the backwater effect induced by the downstream boundary. [ABSTRACT FROM AUTHOR]

Practical Application The heat and momentum transfer of tomato puree through a concentric‐tube heat exchanger over a range of generalized Reynolds number (0.05 < Re < 66.5) was experimentally and numerically analyzed. Thermophysical and rheological properties of tomato puree (12°Brix) were measured from 20 to 60°C. The velocity, pressure, and temperature were calculated using the computational fluid dynamics (CFD) software FLUENTTM with temperature‐dependent transport properties. The thermal operation of the concentric‐tube exchanger was satisfactorily predicted using CFD, indicating accurate measurement of tomato puree properties with temperature variations. A concordance was found between the calculated Fanning friction factor and generalized Reynolds with the experimental correlation. A modified Sieder–Tate correlation was established, which allows properly expressing the Nusselt number as a function of the Peclet number. Simple correlations for the mechanical work and the heat transfer rate as a function of the volumetric flow rate were derived. The thermal efficiency was high at low puree flow rates but decreased with higher rates. However, at high flow rates, ceased its decline, instead showing a slight improvement. The analysis confirmed higher heat transfer rates in the concentric‐tube heat exchanger compared to a plain tube at low puree flow rates. The results offer valuable insights for assessing diverse operational conditions in dairy, beverage, sauce, and concentrated food industries. Additionally, they also enhance the analysis and design of concentric‐tube heat exchangers.The knowledge of the rheological and hydrodynamical behavior of fluids in concentric‐tube heat exchangers allows to explore a set of different operating conditions to improve the yield and effectiveness on the system heating/cooling design. [ABSTRACT FROM AUTHOR]

This work explores the effect of activation energy on bioconvection flow of oxytactic microorganisms with nano-encapsulated phase change materials in complex shaped enclosure. The inner wavy wall is partially fixed at the constant high temperature. The proposed problem has been modeled first using the conservation laws and then simulated by utilizing finite element method. The discretized system of nonlinear algebraic equation is computed using the Newtons method. The obtained results have been analyzed for the several important controlling parameters. It has been observed that the vortex centers have been established near the adiabatic walls for lower values of Lewis number. The average Sherwood number and density of motile microorganism are the increasing functions of chemical reaction parameter. Moreover, the average Nusselt number declines with rising values of Peclet number. [ABSTRACT FROM AUTHOR]

Since the 1980s, low-permeability slurry trench cutoff walls have been widely constructed as barriers to retard the migration of contaminants. The thickness of the cutoff walls is a key determinant of the wall service life. Through a series of theoretical derivations, simplified methods for determining the flux limit and concentration limit were proposed to determine the thickness of cutoff walls for contaminated sites with constant pollutant flux. The relative errors of both the flux-based and concentration-based methods increase as the breakthrough criterion of the ratio between the specified limit concentration of the contaminant to the source concentration (C*) and the ratio of the limited value of contaminant flux to the constant source flux (F*) increases, with a given Peclet number PL. The maximum relative error reaches 4% and 6% when C* and F* are both 0.1, which covers most practical situations in cutoff wall design. Good agreements of wall thickness were obtained between the proposed simplified methods and analytical solutions via a clear example. The proposed method can efficiently simplify the design process of cutoff walls with high accuracy, providing a basis for containing contaminated sites. [ABSTRACT FROM AUTHOR]

Crossflow filtration is a separation technique where fluid flows tangentially across a membrane or porous media, reducing clogging by sweeping away retained particles and allowing continuous filtration. Dispersion of solute matter in crossflow filtration plays an essential role in the separation performance of many industrial processes. The current work aims to generalize the Taylor dispersion theory and study the solute transport in a slit–porous medium system with a crossflow. The solute is depleted by the porous medium at the slit top porous wall or the interface between the slit and the porous medium, where the continuity of the solute concentration and mass flux is applied. The solute is simultaneously transported axially by the main flow along the slit and vertically by the crossflow perpendicular to the slit. Using the Reynolds decomposition and cross-sectional averaging techniques, the generalized reduced-order model for the advection-dispersion solute transport in the slit–porous medium system with the presence of a crossflow is established, where the effective velocity of the main flow and the effective dispersion coefficient are obtained. The analysis of the results reveals that the nondimensional Taylor dispersion coefficient scales with the Peclet numbers for the crossflow and the main flow, respectively, as D T ∼ Pe v − 5 / 3 (when Pe v ≥ 20) and D T ∼ Pe u 2 . The proposed theoretical model, along with the findings of this study, paves the way for the fundamental study of dispersion in more complex systems. [ABSTRACT FROM AUTHOR]

In recent times, bioconvection has numerous uses, like, biological and biotechnological problems. The present study describes the magnetic bioconvective Buongiorno's flow model with microorganisms in a stretchable area with convective heat transfer and second‐order velocity slip in a non‐Darcian porous regime. Here, the influence of variable viscosity, viscous dissipation, Joule heating, and heat source/sink are considered in the occurrence of higher‐order chemical reactions. Employing proper similarity transformations leading equations are transformed to dimension‐free form. The transformed equations are solved via MATLAB bvp4c problem solver. This study's main objective is to graphically analyze the effects of different pertinent factors on the density of motile microorganisms, velocity, concentration, temperature, number of motile microorganisms' density, skin friction, mass transport rate, and heat transport rate. The main findings drawn from this study are viscosity (−5≤θr≤−1) $(-5\le {\theta }_{r}\le -1)$ and magnetic parameter (0.5≤M≤3) $(0.5\le M\le 3)$ lowers the fluid velocity. Biot number (0.4≤Bi≤0.6) $(0.4\le {B}_{i}\le 0.6)$ increases fluid temperature, but reduces heat transport rates and skin friction. Schmidt (0.5≤Sc≤1) $(0.5\le Sc\le 1)$ and Eckert numbers (0.1≤Ec≤3) $(0.1\le {E}_{c}\le 3)$ reduce the fluid concentration. A rise of 0.3 in bioconvective Rayleigh number (0.3≤Rab≤0.9) $(0.3\le R{a}_{b}\le 0.9)$ and 0.2 in buoyancy ratio number (0.1≤Nr≤0.5) $(0.1\le {N}_{r}\le 0.5)$ causes a percentage drop in velocities of 8.79% and 3.91% (approximately), respectively, in the neighborhood of the sheet. Furthermore, the increase in Peclet number (0.8≤Pe≤1.5) $(0.8\le {P}_{e}\le 1.5)$ by 0.2 lowers the density number of microorganisms by 28%. Additionally, the profile of motile microorganisms is improved by thermophoresis impact, while it is diminished by chemical reaction. [ABSTRACT FROM AUTHOR]

We consider heat transfer with convection and radiation effect on a longitudinal wet and porous fin. The trapezoidal fin moving at a constant speed is subject to stretching and shrinking, and their influence on the fin's heat transfer rate and thermal distribution is investigated. The governing equation of the model mentioned above is nondimensionalized, and the resultant second‐order nonlinear boundary value problem is solved numerically using the Chebyshev collocation method and validated using the shooting technique. All the simulations are carried out using MATLAB software. The impact of the critical dimensionless parameters on the fin tip temperature, the thermal profile, and the base heat transfer rate are analyzed graphically. Fin efficiency is also computed, and the influence of the pertinent parameters on it is inferred. For a moving fin, the shrinking mechanism favors a faster base heat transfer, an uptick of about 9%, and the stretching fin enhances thermal distribution and efficiency by around 3% and 14%, respectively. The rise is further accelerated with the enhancement of the Peclet number. The fin tapering from that of a rectangular profile (C=0) helps achieve a faster heat transfer rate along the fin length, a gain of nearly 22%, when the fin taper ratio C varies from 0 to 0.8. [ABSTRACT FROM AUTHOR]

Bioconvection in hybrid nanofluids refers to the phenomenon where biological microorganisms such as algae or bacteria exhibit collective movement or pattern formation in a suspension containing nanoparticles. This phenomenon has significance in various fields, including biology, nanotechnology, and engineering. The current investigation emphasizes the bioconvective flow of a water (H2O)−ethylene glycol (C2H6O2)-based hybrid nanofluid flow by a curved stretched sheet. Copper (Cu) and silver (Ag) nanoparticles are suspended in the base fluid. The thermal field is analyzed in the presence of heat generation, dissipation, Joule heating, and the impact of thermal radiation. Binary reactions associated with Arrhenius energy are accounted in the modeling of mass concentration. The phenomenon of bioconvection is considered to regulate the random movement of tiny solid particles within the flow. Boundary layer constraints are implemented to eliminate ineffective terms from modeling. The transformation procedure is adopted to obtain the flow governing system of ODEs. The built-in code of Mathematica (NDSolve) is implemented to obtain the graphical and numerical results. The results show that the velocity field decreases with increasing porosity variable and Hartmann number. An opposite impression of the Eckert number and Schmidt variable on the thermal field is noticed. Bioconvection Peclet and Lewis numbers have a direct relationship with motile density. [ABSTRACT FROM AUTHOR]

In this paper, the thermal behavior of cylindrical and conical pin fin structures operating in a convective–radiative environment has been examined. The fully wet porous fin structures are assumed to be mounted with a stretching/shrinking mechanism similar to a conveyer belt. The conical pin fin has been comparatively analyzed with the cylindrical one for three distinct cases of stretching, stagnant, and shrinking. Further, the Darcy model has been employed to analyze the fluid–solid interactions. The differential transformation method (DTM) has been used to solve the resulting second-order nonlinear ordinary differential equations. On the thermal performance of conical and cylindrical pin fin structures, the effects of the stretching/shrinking parameter, Peclet number, wet porous parameter, convective parameter, and radiative parameter have been established graphically. The conical pin fin is found to aid the heat transmission process better than the cylindrical one. The work is also helpful in the realm of microelectronics, particularly in the development of micro-pin-fin structures. [ABSTRACT FROM AUTHOR]

The traditional craft villages in Vietnam in general and in Bac Ninh province in particular have been exposing many negative impacts on the environment. The heavy metal-rich wastes from the metal recycling casting craft villages in the field of metal recycling and metal casting are causing severe heavy metal pollution not only to the air, soils, and sediments but also to the groundwater resources. In Da Hoi iron recycling craft village in Chau Khe ward, Tu Son town, Bac Ninh province, Vietnam, the Holocene aquifer is exposed to the Ngu Huyen Khe River's sediments contaminated with heavy metals Lead, Cadmium, Nickel, and Zinc. Freundlich isotherm parameters of the Holocene aquifer have been selected for finite element modeling of heavy metal transport with high temporal and spatial varying retardation factors to get reliable quantitative heavy metals' distribution in depth and time. Initial and boundary conditions have been augmented to be established. The retardation factors of the advection and dispersion transport in the Holocene aquifer for heavy metals Pb, Zn, Cd, and Ni are very highly none-linear and very much varying in time and space: 8.7–66.4 for Pb, 2.0–12 for Zn, 1.7–4.8 for Cd and 1.1–5.9 for Ni. The results of the numerical modeling show that heavy metal transport in the Holocene aquifer is very fast and the entire aquifer thickness has equilibrium aquifer formation and aquifer water heavy concentrations after around 2–2.5 years for Cd and Ni, around 4 years for Zn and around 27 years for Pb. The heavy metals' fluxes from the Holocene aquifer to the Pleistocene aquifer are maximal and more or less constant from the equilibrium time and would cause severe contamination of the Pleistocene aquifer. [ABSTRACT FROM AUTHOR]

Particular interest has been paid to the consequences of nanofluid owing to the significant energy shortage in the modern world due to its ultra-high thermo-physical properties. Recent researchers have paid huge attention to enriching energy output through the interaction of nanoparticles to resolve this perilous problem. In this work, the magnetized transport of micropolar nanoliquid under the influence of variable thermal conductivity and thermally radiation over a vertical stretching surface with motile microorganisms is analyzed. The heat source/sink and the magnetic field impacts are also considered. The converted non-dimensional controlling ODEs are solved with bvp4c solver (shooting technique) in MATLAB mathematical software. Results of numerical computation are displayed graphically. Prominent parameters such as magnetic parameter, Prandtl number, thermophoresis parameter, thermal radiation, Peclet number, mixed convective number, Lewis number, microrotation parameter, and bioconvection Lewis number are evaluated by plotting graphs for the characteristics of velocity, temperature, volumetric concentration, and microorganism concentration. Efficient heat transfer in macro-tech processes will benefit from the process and findings of this research. The presented model is important in the fields of nanotechnology and bioengineering. [ABSTRACT FROM AUTHOR]

The thermal bioconvective investigation of magnetized Reiner-Rivlin nanofluid is the focus of research. The suspension of microorganisms is necessary to assess the stability of nanofluids and their consistent functioning. The heat transfer results are influenced by the radiated impact and the impacts of an external heating source. One might propose the use of the Cattaneo-Christov heat flux technique to simulate heat and mass transport difficulties. The convective boundary conditions are used for the analysis of the flow problem. The issue is modeled using a differential system. Incorporating dimensionless variables greatly simplifies the translation of the governing issue. The numerical simulation of the final system is performed using the shooting approach. The impact of settings on the thermal issue is evaluated and shown visually using graphs. Various uses of parameters in the thermal model have been presented. The heat transfer is found to increase because of the Reiner-Rivlin fluid parameter. The concentration profile decreases because of the concentration relaxation parameter. The profile of the microorganism decreases as the Peclet number increases, while the constant for Reiner-Rivlin fluid leads to increased observations. [ABSTRACT FROM AUTHOR]

In this investigation, we delve into the influence of throughflow on the phenomenon of bi-disperse convection within Rivlin-Ericksen fluid. In the context of examining bi-disperse convection within this specific type of fluid, the throughflow effect is considered to have a uniform vertical distribution. The primary focus of this study centers on evaluating the system’s linear stability. To achieve this, we employ normal mode analysis to compute the Darcy-Rayleigh number at the onset of convection. This Darcy-Rayleigh number is computed for both stationary and oscillatory convection modes. Furthermore, we conduct a comprehensive analysis and present the results in graphical form to illustrate the impact of various parameters, including Peclet number and kinematic viscoelastic parameter, on both stationary and oscillatory convection. Our research findings demonstrate that when Peclet number Pr1 < 0, it leads to destabilising effect on both stationary and oscillatory convections. Conversely, when Peclet number Pr1 > 0, it induces stabilising effect on both stationary as well as oscillatory convections. [ABSTRACT FROM AUTHOR]

In the present arena, the tools of artificial intelligence (AI) play a significant role in research across various fields by enabling advanced data analysis, pattern recognition and decision-making. This research work presents the numerical investigation of bioconvective micropolar nanofluidic model (BCMNFM) by employing the knacks of AI-based nonlinear autoregressive (NAR) approach with a combination of backpropagated Levenberg–Marquardt neural networks (BLMNNs) represented as NAR-BLMNNs. This research work investigates the flow design to highlight the attributes of mass and heat exchange. A dataset for BCMNFM is created by applying the Adam numerical procedure by variation of unsteadiness parameter (A), magnetic field parameter (M), thermophoresis parameter (Nt), Brownian motion parameter (Nb), bioconvection Peclet number (Pe) and spin gradient viscosity parameter (λ). The skills of AI-based NAR-BLMNNs technique is then utilized on the dataset created for BCMNFM to investigate the approximate solutions. The achieved and impactful values of performance consistently range between E−10 and E−14 across all scenarios of BCMNFM. The precision and the validation of predicted approach NAR-BLMNNs is exceptionally established by the graphical demonstration for all scenarios of MSE, regression metrics, error histograms and time series graphs. The numerical calculations attained through AI-based NAR-BLMNNs technique further rationalize the precision of the proposed methodology for solving the BCMNFM effectively and efficiently. [ABSTRACT FROM AUTHOR]

AbstractIncorporating slip conditions into computational fluid dynamics (CFD) simulations and experiments helps engineers predict and improve the effectiveness of superhydrophobic surfaces in reducing drag. This optimization approach leads to significant enhancements in fuel efficiency and performance across a range of fluid-flow systems, including marine vessels and aircraft. This study models the phenomena of velocity and temperature slip, coupled with MHD, within the context of nanofluid flow undergoing bioconvection over a stretching sheet. Subsequently, the study seeks to analyze the resulting effects on heat and mass kinematics. The bvp4c solver effectively calculates analytical solutions for the reduced problem obtained through similarity transformation from the underlying partial differential equations. Velocity and temperature slip both impact temperature, with velocity slip increasing heat transfer rates and temperature slip decreasing them. The thermal radiation parameter enhances nanoparticle concentration, although it’s offset by an increased Lewis number. Brownian motion amplifies mass transfer, but the thermal radiation parameter hampers it. The escalation in the microorganism density profile correlates with the increase in both the Bioconvection Lewis number and the Peclet number. Likewise, as thermophoresis parameters and the bioconvection constant increase, the microorganism density along the profile also rises. [ABSTRACT FROM AUTHOR]

It is crucial to investigate fluid flow velocity and temperature distribution for theoretical and practical purposes. Determining the velocity and temperature distributions in fluid flows is necessary for designing effective heat exchange equipment, creating heat and thermomechanical modes of product treatment, and calculating heat losses in pipeline systems. The present article elaborates on the thermal analysis of Carreau fluid inside a horizontal passage. The influence of the small Peclet number and Brinkman number is also considered. The energy equation is tackled by Graetz's traditional approach for fixed wall temperature conditions. A MATLAB function bvp5c is employed for the numerical solution of the eigenvalue problem in the form of eigenvalues and related eigenvectors. Local Nusselt number and mean temperature are thoroughly elaborated under the influence of emerging parameters and displayed through several graphs. A numerical validation is also presented with already existing literature. The findings reveal that when the small values of Peclet number are taken into account, the axial conduction is dominant in upstream region. In addition, the flow index and Weissenberg number assist the temperature profile. [ABSTRACT FROM AUTHOR]

Thermotaxis, the movement in response to temperature gradients, is a widely observed phenomenon prevalent in various natural occurrences, spanning from biological processes to the migration of colloidal particles. Results from studies of thermotaxis may inspire the development of new technologies, such as sensors that mimic the navigation strategies of organisms that respond to temperature gradients. By adjusting temperature gradients through temperature modulation, microorganisms can be manipulated. Therefore, the main aim of this study is to investigate the effect of thermal modulation on biothermal convection in a layer of liquid that contains thermotactic microorganisms. In this study, we explore the impact of non-uniform, time-varying boundary conditions on the system. Our study involves an analysis of weak nonlinear stability based on the Ginzburg-Landau model, leading to the derivation of heat (Nusselt number Nu) and mass (Sherwood number Sh) transfer coefficients that are dependent on various system parameters. In-phase modulation (IPM) has a relatively weak effect on both heat transfer and mass transfer, which closely resembles the unmodulated scenario. On the contrary, in the cases of out-of-phase modulation (OPM) and lower bound modulation (LBM), significant changes in heat and mass transfer are observed. It has been determined that the Peclet number, a parameter characterizing thermotaxis, can either induce stabilization or destabilization within the system. TM instability. [ABSTRACT FROM AUTHOR]

It is proposed to determine the main parameters of the structure of flows in objects by velocity profile without taking response curves using the indicator method in heat and mass transfer apparatuses and reactors. A formula is derived for calculating the variance (central moment of the second order) and the flow structure function for a half-open vessel. An algorithm is also proposed for calculating the average residence time, the Peclet number of longitudinal diffusion for a one-parameter diffusion model, the number of cells and the differential response function of a combined model with a sequential connection of ideal displacement and mixing zones for a cell model. Moreover, calculation of the distribution density of the differential and integral response curves corresponding to a given velocity profile is provided. [ABSTRACT FROM AUTHOR]

In the present study, the thermal behavior of a longitudinal fin considering three types of heat transfer mechanisms (conduction, convection, and radiation) is investigated. For this research, thermal conductivity, heat source, and heat transfer coefficient are assumed nonindependent. A semianalytical scheme called the Galerkin Method is utilized for solving the dimensionless governing equation. The impacts of important physical variables like Peclet number, gradient of thermal conductivity, thermo‐geometric parameter, and radiation–conduction parameter on temperature profiles are analyzed comprehensively. The obtained results indicate that raising the thermo‐geometric parameter from 0 to 2 leads to a 32% reduction in the temperature profile. Also from the results, it can be found that a 28% increment in the temperature is observed by changing the gradient of thermal conductivity from 0 to 2. [ABSTRACT FROM AUTHOR]

We investigate crystallization-driven convection in carbon–oxygen white dwarfs. We present a version of the mixing length theory that self-consistently includes the effects of thermal diffusion and composition gradients, and provides solutions for the convective parameters based on the local heat and composition fluxes. Our formulation smoothly transitions between the regimes of fast adiabatic convection at large Peclet number and slow thermohaline convection at low Peclet number. It also allows for both thermally driven and compositionally driven convection, including correctly accounting for the direction of heat transport for compositionally driven convection in a thermally stable background. We use the MESA stellar evolution code to calculate the composition and heat fluxes during crystallization in different models of cooling white dwarfs, and determine the regime of convection and the convective velocity. We find that convection occurs in the regime of slow thermohaline convection during most of the cooling history of the star. However, at the onset of crystallization, the composition flux is large enough to drive fast overturning convection for a short time (∼10 Myr). We estimate the convective velocities in both of these phases and discuss the implications for explaining observed white dwarf magnetic fields with crystallization-driven dynamos. [ABSTRACT FROM AUTHOR]

A numerical study of the processes of heat and mass transfer in the furnace of a thermogravimetric analyzer was carried out, aimed at improving the accuracy of determining the kinetic characteristics of samples during their thermal transformations in different media. Validation of the model and prognostic estimates were carried out in relation to specially conducted thermogravimetric studies of the conversion of fossil and renewable carbon-containing raw materials in successive processes of decarbonization (combustion) and carbonation (mineralization of ash residue). The application of the study results allows to calculate the actual concentrations of the reagent over the sample uncontrolled by the device during pulsed switching of media and the actual temperatures of the sample during its thermochemical transformations. [ABSTRACT FROM AUTHOR]

Rivers, as water resources, are considered an origin of supply for many requirements of urban communities. River networks consist of many branches that connect at river confluences. Because pollutants usually enter the river in different situations from the upstream branches of river intersections, it is essential to investigate the mixing process through the river network. For this purpose, precise analytical and numerical models should be used to evaluate this phenomenon quantitatively. Based on the cell concept and separation of advection and dispersion operations, this study developed a new analytical relationship through the confluences of rivers. A physical model of the Y-shaped junction was created in the laboratory, and four inlet flow discharges 25, 21, 12, and 9 l/s and three initial concentrations of sodium chloride solution 80, 160, and 200 g/L were selected as study parameters. Then, the concentration-time curves along the sub-branches, the intersection, and the downstream of the river's main channel were taken at 2-second intervals. In order to evaluate the efficiency of the analytical model, the parameters of the model were first calculated by coding based on its framework and using the least squares method. Then the analytical curves were outlined versus the experimental results. It was observed that the presented model could produce double-peaked curves and also cover experimental data series precisely. The dispersion coefficients and the related time parameter in the presented model (T) were found to increase by moving downstream of the river junction. It was also observed that the Peclet numbers (Pe = xu/D ) are increased like dispersion coefficients by increasing the distance downstream of the confluence. In addition, the research results showed that increasing the residence time parameter in dispersion cells (T) causes growth in the dispersion coefficient, despite increasing the residence time in advection cells (β), compelling the movement of the pollutant breakthrough curves. [ABSTRACT FROM AUTHOR]

Inspired by significant physiological applications of peristaltic transport, a mathematical model for the peristaltic pumping of a Jeffrey nanofluid containing gyrotactic microorganisms through a flexible and vertical symmetric channel is investigated, along with the effects of thermal radiation, heat source/sink, chemical reaction, porous medium and Hall current. Swimming microorganisms in a model of non-Newtonian fluid has several biological and ecological benefits, including in the pharmaceutical industry, biofertilizers, biofuel technology, biosensors, etc. With these presumptions in mind, a conducting Jeffery fluid flow containing microorganisms via a porous vertical conduit is proposed. The expressions for the flow quantities are established by solving the governing equations of this study analytically using the homotopy perturbation method (HPM). A detailed examination is performed using the tables and graphical representations to comprehend the impact of significant components on this analysis. In addition, the results for Newtonian nanofluid are obtained as a special case and discovered that its velocity is lower than the Jeffrey nanofluid. It is observed that the best velocity distribution can be seen at larger thermal Grashof number and Darcy number. The size of the trapped bolus enhances with the increase of the Hall parameter. Furthermore, the density of the motile microorganism distribution declines for higher bioconvection Peclet number and bioconvection constant. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose an efficient numerical scheme to deal with heat transfer problems in pipe flow with a large length/diameter ratio. The generalized finite difference method (GFDM) is combined with a space stepping algorithm (SSA) for the solution. The SSA divides the solution domain into a number of overlapping sections in the length direction of the pipe. Due to the large Peclet number, the heat transport process is dominated by advection, which allows an approximate boundary condition to be applied at the downstream cross section. The problem is then solved section by section. Using the uniform distributed points, the solution matrix for each section does not change, and only the right hand side needs to be refreshed for the changing boundary conditions. This leads to a highly efficient scheme for problems with a large pipe length. To show the accuracy of the numerical scheme, a problem with available analytical solution is studied. Then the method is applied to problems of single pipe with different pipe wall temperature and flow Reynolds number, and concentric annular pipe. Numerical results confirm the stability and efficiency of the GFDM-SSA. The method can be applied to many real world transient heat transfer problems in which the pipe is heated or cooled along its length with arbitrary wall temperature for heat exchange and other purposes. [ABSTRACT FROM AUTHOR]

Quantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks. Plain Language Summary: Electrical and electromagnetic geophysical methods provide information about the spatio‐temporal distribution of average electrical conductivity of porous media. This property is affected by the transport of electrically conductive solutes, which unfolds over a wide range of spatial scales. However, when translating electrical data into solute concentration, almost all studies to date have ignored solute heterogeneity below the averaging volume inherent to geophysical measurements or modeling, leading to unphysical results. We introduce the mixing factor M, an electrical parameter that links small‐scale solute heterogeneity and average electrical conductivity, via a closed‐form expression depending on the small‐scale features of electric and solute concentration fields. We show that observation of the M‐tensor allows recovering the variance and anisotropy of the solute field in a time‐static setting. For diffusion‐limited transport, the time‐series of M help distinguishing the initial length scales of the fields, whereas for advective‐diffusive transport, these data help distinguishing the Peclet number. The presented framework helps to decode information about solute heterogeneity that is contained in geoelectrical measurements, while also avoid making biased hydrological estimates. Future venues of research will investigate how to incorporate M in available (hydro)geophysical modeling workflows. Key Points: Petrophysical parameter generalizing the high‐salinity limit of electrical conduction for heterogeneous fluid conductivity in porous mediaFormal expression for M provides framework to interpret impact of small‐scale fluid conductivity heterogeneity on electrical measurementsThe mixing factor M depends on geostatistical properties of solute concentration fields and thus on transport characteristics [ABSTRACT FROM AUTHOR]

This paper presents research on the mass dispersion and adsorption of organics present in tap water on powdered activated carbon (PAC) in a two-layer filter column. The adsorption rate depends on the difference between the concentration of organics and the equilibrium concentration. In homogeneous flocculators with simultaneous adsorption on PAC, the concentration difference is lower than in a filter column with PAC. Therefore, the utilization of the PAC's adsorption capacity in filters is higher than in homogeneous flocculators. PAC is introduced into the upper anthracite layer of a filter bed, while the bottom layer is a sand layer, which protects the underdrain system from becoming clogged with PAC particles. The sorbent wis introduced into the bed in the final phase of filter backwashing. The authors present a model of adsorption on PAC in a filter column. Both experiments and calculations confirmed a better utilization of PAC's adsorption capacity in the filter column compared to its utilization in a homogeneous flocculator. Three criterion equations were developed using dimensionless numbers, Re, Pe and Nu, as well as two similarity moduli related to a sorbent apparent density and an adsorption coefficient. Additionally, a relationship between the Peclet number (Pe) and the Reynolds number (Re) as well as the similarity modulus for the sorbent apparent density were determined for the mass dispersion process. The relationship between the diffusive Nuselt number (Nu) and the Re number as well as the similarity modulus for the sorbent apparent density were determined for the parameter describing an adsorbate permeation rate across a water–sorbent interface. The impact of the Re number and the similarity modulus for the sorbent apparent density on the Henry constant was also investigated. The criterion equations can be used to determine the adsorption model parameters; they may be helpful in designing a filtration system supplemented with PAC. In the capillary velocity range V x * ∈ 〈0.15·10−2; 0.72·10−2〉 m/s and with a change in the apparent density of the sorbent ρ p , s o r b from 3000 to 12,000 g PAC/m3 of the bed, as a result of the experimental tests carried out, it was established that the actual coefficient of longitudinal dispersion D x * varied in the range of 0.16·10−4 to 2.03·10−4 m2/s, the product of the constant mass transfer rate and the specific outer surface of sorbent k ⋅ a m varied in the range of 2.23·10−7 to 1.70·10−6 (m/s)·(m2/g PAC), while the Henry constant Γ* varied in the range of 7.24 to 44.20 1/m3 of sorbent and the Henry constant Γ varied in the range of 0.0012 to 0.0019 m3 of water/g PAC. [ABSTRACT FROM AUTHOR]

To assess the water quality within the distribution networks, simplified models are used, which adopt an advective–reactive approach and neglect diffusion–dispersion phenomena. Although such simplifications can be sufficiently accurate in complete turbulent uniform flow regimes, literature works demonstrated that they could produce wrong results in laminar and transitional regimes that are relevant when analysing low flows, dead-end pipes in looped distribution networks or service connections. On the other hand, advective simplification allows for considerable computational savings during the simulation of large networks. Therefore, a criterion is needed for better discriminate pipes in which the advective approach is sufficient or the diffusive approach is required. The present study aims to investigate the use of the Péclet number to discriminate the use of advective simplification both adopting the two-dimensional (2D) advection–dispersion equation and the one-dimensional (1D) cross-section averaged advection–dispersion equation. The numerical analysis was applied to a linear pipeline using the EPANET, 1D advective–dispersive–reactive, and EPANET-DD (Dynamic–Dispersion) models. The results showed the inadequacy of the Péclet number in discriminating the dominance of the advective–dispersive process in real systems, as it is linked to the pipe's length, regardless of the flow regime occurring on the pipeline. HIGHLIGHTS Application of Péclet number to the two-dimensional advection–dispersion equation and the 1D cross-section mean advection–dispersion equation to discriminate the use of advective simplification.; Complexity of contaminant transport mechanisms within water distribution networks, due to the critical role of diffusive-dispersive processes.;

It is of significance to investigate the effect of H 2 on the combustion of NH 3 /DME blends since NH 3 can partially decompose to produce hydrogen (H 2) in the combustion process. However, few studies were conducted on NH 3 /DME/H 2 mixtures, especially for flame instability. This work presents an experimental study of the flame instability of NH 3 /DME blends with H 2 addition. Experiments were conducted using the spherical constant-volume combustion method at φ = 0.7 – 1.4, T u = 298 K. The influences of NH 3 /DME blend ratio (B NH3/DME = 80/60, 60/40, 40/60, and 20/80), initial pressure (P u = 0.1 – 0.5 MPa), and H 2 fraction (X H2 = 0%, 20%, and 40%) on the flame instability were examined in detail. The results show that increasing either DME fraction or initial pressure can promote the hydrodynamic instability of NH 3 /DME/air flames because of the decreased flame thickness. For both X H2 = 0% and 20%, the cellular flame instability with B NH3/DME = 40/60 and 20/80 increases with increasing equivalence ratio. For X H2 = 40%, the flame instability shows a similar trend with B NH3/DME = 20/80, but the most unstable flame appears around stoichiometric combustion with B NH3/DME = 40/60. This is due to the compound effects of the diffusive-thermal imbalance and hydrodynamic instability for lean or rich fuel, while the diffusive-thermal instability can be neglected for stoichiometric combustion. Therefore, an effective control of H 2 or DME addition can help enhance the combustion performance of the fuel while reducing the occurrence of dangerous events caused by potential flame instabilities. In addition, critical parameters, i.e., critical flame radius r cr , critical Peclet number Pe cr , and critical Karlovitz stretch factor Ka cr were analyzed to quantify the onset of flame instability. This work provides insights into the flame instabilities of NH 3 /DME with H 2 addition. • Influence of H 2 additions on the flame instability of NH 3 /DME blends was studied. • The effect of the diffusive-thermal and hydrodynamic instability was discussed. • H 2 addition can enhance or weaken the flame instability of NH 3 /DME blends by controlling the fuel ratio. • Critical parameters were analyzed to quantify the onset of cellular instability. [ABSTRACT FROM AUTHOR]

Fins are extended surfaces that are designed to dissipate heat from hot sources to their surroundings. The different profiles of fins are used on the equipment surface to improve heat transfer. Fins are extensively used in refrigeration, solar panels, superheaters, electric equipment, automobile parts, combustion engines, and electrical equipment. On the basis of these applications, we study the thermal performances of magnetized convective–radiative‐rectangular fins with magnetized trapezoidal fins with internal heat generation. The shooting technique is used to numerically study the suggested model. It is revealed that magnetized trapezoidal fins transfer more heat than magnetized rectangular fins. It is also revealed that magnetized trapezoidal fins have higher thermal transfer competence than magnetized rectangular fins. When thermal conductivity, radiation–conduction number, and convection–conduction number increase, the fin's efficiency increases. In addition, a Hartmann number indicating the magnetic effect is found to improve heat transfer from the fins. Increasing the magnetism parameter from 0.1 to 0.3 reduced temperature by approximately 4.5%, changing internal heat generation from 0.1 to 0.5 increased temperature distribution by approximately 16%, and changing the Peclet number from 0.1 to 0.3 increased temperature distribution by approximately 15%. The effect of heat transfer coefficient, thermal radiation–conduction and convection–conduction, and dimensionless radiation are also investigated on the performance of the fins. [ABSTRACT FROM AUTHOR]

The series representation of the reactant concentration in one-dimensional advection-dispersion-reaction problems within a container of finite length is derived in a compact and computationally less complex form than other representations found in the literature. The initial concentration of the reactant is assumed to be uniform (C0), while the boundary conditions are assumed to be a constant reactant flux ( U C e ) at the inlet and a zero concentration gradient at the outlet of the container, where U is the average fluid velocity. The concentration is expressed in terms of the introduced constants a and b for the steady-state part, and In, Jn and Kn for the transient part of the response. The derived solution to the advection-dispersion-reaction problem can be readily generalized to include a uniform source/sink term (zero-order production rate σ) by making the replacements of C0 and C e with C 0 − σ / k and C e − σ / k , where k is the reaction rate constant, and by adding the particular solution σ / k. A simple form of the solution to the advection-dispersion equation with a source term is also derived; its transient part is expressed in terms of the integrals In and Kn only. The formulation of the analysis is cast in such a way that the same eigenfunctions and the same eigenvalue condition apply to all three considered cases, advection-dispersion-reaction with and without a source-term, and advection-dispersion with a source term, independently of the values of k and σ. [ABSTRACT FROM AUTHOR]

This study describes thermal transmission features across a gravity-driven bioconvection flow of the viscoplastic-type Casson nanofluid caused by a vertically rotating cylinder under gyrotactic microorganisms. The research further quantifies the impact of nonlinear thermal radiations, heat source/sink and convective interface on the temperature and heat transmission rate of a nanofluid rotating on a cylindrical surface. The Buongiorno two-phase model characterizing Brownian diffusion and thermophoretic properties is utilized to examine the nanoparticle's effect on the Casson nanofluid. A system of strongly nonlinear PDEs is converted into a system of ODEs by using the appropriate variables. The MATLAB technique is used to build a numerical solution for nonlinear flow equations. The influences of various parameters on the volumetric concentration of nanoparticles, velocities, thermal fields, and microorganism profiles are examined. The finding indicates that an upsurge in the bioconvection Lewis parameter causes declines in the microorganism profile. The thermal and solutal distribution of species increases with an increase in thermophoresis parameter estimations. Significant thermal transport is acquired with greater radiation impacts. The microorganism's distribution is improved with a larger Peclet number. [ABSTRACT FROM AUTHOR]

This note describes the development and testing of a novel, programmable reversing flow 1D (R1D) experimental column apparatus designed to investigate reaction, sorption, and transport of solutes in aquifers within dynamic reversing flow zones where waters with different chemistries mix. The motivation for constructing this apparatus was to understand the roles of mixing and reaction on arsenic discharging through a tidally fluctuating riverbank. The apparatus can simulate complex transient flux schedules similar to natural flow regimes The apparatus uses an Arduino microcontroller to control flux magnitude through two peristaltic pumps. Solenoid valves control flow direction from two separate reservoirs. In‐line probes continually measure effluent electrical conductance, pH, oxidation–reduction potential, and temperature. To understand how sensitive physical solute transport is to deviations from the real hydrograph of the tidally fluctuating river, two experiments were performed using: (1) a simpler constant magnitude, reversing flux direction schedule (RCF); and (2) a more environmentally relevant variable magnitude, reversing flux direction schedule (RVF). Wherein, flux magnitude was ramped up and down according to a sine wave. Modeled breakthrough curves of chloride yielded nearly identical dispersivities under both flow regimes. For the RVF experiment, Peclet numbers captured the transition between diffusion and dispersion dominated transport in the intertidal interval. Therefore, the apparatus accurately simulated conservative, environmentally relevant mixing under transient, variable flux flow regimes. Accurately generating variable flux reversing flow regimes is important to simulate the interaction between flow velocity and chemical reactions where Brownian diffusion of solutes to solid‐phase reaction sites is kinetically limited. Article impact statement: We developed a low‐cost programmable column experiment apparatus capable of automating reversing flows a range of flux magnitudes. [ABSTRACT FROM AUTHOR]

Dissolution and precipitation processes in reactive transport in porous media are ubiquitous in a multitude of contexts within the field of Earth sciences. In particular, the dynamic interaction between the reactive dissolution and precipitation processes and the solute transport is of interest as it is capable of giving rise to the emergence of preferential flow paths in the porous host matrix. It has been shown that the emergence of preferential flow paths can be considered to be a manifestation of transport self-organization in porous media as these create spatial gradients that distance the system from the state of perfect mixing and allow for a faster and more efficient fluid transport through the host matrix. To investigate the dynamic feedback between the transport and the reactive processes in the field and its influence on the emergence of transport self-organization, we consider a two-dimensional Darcy-scale formulation of a reactive-transport setup, where the precipitation and dissolution of the host matrix are driven by the injection of an acid compound, establishing local equilibrium with the resident fluid and an initially homogeneous porous matrix, composed of a calcite mineral. The coupled reactive process is simulated in a series of computational analyses employing the Lagrangian particle-tracking (LPT) approach, capable of capturing the subtleties of the multiple-scale heterogeneity phenomena. We employ the Shannon entropy to quantify the emergence of self-organization in the field, which we define as a relative reduction in entropy compared to its maximum value. Scalability of the parameters, which characterize the evolution of the reactive process, with the Peclet number in an initially homogeneous field is derived using a simple one-dimensional ADRE model with a linear adsorption reaction term and is then confirmed through numerical simulations, with the global reaction rate, the mean value, and the variance of the hydraulic-conductivity distribution in the field all exhibiting dependency on the reciprocal of the Peclet number. Our findings show that transport self-organization in an initially homogeneous field increases with time, along with the emergence of the field heterogeneity due to the interaction between the transport and reactive processes. By studying the influence of the Peclet number on the reactive process, we arrive at a conclusion that self-organization is more pronounced in diffusion-dominated flows, characterized by small Peclet values. The self-organization of the breakthrough curve exhibits the opposite tendencies, which are observed from the perspective of a thermodynamic analogy. The hydraulic power, required to maintain the driving head pressure difference between the inlet and outlet of the field, was shown to increase with the increasing variance, as well as with the increasing mean value of the hydraulic-conductivity distribution in the field, using a simple analytic model. This was confirmed by numerical experiments. This increase in power, supplied to the flow in the field, results in an increase in the level of transport self-organization. Employing a thermodynamic framework to investigate the dynamic reaction–transport interaction in porous media may prove to be beneficial whenever the need exists to establish relations between the intensification of the preferential flow path phenomenon, represented by a decline in the Shannon entropy of the transport, with the amount of reaction that occurred in the porous medium and the change in its heterogeneity. [ABSTRACT FROM AUTHOR]

The diffusive wave model is one of the simplified forms of Saint-Venant equations, and it is often used instead of the full model. In this paper, we present an analytical solution for the linearized diffusive wave model represented by a simultaneous system of two first-order partial differential equations focused on spatial variation of a lateral inflow in a finite channel. A concentrated lateral inflow from a small-width tributary is considered through the Dirac delta function. We use the Laplace transform method to solve these equations analytically. Two types of upstream boundaries are considered here in the form of a flow-discharge hydrograph and a flow-depth hydrograph, while keeping a flow-depth hydrograph as the downstream boundary. Using unit-step responses of the lateral inflow, the effect of different boundaries on the flow-depth responses and the flow-discharge responses is studied for different values of the Peclet number ( P e ). The flow depth is observed to be more sensitive to the downstream boundary and other parameters used in this work. Consideration of the flow depth as the upstream boundary reflects the effect of all the parameters on the unit-step responses presented. These responses are compared with the available semi-infinite channel responses, which are found to be an inappropriate substitute for the finite channel responses for P e < 5 which implies that the downstream boundary cannot be ignored for these cases. However, for the case P e > 5 , although the semi-infinite channel responses are found to satisfactorily estimate the discharge along the entire channel, they can approximate the flow depth at the locations closer to the upstream boundary only. [ABSTRACT FROM AUTHOR]

The effective diffusion of a solute in a rectangular two-dimensional channel is experimentally studied. We experimentally examine the effective diffusion of Rhodamine B dissolved in water oscillating in a rectangular Hele–Shaw cell. The concentration of Rhodamine B in water is measured by the intensity of its fluorescence emission. In particular, we consider two problems: (i) effective diffusion of solute in water oscillating in a two-dimensional rectangular channel (Hele–Shaw cell) and (ii) effective diffusion of solute in pores between monosized hard spheres randomly packed in a rectangular Hele–Shaw cell. It is revealed that the rate of solute mass transfer exceeds the molecular diffusion rate in both cases. It has been demonstrated that when water oscillates between parallel walls, diffusion is accelerated by Taylor dispersion with the effective diffusion coefficient D eff exceeding the molecular diffusion coefficient D m by 1–2 orders of magnitude. The effective diffusion coefficient D eff depends only on the relative amplitude but not on the frequency of the fluid oscillations in the studied range of frequencies and amplitudes. When the fluid oscillates in the pores of the porous medium, solute transport is faster than in the case of Taylor dispersion. Here, the effective diffusion coefficient depends on both the frequency and amplitude of oscillations. The analysis shows that the experimental data obtained at various frequencies and amplitudes of oscillations are consistent with the relation D eff / D m ∼ P e 2 (Pe is the Peclet number). We suggest that the enhanced solute mass transfer is associated with the time-averaged fluid flows that arise due to spatial heterogeneity of the amplitude of water oscillations in the pores between randomly packed hard spheres. [ABSTRACT FROM AUTHOR]

This study explores the impact of axial conduction and viscous dissipation on heat transfer inside a tube by employing the Casson fluid model. A semianalytical approach is employed to handle the considered problem. The application of the separation of variable technique converts the heat equation into a set of ordinary differential equations. A built‐in function bvp4c in Matlab is adopted for numerical solutions in terms of eigenvalues and eigenfunctions. The obtained results are thoroughly discussed through pictorial representations. The finding shows that the Peclet and Brinkman numbers could not be ignored where an accurate temperature is essential for the final product. The both Peclet numbers and Brinkman numbers have a strong influence on the entrance temperature profile of the tube. In addition, the viscoplastic parameter raises the local Nusselt number in developing and fully developed regions of the tube. This analysis may be helpful in the advancement of thermal devices that are used to diagnose many diseases. [ABSTRACT FROM AUTHOR]

The researchers have reported numerous numerical and analytical efforts in recent years to understand technological and industrial processes. Microelectronics, heat exchangers, solar systems, energy generators are just a few numbers of recent applications of heat and mass transfer flow. Two dimensional steady incompressible MHD flow of micropolar fluid over an inclined permeable surface with natural convection is investigated in this research work, with the contribution of thermal radiation under thermophoretic effects as a heating source. As a result of this infestation, mathematical model of the problem equations based on energy, momentum, angular momentum, mass, and concentration are developed. To convert the current problem into dimensionless ordinary differential equations, non-dimensional variables have been assigned. The evolved mathematical model is numerically solved aside utilizing Shooting technique along with 4th order R-K method solver in MATHEMATICA. The outcomes are displayed and analyzed through figures and tables. Finally, skin friction, Nusselt and Sherwood numbers are tabulated for distinct parameter-factors. To validate the accuracy of numerical method used in this problem, we compare the numerical results with available findings, and it is evident that the outcomes of current work are in good agreement with those reported in the literature. Improving the values of thermophoresis, radiation factors, and Schmidt number, declines the velocity. Higher values of radiation parameter, thermophoresis parameter, the microrotation increase near plane-surface and gradually diminishes far away from plane-surface. Profiles of temperature enhances with increasing the viscous dissipation parameter. Profiles of the concentration decreases by increasing the thermophoresis parameter and Schmidt number. Profiles of Skin friction and mass transfer rate decreases for magnetic field, thermal radiation and Schmidt number values. [ABSTRACT FROM AUTHOR]

The paper deals with the combined effect of non-Newtonian saturating fluid and horizontal flow rate on the thermal convection in a highly permeable, porous plane layer saturated with a power-law model. Asymmetric boundary conditions are assumed, with a cooled free surface at the top and a heated, impermeable, rigid wall at the bottom. The generalised Forchheimer equation is employed to model the power-law fluid movement. Convection cells emerge in the power-law fluid because of vertical temperature gradient imposed by the thermal boundaries. The onset of this scenario can be studied using linear stability theory, which leads to an eigenvalue problem. The latter is solved either numerically, employing shooting schemes, or analytically, using one-order Galerkin approach. The present study is considered an extension of the classical Prats problem. When the Peclet number, which defines the flow rate, is negligible, the configuration switches to the special case of Darcy-Rayielgh instability. The results show that the form drag exhibits a stronger stabilizing influence in shear-thinning fluids compared to shear-thickening and Newtonian ones since the saturating fluid is described by the power-law model. This scenario appears in the specific range of the Peclet number. In general, this investigation can be used to understand the heat transfer process in subsurface hydrocarbon reservoirs where the fluid may exhibit non-Newtonian behaviour. [ABSTRACT FROM AUTHOR]