Homogeneous-heterogeneous Reactions Research Articles

Unusual facet and co-catalyst effects in TiO2-based photocatalytic coupling of methane

Photocatalytic coupling of methane to ethane and ethylene (C2 compounds) offers a promising approach to utilizing the abundant methane resource. However, the state-of-the-art photocatalysts usually suffer from very limited C2 formation rates. Here, we report our discovery that the anatase TiO2 nanocrystals mainly exposing {101} facets, which are generally considered less active in photocatalysis, demonstrate surprisingly better performances than those exposing the high-energy {001} facet. The palladium co-catalyst plays a pivotal role and the Pd2+ site on co-catalyst accounts for the selective C2 formation. We unveil that the anatase {101} facet favors the formation of hydroxyl radicals in aqueous phase near the surface, where they activate methane molecules into methyl radicals, and the Pd2+ site participates in facilitating the adsorption and coupling of methyl radicals. This work provides a strategy to design efficient nanocatalysts for selective photocatalytic methane coupling by reaction-space separation to optimize heterogeneous-homogeneous reactions at solid-liquid interfaces.

Thermal and reactive effects in nanofluid flow around a contracting cylinder under magnetic field influence

This study investigates the dynamic behavior of natural ester-based ferrous oxide (Fe3O4) nanofluid flow around an unsteady contracting cylinder under the influence of a magnetic field, heat generation, and homogeneous-heterogeneous reactions. The governing equations for the flow, heat transfer, and chemical reactions are solved numerically using appropriate mathematical models. The bvp4c built-in MATLAB package is applied to address the complexity of the problem. The effects of magnetic field, heat generation, and reactive chemistry on the flow field, temperature distribution, and species concentration profiles are analysed comprehensively. As part of the validation process, we validate the reliability of our findings by comparing them to established benchmarks. Motivated by the increasing interest in environmentally friendly and sustainable fluid mediums, natural esters are chosen as the base fluid due to their biodegradability, low toxicity, and excellent insulating properties. This research aims to provide valuable insights into optimizing processes involving nanofluid flow in magnetohydrodynamic systems with reactive heat generation, utilizing natural esters as a promising alternative to conventional fluids. Insights gained from this study offer potential applications in various engineering and industrial contexts, contributing to the advancement of eco-friendly technologies.

Numerical spectral approach for studying activation energy behavior in viscoelastic fluid flow through non-Darcian medium

The work examines the effects of MHD incompressible viscoelastic fluid under nonlinear thermal radiation while flowing in a non-Darcy porous medium. The utilization of the Darcy-Brinkmann-Forchheimer model has thus been implemented in the formulation of the momentum equation. The study posits the existence of a chemical phenomenon which involves elements A and B as two chemical species. The diffusion coefficient of chemical species exhibits inequality when considered for viscoelastic fluid. Numerical solutions are generated using SRM, spectral relaxation technique for governing flow problems. The current algorithm is formulated and implemented using the computational software MATLAB. The results exhibit a considerable degree of agreement with formerly established numerical outcomes within the framework of a specific scenario. The observations from this study provide evidence that chemical species B operates as a catalyst in a subsurface environment that is oriented horizontally. As a result, the connection between the homogeneous-heterogeneous scheme can be observed in the context of isothermal cubic autocatalytic occurrences and processes of the first order, subsequently. The utilization of the heterogeneous reaction parameter offers notable advantages in reducing the concentration of the bulk-fluid while simultaneously enhancing the concentration of the catalyst situated over the surface. The current findings contribute to the exploration of the computational study of diffusivities in MHD viscoelastic fluid flow. Specifically, this research inquires the effects of nonlinear thermal radiation and homogeneous-heterogeneous reactions.

Dynamic interactions in MHD Jeffrey fluid: Exploring peristalsis, electro osmosis and homogeneous/heterogeneous chemical reactions

This paper investigates the behavior of magnetohydrodynamic (MHD) peristaltic flow with electroosmosis. The Jeffrey fluid in microchannel under the influence of homogeneous-heterogeneous chemical reaction has been taken. The heat absorption and nonlinear radiation are also scrutinized here. This study contributes to the fundamental understanding of complex fluid dynamics in microscale systems and offer valuable insights for designing and optimizing microfluidic devices. In the framework of mathematical simulation, the relevant dimensional nonlinear equations are reduced into dimensionless equations by using linear transformations. Thus Debye-Hückel linearization has been employed. The streamline approach with mathematical modelling has been performed within the limits of δ≪1 and Re→0. The appropriate equations for temperature and concentration with boundary conditions are solved by using perturbation approach whereas, the exact solution is found for velocity equation. A graphical depiction of crucial physical characteristics on velocity, temperature, concentration and streamlines are reported in the last section. It is observed that the velocity distribution decreases for the higher value of M (0.5≤M≤2) however, it increases for the escalating values of Uhs (−0.5≤Uhs≤1.5). When Rn(0.1≤Rn≤0.6) gets stronger then temperature profile decreases. It is noticed that the concentration profile decays owing to enhancement in Sc(−0.5≤Sc≤1.5). As the M (0.5≤M≤2) increases, the size of trapped bolus decreases. Escalating values of temperature ratio parameterθw(1.0≤θw≤1.6)enhances the Nusselt number. The novelty of this study lies in the comprehensive analysis of multiple complex phenomena in a single framework. The interplay between MHD electroosmotic flow, homogeneous heterogeneous chemical reactions, peristalsis, nonlinear thermal radiation, heat absorption and no-slip condition has not been explored in previous research.

Numerical and artificial intelligence analysis of squeezing flow between parallel disks under complex physical fields

This study presents the time-dependent squeezing flow between parallel discs under the influence of various physical processes such as magnetohydrodynamics, micropolarity, thermophysics, homogeneous-heterogeneous chemical reactions, and bioconvection. The slip and permeability effects are considered at the boundaries. The nonlinear system is simplified through scaling transformations and subsequently solved numerically. Besides, an artificial neural network (ANN) model is developed to predict the values of skin-friction coefficients, heat transfer rates, and mass transfer rates at both discs. The performance of the ANN model is validated against the computational results, demonstrating robustness with correlation coefficients being almost close to 1. The ANN model performs more robustly for instance, skin-friction coefficient model revealed correlation (R) equaling 0.99775 and 0.99537 for the test data of the lower and upper discs, respectively. The values for heat and mass transfer observe as 0.99999, 0.99938, and 0.99839, 0.99167 for the test data of lower and upper discs. Parametric and sensitivity analyses produce results that are comparable to the numerical findings. Graphical and tabular representations are provided for various dimensionless parameters. Results indicate that the developed model is reliable and capable of accurately predicting multiple physical processes.

Role of catalytic reactions in a flow-induced due to outer stationary and inner stretched coaxial cylinders: An application of Probabilists’ Hermite collocation method

This paper investigates the impact of homogeneous-heterogeneous chemical reactions on the flow between the coaxial cylinders with heat generation/absorption. From an engineering perspective, in energy absorber design for the shrinking and expanding of a circular metal tube in the production of extruding materials by stretching cylinders designing with great care is necessary to regulate skin friction and heat transfer rate. Studying processes in confined geometries enhances the basic knowledge of chemical kinetics and fluid dynamics. Researchers may increase the chemical processes efficiency/heat transfer activities by designing systems with an optimized flow and analysing the effects of reactions on flow. Both cost reductions and higher-quality products may result from this optimization. This research may yield insights with far-reaching implications across multiple disciplines. The modelled equations are transformed into ordinary differential equations by employing apt similarity transformations and obtained equations are solved using the collocation method with Probabilists’ Hermite polynomial. Graphs illustrating the variation of velocity, thermal, and concentration profiles have been plotted using the influence of various parameters. The increase in curvature parameter causes the velocity and thermal profile upsurge. The rise in heat source/sink parameter improves the heat transport. As the heterogeneous and homogeneous parameters upsurge, the concentration profile decreases.

Numerical computation of magnetic field with melting heat and homogeneous-heterogeneous chemical reaction effects on oblique stagnation flow of variable viscosity micropolar Fe3O4 nanofluids

The complex micro-structural characteristics of electro-conductive sol gel materials require simultaneous consideration of magneto-hydrodynamics, micro-rheology and also physico-chemical phenomena. In this editorial, a mathematical model is therefore developed to simulate the steady-state, oblique (non-orthogonal) stagnation flow of electro-conductive micropolar magneto-nano-liquid flow impacting on an extending horizontal plane under the impact of transverse magnetic field. To capture the sophisticated physico-chemistry, the simultaneous presence of homogeneous and heterogeneous chemical reactions is considered. Viscosity depending upon temperature is taken into consideration with Reynolds’ exponential model. Tiwari-Das and Maxwell-Garnett nano-liquid models are deployed which modifies density, thermal conductivity and electrical conductivity with volume fraction of nano-sized particles.

Insight of mixed convectional heat transport in molybdenum disulfide-water nanofluid flow on moving vertical permeable plate with homogeneous-heterogeneous reactions

This analysis is framed to take care of the high heat transfer demand from various application prospects and in this context nanofluid may be in consideration because nanofluids are well-known liquids with higher heat transfer capabilities. Here, a mixed convection flow of Molybdenum disulfide-water (MoS2-H2O) nanofluid on a moving vertical plate is examined when there are chemical reactions. Nanofluid problem is investigated using Tiwari and Das model, and numerically solved by “bvp4c” method. For the considered effects in the study, overshoots in temperature profile of nanofluid are observed. Momentum and thermal layer thicknesses become thinner with suction and thicker with blowing. Temperature overshoot is higher for blowing cases. Enhanced homogeneous–heterogeneous reactions lead to rise of the concentration boundary layer’s thickness. Also, magnitude of surface-drag force decays and cooling rate enhances with MoS2-H2O nanofluid mixed convection. For weaker suction and for blowing, cooling of nanofluid is faster with larger volume fraction of nanoparticles, but contrast results are obtained for greater suction. Importantly, compared to the homogeneous reaction, the heterogeneous reaction exhibits more impactful influences on flow and heat-mass transport characters.

Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid

Abstract With particular attention to the effects of an electromagnetically induced resistive force on homogeneous–heterogeneous processes and the related homogeneous heat effects, the Casson fluid flow towards a stretching sheet at the magnetohydrodynamic stagnation point is investigated in detail. In this situation, the Laplace approach helps decipher the subtleties of the first-order kinetics governing the fluid’s motion. Notably, the fluid dynamics are largely determined by the homogeneous behaviour expected in the surrounding environment, forming a strong correlation between catalyst temperature on the wall and surface activity. Using conventional differential systems, our analysis gains a great deal from the modified Laplace decomposition method, which allows non-linear systems to be computed and examined. In order to improve understanding, numerical findings are included, and graphs are skillfully used to examine the subtleties of different factors. The in-depth examination also includes the complicated patterns of concentration and temperature, providing insightful information on the intricate interactions between forces and effects in this dynamic system.

Impact of induced magnetic field on Darcy–Forchheimer nanofluid flows comprising carbon nanotubes with homogeneous-heterogeneous reactions

The appealing traits of carbon nanotubes (CNTs) encompassing mechanical and chemical steadiness, exceptional electrical and thermal conductivities, lightweight, and physiochemical reliability make them desired materials in engineering gadgets. Considering such stimulating characteristics of carbon nanotubes, our goal in the current study is to scrutinize the comparative analysis of Darcy–Forchheimer nanofluid flows containing CNTs of both types of multi and single-wall carbon nanotubes (MWCNTs, SWCNTs) immersed into two different base fluids over a stretched surface. The originality of the model being presented is the implementation of the induced magnetic field that triggers the electric conductivity of carbon nanotubes. Moreover, the envisioned model is also analyzed with homogeneous-heterogeneous (h-h) chemical reactions and heat source/sink. The second-order slip constraint is assumed at the boundary of the surface. The transmuted high-nonlinearity ordinary differential equations (ODEs) are attained from the governing set of equations via similarity transformations. The bvp4c scheme is engaged to get the numerical results. The influence of different parameters is depicted via graphs. For both CNTs, the rate of heat flux and the surface drag coefficient are calculated using tables. It is highlighted that an increase in liquid velocity is witnessed for a varied counts volume fraction of nanoparticles. Also, Single-wall water-based carbon nanotube fluid has comparatively stronger effects on concentration than the multi-walled carbon nanotubes in water-based liquid. The analysis also indicates that the rate of heat flux and the surface drag coefficient are augmented for both SWCNTs and MWCNTs for different physical parameters. The said model is also validated by comparing it with a published result.

Irreversibility and nanomaterials shape consequences on peristalsis of magneto hybrid nanofluid via curved configuration with homogeneous–heterogeneous chemical reactions

Over the last decade, research on nanofluids has grown at a breakneck pace. As part of their nanofluid research, researchers have recently attempted to use hybrid nanofluids, made by combining different nanomaterials. The novelty of this analysis is to inspect the consequences of entropy generation on the peristalsis of a hybrid nano-liquid via a curved conduit with homogeneous and heterogeneous chemical reactions. Hybrid nanofluid is formed of copper and iron oxide nanomaterials added to water. Furthermore, the simplified model also considered the Hall current, viscous dissipation, and electrical resistance heating effects. The Hamilton–Crosser thermal conductivity model is used to study the nanomaterials shape effects (i.e. sphere, platelet, and blade) on the thermal features of hybrid nano-liquids. Mathematical expressions for the flow problem are simplified by employing the small wave and Reynolds numbers assumptions, which are then resolved analytically and numerically. Analytical results are used to scrutinize the impacts of several included quantities on the flow and thermal characteristics, chemically reactive concentration, and entropy creation. It is found that with a rise in Hartmann number, the velocity reduces, whereas an improvement is noted in temperature and entropy production for large values of Hartmann number. The noteworthy discoveries indicate that hybrid nano-liquids exhibit enhanced thermal efficiency when compared to conventional nanofluids. Specifically, the introduction of a small quantity of ferrous oxide nanoparticles into the copper–water nanofluid led to less than 2% increase in the thermal transport rate. Additionally, it was observed that spherical-shaped nanoparticles generate more heat in comparison to platelets and blade-shaped nanoparticles. Furthermore, the homogenous reaction parameter and Schmidt number lead to a drop in the concentration profile.

Hall current and ion slip effects on a ternary hybrid nanofluid flow over a bidirectional surface with chemical reaction and Cattaneo–Christov heat flux

The interaction between fluid flow and magnetic fields finds real-life applications in various industries, including semiconductors, fusion energy, plasma processing, and spacecraft propulsion. In this study, our objective is to investigate the behavior of a ternary hybrid nanofluid as it flows over a surface stretched in two directions. We consider the amalgamation of Hall current and ion slip effects, as well as homogeneous–heterogeneous reactions. The flow is influenced by Cattaneo–Christov heat flux, heat generation/absorption, and slip and convective conditions at the surface boundary. This ternary hybrid nanofluid comprises three types of nanoparticles—silicon carbide (SiC), copper oxide (CuO), and titanium oxide (TiO2)—suspended in a base fluid of diathermic oil (DO). We employ numerical methods to solve this system, utilizing the bvp4c function in MATLAB software. The results are presented graphically, demonstrating the correlation between key parameters and associated profiles. The findings reveal that the thermal profile diminishes with increasing Biot number but improves with the thermal relaxation effect. Furthermore, it is examined that the performance of the ternary hybrid nanofluid flow surpasses that of both hybrid and simple nanofluid flows. To corroborate our model, we provide a comparison with a published work in a limiting case within this study.

Homogeneous-heterogeneous reactions on Darcy-Forchheimer nanofluid flow system

The use of artificial neural networks (ANNs) to solve complex fluid dynamics problems has revolutionized computational approaches. This article explores novel ANN solutions for fluid problems. ANNs have demonstrated unmatched effectiveness in comprehending and forecasting fluidic behaviors, from mimicking complex fluid flow trends to optimizing structures for dynamics. This study emphasizes the significance of neural networks in revolutionizing our understanding and control of fluidic systems by using ANNs and Bayesian Regularization. This study examined the 3D Darcy-Forchheimer stretching flow (TDDFSF) of nanofluid under convective conditions along with homogeneous and heterogeneous reactions by employing the scheme of Bayesian Regularization with the procedure of backpropagation in neural networks (SBR-BNNs). The flow is influenced by Brownian diffusion, thermophoresis and zero nanoparticles mass flux condition. The PDEs given in this model are converted into nonlinear ODEs. Results from MSE, regression analysis, and error histogram are used to verify the performance of SBR-BNNs. The absolute errors lie in the ranges up to 10−9, which depict the worth of the solver SBR-BNNs. The absolute error measures the discrepancy between the values actually observed and those predicted by the SBR-BNNs model. SBR-BNNs' high precision in TDDFSF models can lead to more effective and reliable solutions.

Numerical simulation for MHD flow of Powell Eyring nanofluid with heterogeneous–homogeneous reactions, Arrhenius energy over a variable thickness stretching surface

The paper deals with the viscous incompressible flow of Powell Eyring type nanofluid over a variable thicker stretching surface induced by heterogeneous-homogeneous reaction and Arrhenius activating energy in a porous medium. Brownian motion and thermophoresis effect also considered to define flow regime. Boundary layer approximations of the governed flow are described by the partial differential equations which are laidback to handle by reducing them into coupled nonlinear ordinary differential equations. A MATLAB package BVP 4c is used to simulate the equations very contentedly to describe the behavior of several parameters graphically. Impact of several governing parameters are discussed. Rationality of the resolution is scrutinized by the comparison with previous literature in Tables 1 and 2. Numerical values of the Nusselt number and Sherwood parameters are discussed in Table 3. velocity profile diminishes for magnetic parameter, variable thickness, first slip and second slip parameters. while uplifted for mixed convection parameter. Temperature profile tumbling for Prandtl number and uplifted for radiation parameter, Brownian motion, thermophoretic effects, Grashof number and Magnetic field effects. Concentration profile declines for Schmidt number, chemical species and homogeneous heterogenous parameters.

Numerical investigation of homogeneous–heterogeneous reactions in 3D MHD non-Newtonian hybrid nanofluid with heat source and shape factor in permeable media over a stretching sheet

Numerical investigation of homogeneous–heterogeneous reactions in 3D MHD non-Newtonian hybrid nanofluid with heat source and shape factor in permeable media over a stretching sheet

A comparative analysis of ternary-hybrid nanofluid flows through a stretching cylinder influenced by an induced magnetic field with homogeneous–heterogeneous reactions

This study investigates the flow of three different ternary hybrid nanofluids (THNFs) over a stretching cylinder in a Darcy–Forchheimer permeable medium. The THNFs are made of a mixture of silver, titanium dioxide, and graphene oxide nanoparticles dispersed in water, kerosene oil, and engine oil, separately. The study compares the behavior of the three THNFs and considers the effects of an induced magnetic field, homogenous–heterogeneous reactions, slip boundary conditions, and convective conditions. A bvp4c package of MATLAB software is engaged to find the numerical solution of the modeled equations system and the outcomes are displayed through graphs. It is witnessed that large estimates of the curvature parameter boost the fluid velocity and temperature. Additionally, the surface drag coefficient improves with increasing Darcy–Forchheimer effect. Of the three THNFs, the one with kerosene oil as the base fluid has the best performance. It is witnessed that for the heat transfer rate for engine oil is 19.14% more in comparison to kerosene oil. Similarly, it is 12.83% higher than water. The same is the case for and In addition, the volume fraction of nanoparticles decreases the velocity profile, while the Biot number increases the thermal profile. The chemical reaction parameter decreases the concentration profile. This is justified by comparing the results with previous studies.

Response surface methodology in optimizing heat transfer rate for homogeneous–heterogeneous reactions with thermal radiation effect on the micropolar nanofluid

The non-Newtonian characteristic of the fluid flow phenomena has several applications in industries, engineering gadgets, biomedical sectors, etc. Based upon the aforementioned role, the present work deals with the nanofluid flow of micropolar fluid through an elongated surface is investigated. Further, the influence of radiating heat due to thermal radiation, and nanoparticle concentration is presented which are vital for the heat transfer enhancement. However, the inclusion of homogenous as well as heterogeneous chemical reactions enriches the study. Additionally, carbon nanotube (CNT) nanoparticles such as “Single-Wall Carbon Nanotube (SWCNT) and Multi-Wall Carbon Nanotube (MWCNT)” nanoparticles are used in water to perform the behavior of different nanofluids. The designed model with dimensional form is developed by converting these to dimensionless forms with the help of similarity transformation rules. The finalized transformed equations are handled numerically with the help of the shooting-based Runge-Kutta-fourth-order technique in a MATLAB environment. The proposed study became novel due to the statistical analysis for optimizing heat transfer rate for several components using “Response Surface methodology” based on the “Central Composite Design” model. Further, the ANOVA (Analysis of Variance) test is carried out for the best-fit model which is beneficial for the regression analysis. The exact solution for the velocity profile using the proposed method is validated by comparing it with a previously published numerical result in some limited cases, and an excellent agreement is established. However, the observation shows that the particle concentration of both the CNT particles augments the axial velocity and fluid temperature whereas reverse impact is rendered for the angular velocity.

COMPUTATIONAL STUDY OF UNSTEADY PULSATILE BLOOD FLOW THROUGH A POROUS MULTI-IRREGULAR VERTICAL STENOSED ARTERY: IMPACTS OF HOMOGENEOUS–HETEROGENEOUS REACTIONS

Homogeneous and heterogeneous reactions are significant because many chemically reactive systems, such as biochemical systems, involve both types of reactions. This paper sheds light on the effects of homogeneous–heterogeneous reactions on magnetohydrodynamic blood flow through the catheterized multi-irregular vertically stenosed artery in non-Darcy porous media. The governing partial differential equations are simplified using mild stenosis approximations and then transformed into the computational domain to simplify the numerical calculations. It has been noticed that the fluid velocity and the flow rate go to their maximum values after a short time, and they decrease with fluctuation in the case of pulsating, but in the case of nonpulsatile, the behavior is steady. Moreover, an increase in the homogeneous heat reaction parameter decelerates the blood velocity, the flow rate and elevates the fluid temperature. Furthermore, the concentration reaches the steady state faster in the absence of a homogeneous thermal reaction.

Effectiveness of thermal radiations and homogeneous–heterogeneous reactions in Maxwell flow field across a rotating cylinder

This paper investigates the impact of cubic autocatalysis on energy transport in Maxwell fluid flow induced into a rotating cylinder inspired by a solar radiative surface. The homogeneous-reaction is assumed to be furnished by the kinetics of isothermal cubic autocatalytic and the heterogeneous reaction by kinetics of first order. To prevent induced axial secondary flow, the cylinder's rotation is maintained at a constant rate. The characteristics of thermal radiation are also investigated to regulate the pace of heat transmission. A magnetic beam is projected in the upward radial direction to control the fluid momentum. A suitable flow ansatz is used to convert the entire physical problem of thermal energy transmission and fluid flow from partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). Results obtained numerically with the bvp4c approach are presented graphically and explained physically. It is observed that by flourishing the Reynolds parameter, the penetration depth decreases. Further, when the thermal relaxation period increases, the temperature field degrades. Moreover, when the homogeneous–heterogeneous reaction's strength is increased, a reduction in fluid concentration is shown.

Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source

Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source