Cross-diffusion Effects Research Articles

Model order reduction for the cross-diffusive Brusselator Equation

The cross-diffusive Brusselator equation is a reaction-diffusive system that models complex chemical and biological process with both self-diffusion and cross-diffusion effects. These equations exhibit rich spatiotemporal dynamics, including Turing patterns and instability-driven pattern formations. Despite its significance, the computational cost of solving high-dimensional discretized versions of the cross-diffusive Brusselator equation can be prohibitive, particularly in parameter-dependent or long-time simulations. This study presents a model order reduction (MOR) framework tailored to the Brusselator equation, leveraging Proper Orthogonal Decomposition (POD) combined with Galerkin projection along with the Discrete Empirical Interpolation Method (DEIM) and the Dynamic Mode Decomposition Method (DMD) to efficiently approximate nonlinear dynamics. The reduced models are constructed to preserve key features of the original system, including stability and accuracy, while achieving substantial computational savings. Numerical experiments validate the proposed approach, demonstrating its effectiveness in capturing the essential dynamics of the Brusselator equation under various parameter settings. These findings provide a robust pathway for efficient simulation and analysis of reaction-diffusion systems in scientific and engineering applications.

Chemical Reaction and Cross Diffusion Effects on Heat and Mass Transfer Characteristics of Viscoelastic Oil-Based Nanofluid Over a Porous Nonlinear Stretching Surface

The impact of chemical reaction and cross diffusion on heat and mass transport characteristics of viscoelastic flow of Al2O3 and CuO oil-based nanofluids past a porous nonlinear stretching surface has been examined. Similarity transformation was used to transform the governing partial differential equations into coupled nonlinear ordinary differential equations and solved numerically by employing the fourth order Runge-Kutta algorithm with a shooting method. Results for the entrenched parameters controlling the flow dynamics have been tabulated and illustrated graphically. The results foundCuO-oil based nanofluid to exhibit higher mass transfer rate and lower heat transfer rate and skin friction coefficient than Al2O3-oil based nanofluid under the same viscoelastic condition. This indicates that CuO-oil based nanofluid can be used as the working fluid in mechanical dampers.

Optimization using Response Surface Methodology for Eyring-Powell Fluid Flow with Cattaneo-Christov Heat Flux and Cross Diffusion Effects

The optimization of heat transfer in engineering applications has significant implications for product performance and efficiency. This study investigates the flow and heat transfer characteristics of Eyring-Powell fluid over a curved sheet, incorporating complex phenomena such as magnetic dipoles, Cattaneo-Christov heat flux, and cross-diffusion effects. Navier's slip and melting boundary conditions are applied to model realistic physical constraints. The study employs response surface methodology (RSM) and sensitivity analysis to evaluate the parametric influences on skin friction and the Nusselt number, providing statistical insights into their behavior. Using similarity transformations, the governing partial differential equations are converted into ordinary differential equations, which are numerically solved using the Runge-Kutta-Fehlberg 4th-5th order method. Key findings include the reduction in velocity due to higher Eyring-Powell parameters, ferrohydrodynamic interactions, and slip effects. Similarly, increased melting and ferrohydrodynamic interactions lower the fluid temperature, while the Dufour number enhances it. The concentration is positively influenced by higher Soret numbers. Statistical results demonstrate a perfect fit with a squared-R coefficient of 100%, and the Pareto chart identifies critical points at 2 for skin friction and the Nusselt number. Sensitivity analysis reveals negative sensitivity for most parameters across ferrohydrodynamic interaction levels, except for the Prandtl number, which exhibits positive sensitivity at low and medium Eyring-Powell parameter levels but turns negative at higher levels. This work provides a robust framework for understanding and optimizing the thermofluidic behavior of non-Newtonian fluids under complex physical conditions, offering valuable insights for industrial applications.

Turbulent pipe flow and heat transfer of a binary mixture at supercritical pressure: Influences of cross-diffusion effects

Cross-diffusion effects, including Soret and Dufour effects, are enhanced around the pseudo-critical temperature (Tpc) of a binary mixture. Their influences on heat transfer at supercritical pressure have been scarcely studied. To bridge this gap, large-eddy simulations (LES) are conducted to investigate forced convective heat transfer of a CO2–ethane mixture at supercritical pressures in a circular pipe subject to a uniform heat flux. Both heating and cooling conditions, along with varying initial concentrations and thermodynamic pressures, are included in the simulations. The LES results reveal that the Soret effect causes concentration separation, resulting in a concentration boundary layer. The magnitudes of the thermodiffusion factor (kT) and the radial temperature gradient control the intensity of separation, which is more pronounced at near-critical pressure and high heat flux. Since kT is significant only around Tpc, downstream decay of the concentration separation is observed as the loci of T=Tpc migrate away from the wall so that the local radial temperature gradient diminishes. The primary factors affecting heat transfer are the variations in thermal conductivity and isobaric specific heat resulting from concentration separation. In contrast, the Dufour effect and the accompanying inter-diffusion play negligible roles. In deterioration scenarios, the bulk Nusselt number (Nub) shows a maximum relative drop of 8%, whereas in enhancement scenarios, Nub shows a maximum relative increase in 10%, with both deterioration and enhancement decaying downstream. Cross-diffusion effects have negligible impacts on density and streamwise velocity, but noticeably alter streamwise velocity fluctuation and turbulent kinetic energy.

Buongiorno’s radiative Prandtl-Eyring nanofluid flow through porous medium over a stretching surface with cross-diffusion effects

The main focus of the current analysis is to describe the thermo-magnetic flow, heat and mass transport features of two-dimensional dissipative Prandtl-Eyring nanofluid (PE-NF) flow over a stretching sheet under the influence of porous medium and magnetic Ohmic dissipation numerically. An innovative Buongiorno’s nanofluid model in terms of Brownian motion and thermophoresis is deployed to accurately simulate the nano behavior in Prandtl-Eyring within the boundary layer regime. The thermal radiation and heat source/sink effects are also included to describe the thermal transport process. In addition to this, the thermo-diffusion and diffusion-thermo effect are included to demonstrate the temperature and concentration diffusion mechanism under the presence of chemical reaction process. The emerged coupled nonlinear two-dimensional time-independent partial differential equations are rendered to their dimensionless form through appropriate similarity transformations and solved by deploying Matlab-based BVP4C technique. The graphical visualization showed that, the increasing magnetic number diminished the flow field and enhanced the temperature and concentration profiles in the flow regime. Rising porous parameter decayed the Prandtl-Eyring nanofluid velocity. Increasing radiation and Eckert numbers enhance the temperature field in the flow regime. Magnifying Prandtl-Eyring parameter suppressed the velocity diffusion. Increasing Brownian motion and thermophoresis parameters increases the temperature profile. Amplifying Soret parameter upsurges the concentration profile. Skin-friction coefficient amplified with enhanced magnetic and porous numbers. Heat transfer rate acts as increasing function of thermophoresis and Brownian motion parameters. The main objective of this study is the addition of magnetic Ohmic dissipation, radiation, porous medium, thermal source/sink, Soret and Dufour effects and Buongiorno nanofluid model and this consideration generalizes former studies and gives a new re-defined mathematical formulation of heat and mass transport features of Prandtl-Eyring nanofluid flow over a stretching sheet. Finally, the numerical accuracy of the current similarity results is validated with available solutions and noticed a good agreement.

How Can Anomalous-Diffusion Neural Networks Under Connectomics Generate Optimized Spatiotemporal Dynamics.

Spatiotemporal dynamics in the brain have been recognized as strongly related to the formation of perceived and cognitive diseases, such as delusions and hallucinations in Alzheimer's disease. However, two practical considerations are rarely mentioned in related mechanism research: the connectomics networking and the anomalous diffusion generated by the complex medium between neurons and the complex topology of neural networks, respectively. Furthermore, how to optimize the corresponding dynamics behaviors has excellent implications for treating brain diseases. This article first realizes the networking under connectomics for an anomalous-diffusion single-neuron model and applies a nonlinear state feedback control to generate optimized dynamic behaviors, which provides a paradigm of nonequilibrium self-organization driven by anomalous diffusion. Then, by tracing the root distribution of the characteristic equation, some controlled conditions causing or inhibiting Turing instability and Hopf bifurcation are deduced, and the effects of self-diffusion and cross diffusion on Turing instability range are also revealed. At last, thorough numerical simulations are updated to illustrate the results. It is emphasized that delay, self-diffusion, cross diffusion, and fractional order occupy dominant positions in determining the network's spatiotemporal dynamics, and utilizing the control strategy can efficiently reduce Turing instability and delay Hopf bifurcation.

Weakly Non-linear Stability Analysis of Triple-Diffusive Convection in a Bi-viscous Bingham Fluid Layer with Cross-Diffusion Effects

Weakly Non-linear Stability Analysis of Triple-Diffusive Convection in a Bi-viscous Bingham Fluid Layer with Cross-Diffusion Effects

Instability of double-diffusive magnetoconvection in a non-Newtonian fluid layer with cross-diffusion effects

The study explores the initiation of two-dimensional double-diffusive convection in a horizontal layer of an electrically conducting non-Newtonian Navier–Stokes–Voigt fluid, subjected to a uniform vertical magnetic field and cross-diffusion effects. The numerical results are presented by obtaining the analytical solutions for both steady and oscillatory onset scenarios. The viscoelastic nature of the fluid either delays or hastens the onset of oscillatory convection depending on the strength of solute concentration. The analysis also uncovers contradictions in the linear instability characteristics with and without cross-diffusion terms, even when other input parameters are identical. Under specific conditions, three novel phenomena are observed that are not typically seen in double-diffusive cases: (i) an electrically conducting Navier–Stokes–Voigt fluid layer, initially linearly stable in the presence of a magnetic field, can become destabilized with the addition of a heavy solute to the fluid's bottom; (ii) a stable double-diffusive electrically conducting Navier–Stokes–Voigt fluid layer can be destabilized by the application of a magnetic field; and (iii) the requirement of three critical values of the thermal Rayleigh number to determine linear instability, as opposed to the usual single value owing to the existence of disconnected closed convex oscillatory neutral curves. The results are shown to align with previously published findings in the limiting cases.

Mixed Convection Over an Exponentially Stretching Surface with the Effect of Radiation and Reaction

This study investigates the mixed convection on a vertically oriented exponentially stretching surface, considering the exponential distributions of velocity, concentration and temperature. The governing highly nonlinear partial differential equations (PDEs) are transmuted into highly nonlinear ordinary differential equations (ODEs) by considering appropriate similarity variables. The highly nonlinear differential equations are solved numerically using the Hermite wavelet method (HWM) in MATHEMATICA 12. The obtained results show excellent agreement with previous studies focusing on different special cases of the problem. A parametric analysis of the physical parameters is shown and illustrative numerical results are presented graphically. The analysis incorporates the radiation, chemical reaction and cross-diffusion effects. The interaction between radiation and chemical reaction is particularly relevant in high-temperature systems, such as combustion, industrial furnaces, photochemistry, polymerization and certain chemical reactions. The results indicate that an increase in radiation enhances the temperature profile in the momentum boundary layer. Higher reaction rate values lead to a decrease in the concentration profile, while an increase in the Dufour value results in increased velocity and temperature and decreased concentration.

Impact of activation energy and cross-diffusion effects on 3D convective rotating nanoliquid flow in a non-Darcy porous medium

PurposeThis study aims to investigate numerically the impact of the three-dimensional convective nanoliquid flow on a rotating frame embedded in the non-Darcy porous medium in the presence of activation energy. The cross-diffusion effects, i.e. Soret and Dufour effects, and heat generation are included in the study. The convective heating condition is applied on the bounding surface.Design/methodology/approachThe control model consisted of a system of partial differential equations (PDE) with boundary constraints. Using suitable similarity transformation, the PDE transformed into an ordinary differential equation and solved numerically by the Runge–Kutta–Fehlberg method. The obtained results of velocity, temperature and solute concentration characteristics plotted to show the impact of the pertinent parameters. The heat and mass transfer rate and skin friction are also calculated.FindingsIt is found that both Biot numbers enhance the heat and mass distribution inside the boundary layer region. The temperature increases by increasing the Dufour number, while concentration decreases by increasing the Dufour number. The heat transfer is increased up to 8.1% in the presence of activation energy parameter (E). But, mass transfer rate declines up to 16.6% in the presence of E.Practical implicationsThe applications of combined Dufour and Soret effects are in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The nanofluid with porous medium can be used in chemical engineering, heat exchangers and nuclear reactor.Social implicationsThis study is mainly useful for thermal sciences and chemical engineering.Originality/valueThe uniqueness in this research is the study of the impact of activation energy and cross-diffusion on rotating nanoliquid flow with heat generation and convective heating condition. The obtained results are unique and valuable, and it can be used in various fields of science and technology.

Spatiotemporal Patterns in a Space–Time Discrete SIRS Epidemic Model with Self- and Cross-Diffusion

In this work, a two-dimensional Coupled Map Lattice (CML) method is applied to a continuous Reaction–Diffusion (RD) SIRS epidemic model. The model involves a complex, nonlinear incidence rate and the spatially heterogeneous self- and cross-diffusion coefficients. The CML method applied here results in a space–time discrete counterpart of the model. The basic reproduction number is derived, and the local stability of the fixed points of the discrete model is established. The two typical bifurcations of codimension 1, such as the flip and the Neimark–Sacker (NS) bifurcations, are investigated by utilizing the center manifold theory and the normal form theorem. Furthermore, the codimension-2 fold–flip bifurcation about the endemic fixed point is discussed in detail. Turing instability criterion of the cross-diffusion epidemic model is established by utilizing the CML method under periodic boundary conditions. Finally, the numerical simulations clarify both the effectiveness of all theoretical findings and the effects of time step size and cross-diffusion on the spatiotemporal patterns. The main contribution of this work is the discovery of some interesting Turing and non-Turing patterns which may be induced by flip–Turing instability, NS–Turing instability or fold–flip–Turing instability. Concretely speaking, spiral patterns are observed near the flip bifurcation threshold value and ultimately evolve into an irregular defect pattern. Stripe pattern, labyrinth pattern and circular pattern are observed near the NS bifurcation threshold value. The disorderly interwoven ribbon pattern, mosaic pattern and some irregular oscillatory patterns are observed near the fold–flip bifurcation point. Our results greatly help in predicting the long-term behavior of the space–time discrete SIRS epidemic model under study.

Stratified numerical heat and mass transport mechanism in MHD Maxwell fluid flow with nonuniform heat source/sink

The present boundary layer flow of Maxwell fluid over a stretching sheet has good number of practical applications in metallurgy, drawing of plastics, polymer sheet extrusion including hot rolling extrusion, glass blowing, spinning of fibers, rubber and plastic sheets, crystal growing and many more. Due to these extensive applications of Maxwell fluid in engineering, medicine and manufacturing industries including the above-mentioned applications, authors have motived, inspired and investigated the present problem. However, in this research paper, the influences of Soret and Dufour effects on the steady-state Maxwell fluid flow past a stretching sheet with nonuniform heat source/sink are considered numerically. The thermal and concentration stratifications impacts are also incorporated. The viscous dissipation and magnetic field effects are also included in the respective governing equations. The main novelty and uniqueness of this numerical research is to generalize the earlier studies and describe the salient features of magneto-thermo visco-elastic dissipative Maxwell fluid motion about a stretching sheet with cross-diffusion effects under the influence of double stratification phenomena. To differentiate the non-Newtonian fluids from those of Newtonian fluids, a well-known Maxwell fluid flow model is used in the present study. The investigated physical problem results the highly nonlinear coupled partial differential equations (PDEs) and which are not amenable to any of the direct methods. Suitable similarity transformations are deployed to reduce the highly complex PDEs into the system of ordinary differential equations (ODEs). A robust BVP4C Matlab function is employed to solve the rendered dimensionless system of ODEs. The numerically generated computed data is plotted in terms of velocity, temperature and concentration profiles including engineering quantities of interest such as skin-friction, Nusselt and Sherwood numbers in the flow region. It is evident from the current analysis that, the amplified magnetic field decreases the velocity field and increases the thermal and concentration distribution fields. Accelerating Maxwell’s number diminished the flow velocity and increased the temperature field. Increasing Soret and Dufour numbers enhances the concentration and temperature fields, respectively. Amplifying Maxwell’s number raises the skin-friction coefficient and enlarging the thermal stratification parameter magnifies the thermal transport rate. The mass transport rate amplified with a raise in concentration stratification number in the flow region. Finally, it is provided that, the current results are excellently matching with earlier published results in the literature and it confirms the accuracy of the used numerical method and the produced similarity solutions.

Computational analysis of transient thermal diffusion and propagation of chemically reactive magneto-nanofluid, Brinkman-type flow past an oscillating absorbent plate

The current work concentrates on increasing the thermal and solutal performance in exponentially accelerating vertical surfaces via the utilization of nanofluids containing the mixtures of base water fluid and Aluminum oxide (Al2O3), Copper (Cu), Titanium dioxide (TiO2) and Silver (Ag) nanoparticles. During the fully utilize the capabilities of nanoparticles in a variety of applications and to evaluate the effects that they will have on the environment and biological systems, it is crucial to comprehend and manage heat transmission. This motivation allows us to investigate the nanofluid boundary layer flows under cross-diffusion effects, as this model study earlier was not conducted, thus the results of this work are new, which describe the novelty of the current problem. The partial differential equations for the developed model are altered into dimensionless statements first via non-dimensionalization. The numerical simulations implementing a finite difference scheme are applied for the solution description. The physical description of the variation of momentum, temperature, and mass fields for different factors is computed and presented graphically for ramped temperature and isothermal heat cases. Convergence and validation of the problem are checked with the help of tables. We found that enhancement in the Reynolds number, Brinkman parameter and magnetic field mark a downward trend in the fluid velocity, but it strengthens with the porosity parameter and time factor. The temperature distribution expands for advancing diffusion-thermal and radiation effects, whereas a contrary pattern was noted with the Prandtl number and heat consumption parameter. The thermo-diffusion effect enlarges the concentration distribution but decays with chemical reaction and Schmidt number.

Mathematical modeling of cross diffusion effect on bioconvective Casson nanofluid over multi slips porous stretching surface

Purpose and significance Cross diffusion is a phenomenon that arises when various species are diffusing at the same time in a mixture. These are crucial in many industrial, environmental, and material processes for analyzing and forecasting temperature distribution, concentration profiles, and overall system behavior. Thus, cross-diffusion effects on Casson nanofluid across nonlinear stretching sheet are considered. In addition, the influence of magnetohydrodynamics (MHD) with multi slip boundary conditions implanted in porous regime is examined. The novelty of this study is the complex interactions and phenomenon of non-Newtonian Casson nanofluid with bioconvective multi slips conditions, which has an essential contribution in interdisciplinary nature. Methodology By employing similarity transformation, governing equations undergo a transformation into ordinary differential equations (ODEs), and solved using 5th-order Runge–Kutta–Fehlberg method via shooting technique. Graphical representations are utilized to depict effects of various parameters, accompanied by detailed explanations. Outcome The results obtained affirm that nonlinear stretching parameter leads to a deceleration of velocity profile, while temperature profile is observed to enhance with Eckert and Dufour numbers. Additionally, enhancement in the concentration profile occurred due to the Soret number. The comparison of current findings with prior research revealed great accuracy. Meanwhile, a graphical representation of skin friction, Nusselt number, and Sherwood number are presented. This investigation demonstrates that skin friction decreases by 10% with an improvement of M from 0.4 to 1.6. Furthermore, it is identified that there is a 31% rise in Sherwood number when Lewis number is accelerated from 1.0 to 1.5.

Irreversibility analysis of EMHD ternary nanofluid flow: Unveiling the combined effects of thermal radiation, chemical reactions and cross-diffusion

Comprehending the behaviour of ternary hybrid nanofluids with the influence of couple stress effects on a flat plate will provide vital insights for the development of more effective heat exchangers and cooling systems. In this investigation, we analyzed the impact of various factors, including couple stress and cross-diffusion parameters (Dufour and Soret), on a ternary hybrid nanofluid flow [Formula: see text] across a convectively heated flat plate. The analysis takes into account non-Fourier heat flux and irreversibility. The governing equations are converted into a set of ordinary differential equations using appropriate similarity transformations, and then the bvp4c solver is used to find solutions. Outcomes are provided for two instances, that is, nanofluid ([Formula: see text]) and ternary hybrid nanofluid [Formula: see text] The fluid velocity is found to be negatively correlated with the couple stress parameter rises ([Formula: see text]) which is one of the major findings in this study. Within the range of [Formula: see text] it is seen that the friction factor exhibits a gradual increase with a rate of 0.02878 (in the case of nanofluid flow) and 0.038083 (in the case of ternary hybrid nanofluid flow). Additionally, when the Dufour number is between 0 and 0.6, the Nusselt number exhibits a discernible decrease of 0.27678 (in the case of nanofluid flow) and 0.26428 (in the case of ternary hybrid nanofluid flow). Furthermore, at [Formula: see text] (the Sherwood number), the Sherwood number drops at a rate of 0.0786 (in the case of nanofluid flow) and 0.05592 (in the case of ternary hybrid nanofluid flow). It has been observed that an increase in the chemical reaction parameter [Formula: see text] lowers the fluid concentration. It is observed that the Sherwood number increases at a rate of 0.037654 (in the case of nanofluid flow) and 0.037661 (in the case of ternary hybrid nanofluid flow) when [Formula: see text].

Cross-diffusion and heat transfer effects on peristaltic flow of Reiner-Philippoff nanofluid with pseudoplastic and dilatant fluids over tapered channel: Multiple solutions and stability analysis

Peristaltic flow is used in many scientific and technological fields, including biology and medical technology. The goal of this research is to investigate the peristaltic behavior in an asymmetric non-uniform (tapering) channel using a Reiner-Philippoff fluid model (RPFM)-based nanofluid under the influence of dilatant and pseudoplastic fluid behavior. The Buongiorno nanofluid model (BNFM) is considered to investigate heat mass transportation. The channel is transformed from static reference to movement frame using the subsequent set of modifications, and the dynamic frame is transformed back to dimensionless form using the dimensionless parameters. The fundamental equations have been streamlined due to the long wavelength and small Reynolds number. Novelty of the current study is to examine the stability of numerical framework for RPFM-based nanofluid with dilatant and pseudoplastic fluid behavior. The boundary value problem fourth order code (bvp4c) technique is used to obtain the numerical results. With the use of graphs and tables, the physical elements that influence fluid dynamics are further explained. Stability evaluation has been performed mathematically and graphically. The most reliable solution is shown by the lowest positive eigenvalues, while the unreliable solution is indicated by the negative eigenvalues. It has been proven that changing the Reiner-Philippoff fluid (RPF) factor results in a fluid's velocity changing from dilatant to Newtonian as well as from Newtonian to pseudoplastic. According to the findings, the temperature curves rise as thermophoretic components and Brownian motion increase while decreasing as the Prandtl number increases. A brief theoretical and graphical analysis of each important parameter's effects on the flow dynamics is also carried out.

Turbulent Rayleigh–Bénard convection in a supercritical [formula omitted]-based binary mixture with cross-diffusion effects

CO2-based binary mixtures are promising in energy engineering to improve efficiencies of thermodynamic cycles where supercritical CO2 prevails. Indeed, under supercritical pressure and transcritical temperature conditions, special thermophysical properties of binary mixtures make the heat transfer process accompanied by enhanced cross-diffusion effects, i.e., the Soret effect and the Dufour effect. Their influences on heat transfer have not been well understood yet. This paper numerically investigates turbulent Rayleigh–Bénard convection in CO2-C2H6 binary mixture. Calculations are performed based on a spectral element method solver considering various temperature differences and pressures. Results indicate that the flow field presents a double-vortex structure. The thickness of the boundary layer is negatively correlated with the flow intensity. Under a positive separation ratio, the concentration gradient induced by cross-diffusion effects enhances buoyancy, which in turn reinforces the natural convection and heat transfer. The enhancement becomes stronger as the critical pressure is approached. Turbulent fluctuations are also strengthened by cross-diffusion effects, except for temperature fluctuations. The unusual reduction in temperature fluctuations is attributed to the increased size of the thermal plume caused by the Dufour effect.

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Cross diffusion effects on MHD double diffusive viscous flow through Hermite wavelet method

AbstractDouble-diffusive convection is a form of fluid flow that occurs when two processes of molecular diffusion are active in a fluid at the same time, causing instabilities and also complicated behaviour. One chemical or biological species concentration can cause a flux of another species, either linearly or nonlinearly, a phenomenon known as cross-diffusion. The cross-diffusion effects on double-diffusive MHD fluid flow through the Hermite wavelet method is examined. The governing coupled partial differential equations of the problem under consideration are transformed to highly nonlinear ordinary differential equations over a finite domain with the help of similarity transformations. The results are obtained for the skin friction coefficient, as well as the velocity, temperature and the concentration profiles for some values of the governing parameters, namely, the cross diffusion terms, Hartmann number, thermophoresis parameter, squeeze number, Prandtl number and suction/injection parameter. The obtained results are validated against previously published results for special case of the problems.

Influence of thermal radiation and shape factor on a hybrid nanofluid flow over a permeable flat plate with cross-diffusion effects: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. The meticulous investigation uncovers the integration of entropy analysis in the investigation of the flow of convective magnetohydrodynamic hybrid nanofluid via a permeable flat surface, by considering the effects of Dufour, viscous dissipation, Soret, and thermal radiation. The governing equations are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB in-built function. We display the outcomes for three different shape factors: platelet, cylinder, and brick. The skin friction coefficient increases at a rate of 1.5089 for the brick shape, 1.5163 for the cylindrical shape, and 1.5212 for the platelet shape when the mixed convection parameter lies between 1 and 5. In this regard, it is important to point out that there is a direct connection between the increase in temperature transmission rate and a decline in the Dufour number ( Du ). It has been found that when 1 ≤ Du ≤ 2.4 , the Nusselt number decreases by 0.4786, 0.4618, and 0.4512 for brick, cylinder, and platelet shapes, respectively. A decline in the Sherwood number is noticed with an upsurge in the Soret number ( Sr ). There is a noticeable increase of 0.0442 in the Sherwood number for brick shape, 0.0438 for cylinder form, and 0.0435 for platelet form when 1 ≤ Du ≤ 2.4 . Furthermore, we have detected that an increase in the radiation parameter amplifies both the Bejan number and the profiles of entropy formation.