Lewis Number Research Articles

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Background: The mechanics of heat and mass transfer via nanofluid flow across many media are currently being discussed. “Nanofluids” are fluids that include highly heat-conductive nanoparticles, and they are essential for resolving engineering problems. Under the effects of activation energy, thermal radiation, and motile microorganisms, the process of heat and mass transfer through steady nanofluid flow crosses over stretched surfaces in this scenario.Methodology: For mathematical evaluation, the system of partial differential equations (PDEs) is used to describe this physical framework. By introducing suitable similarity variables with a set of boundary conditions, this mathematical system of PDEs has become a system of ordinary differential equations (ODEs). To obtain numerical results, the MATLAB built-in program “bvp4c” is used to solve the system of first-order equations.Results: In the findings and discussion section, the resulting outcomes are thoroughly examined and visually shown. The flow rate in these systems increases due to the erratic movement of microorganisms. The graphical representation shows the impacts of involving physical factors on the microorganism, thermal, concentration, and momentum profiles. Variations/changes in these profiles can be observed by adjusting the parametric values, as depicted in the graphs. Consequently, thermal transport is boosted by 25%. Additionally, the skin friction, Nusselt, Sherwood, and microbe density numbers are determined numerically. The findings demonstrate that increasing the magnetic field parameter causes the velocity profile to decrease, increasing the radiation parameter leads to an increase in temperature description, and increasing the Lewis number causes the microorganism profile’s transport rate to decrease.

Double diffusive mixed convective flow over a wedge and cone in the presence of Brownian diffusion and thermophoresis parameter

The present article examines the double diffusion mixed convective nanofluid flow over a wedge and cone in which slip effects as Brownian motion and the thermophoretic parameter are considered. Mixed convective flow over wedges and cones is applied in different technical fields such as fiber technology, nuclear cooling systems, surface treatment, spray deposition techniques, and polymer production. Double diffusion is increasingly significant in scientific fields like astronomy, geosciences, oceanography, and chemical processes. Mixed convection occurs in several applications such as electric devices, solar panels, nuclear power plants, heat exchangers, radiators, and atmospheric boundary layer fluxes. The governing equations of the study are highly coupled nonlinear partial differential equations with surface constraints. The process of similarity transformation used to converts partial differential equations into nondimensional ordinary differential equations, which can be resolved using the MATLAB Bvp5c function. The graphical representation and detailed analysis of variations in velocity, temperature, and concentration distributions of nanofluids are presented. As the mixed convection parameter increases, the fluid’s velocity rises, with a more pronounced effect observed in the cone compared to the wedge. As the Brownian diffusion parameter grows, the fluid temperature increases, and velocity is more pronounced in the wedge scenario compared to the cone. Moreover, an increase in the thermophoresis parameter results in an elevation in the fluid’s temperature. Additionally, the wedge has a higher concentration of fluid and nanoparticles compared to the wedge. Fluid concentration falls with increasing Schmidt number, but fluid nanoparticle concentration decreases with increasing Lewis number.

Stability analysis of premixed flames with downstream heat gain

Pulsating instability is a kind of combustion intrinsic instability, that can affect the flammable limit and may couple with other processes to generate more complex combustion instability phenomena. Pulsating instability was found in the premixed flame of the double-flame partially premixed flame (PPF), in which the flame patterns change from stable to pulsating unstable, and to stable again as the equivalence ratio or stretch rate increases. To further investigate this phenomenon, a simpler model, stretched premixed flames with downstream heat gain, is analyzed by the asymptotic expansion method in this paper. The downstream heat gain inhibits the steady extinction of stretched premixed flames with a large Zeldovich number. The stability of premixed flames changes in the zero-limit mode, two-limits mode and one-limit mode sequentially as the Zeldovich number increases. The zero-limit mode represents the premixed flame is stable for all stretch rates. The two-limit mode and one-limit represent the premixed flame changes in the pattern of stable-pulsating-stable and pulsating-stable as the stretch rate increases, respectively. The downstream heat gain suppresses the pulsating instability to yield the stable region at the large stretch rate and large Zeldovich number. The influence of other factors, including the Lewis number, the downstream temperature and the downstream boundary position are also discussed. The current theoretical method is also applied to the extracted parameters from numerical calculations of hydrogen/air double-flame PPF. A qualitative similarity is found between the theoretical results and numerical results.

Theoretical analysis of transient counter-flow combustion system fueled by porous biomass particles in a non-premixed configuration under non-adiabatic conditions

The current research aims to implement a reliable analytical model in order to scrutinize the transient behavior of a counter-flow non-premixed combustion system fueled by wet porous biomass particles under non-adiabatic conditions, including several processes such as phase change and dehumidification. A special term is added to the heat equation based on the law of conservation of energy as a means to assess the convective heat loss impacts. In order to analyze the structure of the diffusion flame and predict the time-dependent temperature and mass fractions of reactants distributions, transient forms of energy and mass equations are solved through the asymptotic method. Eventually, the influences of key factors such as equivalence ratio, porosity factor of particles, and reactants Lewis numbers on the flame structure and transient behavior of diffusion flames are elaborately investigated in the non-adiabatic condition, considering convective heat loss and compared to those in the adiabatic condition. The findings reveal that increasing the porosity factor not only improves flame temperature but also leads the flame to be located further from the fuel nozzle. In addition, when the system reaches its steady-state condition, the temperature of the flame formed in the adiabatic condition is about 20 % higher than that formed in the non-adiabatic condition.

The impact of soret, Dufour, and chemical reaction on MHD nanofluid over a stretching sheet

This paper focuses on the effects of DuFour, heat radiation, and chemical reaction on a two-dimensional natural convective flow of stable electrical magnetohydrodynamics (MHD) nanofluid across a permeable stretched sheet, in addition to the effects of suction.This work investigates the boundary layer flow dynamics of a nanofluid via a stretched sheet in the presence of a magnetic field, accounting for DuFour effects and chemical reactions. The non-linear partial differential equations were transformed into a non-linear ordinary differential equation by using the appropriate similarity transformation. The Keller box technique is used to numerically solve ordinary differential equations. Graphs are used to show variations in temperature, concentration, and velocity to different physical constraints. Raising the thermophoresis parameter (Nt) results in inferior concentration profiles due to a decrease in the Lewis number parameter (Le) and Brownian motion parameter (Nb). The concentration profile is reversible with temperature and decreases as the chemical reaction parameter increases. As we increase the Du levels, the temperature declines. The patterns in the altering rates of heat and mass transfer, as well as the skin-friction coefficient, are also analyzed using numerical data.”

A numerical study on MHD Maxwell fluid with nanoparticles over a stretching surface: Impacts of thermal radiation, convective boundary condition and induced magnetic field

The current study investigates the influence of induced magnetic field and convective boundary condition on the behavior of a magnetohydrodynamic (MHD) Maxwell fluid including nanoparticles flowing through a stretching sheet. Furthermore, the analysis considers the existence of radiation. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The primary conclusions of this study are that increasing the Magnetic parameter decreases the Induced Magnetic field while increasing the Deborah parameter improves the velocity profile. Temperature distribution is growing due to increased estimates of the Radiation, Biot number, and Deborah number values. When the Lewis number values are raised, the concentration profiles get smaller but there is an opposite scenario deployed as the Thermophoresis parameter upsurges. The findings of this study are consistent with those that have been previously reported. The phenomenon of flow induced by a stretched surface finds several applications in various industrial and technological domains, including copper wire production, polymer extrusion, article manufacturing, and fiber synthesis. Induced magnetic fields are extremely prominent in many areas of science and technology, including electromagnetism, magnetic materials, and magnetic resonance imaging (MRI).

Non-similar bioconvective analysis of magnetized hybrid nanofluid (Ag + TiO2) flow over exponential stretching surface

Scientists have studied fluid flow over a stretching sheet to explore its potential applications in industries. This study investigates the exponential stretching flow of a bioconvective magnetohydrodynamic (MHD) hybrid nanofluid in porous medium taking into consideration thermal radiations, heat generation, chemical reaction, porosity, and dissipation. Moreover, microorganisms are present in the fluid, so the fluid is more stable, which is crucial in biotechnology, biomicrosystems, and bio-nano coolant systems. Silver and titanium dioxide in a water-based medium are the prototypical nanoparticles. The present study involves a transformation of the governing system into a set of dimensionless, coupled and nonlinear partial differential equations (PDEs) using nonsimilar techniques. The local non-similarity (LNS) technique is used to truncate these equations to ordinary differential equations (ODEs). This technique is also used to estimate transformed equations numerically until the second level of truncation takes place via the bvp4c algorithm, which is a built-in MATLAB solver. Furthermore, tables are provided that presents the drag coefficients, Nusselt numbers, Sherwood numbers, and densities of motile microorganisms. Results show a negative correlation between the velocity and the magnetic field parameter as well as the porosity parameter, as evidenced by a decrease in velocity corresponds to rises in these parameters. The temperature distribution exhibits a positive correlation with the rising values of both radiation parameter and Eckert number. The concentration profiles also exhibit a negative correlation with the increasing values of Lewis and bioconvection Lewis number, chemical reaction parameter, Peclet number and the differences in microbial concentration. This study will improve the future research on hybrid nanofluid regarding industrial applications. There haven't been any previous publications that have investigated the use of this model with the local non-similarity method. The main objective of this article is to enhance the heat transfer performance in a hybrid nanofluid.

Magnetic williamson hybrid nanofluid flow around an inclined stretching cylinder with joule heating in a porous medium

The study of an inclined stretching cylinder in a porous medium holds significant implications for understanding complex fluid dynamics and heat transfer phenomena, mainly when influenced by a hybrid nanofluid containing Cu and Al2O3, Joule heating, and a magnetic field in the presence of Williamson fluid. The nonlinear ordinary differential equations are derived by applying pertinent similarity transformations to partial differential equations. Subsequently, these non-dimensional ordinary differential equations are transformed into a system of first-order ODEs and numerically solved using Maplesoft's symbolic computation software MAPLE 2023. The influence of governing parameters on dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rates is investigated. This investigation is crucial for various practical applications, including geothermal reservoirs, enhanced oil recovery, and environmental processes involving porous media. It is demonstrated that Biot and Eckert numbers and nanofluid parameters contribute to increased surface temperature, while the Lewis number leads to a decrease in dimensionless concentration. Moreover, the curvature parameter is associated with an increase in dimensionless concentration, and skin friction demonstrates a direct relationship with the magnetic parameter while inversely correlating with the cylinder's curvature.These results contribute to the scientific understanding of these complex interactions and provide valuable insights for engineering applications, such as designing efficient heat exchangers, optimizing cooling systems, and advancing technologies involving fluid flow and magnetic fields.

A semi-analytical strategy for mixed convection non-Newtonian nanofluid flow on a stretching surface using Cattaneo-Christov model

This study investigates flow of non-Newtonian fluid containing nano particles and gyrotactic micro-organisms on stretching surface considering magnetic factor and thermal radiations. Cattaneo-Christov model is employed to analyze flow characteristics. The governing Partial Differential Equations (PDEs) along with associated boundary conditions describing the model are converted into Ordinary Differential Equations (ODEs) by suitable transformations. Homotopy Analysis Method (HAM), a semi-analytic solution technique is employed to obtain the solutions. The inspiration of important embedding variables on velocity, temperature, and concentration profiles are presented in tabular and graphical form to elaborate flow properties. It is deduced that the convective parameter and Weissenberg number, both have positive effect on dimensionless velocity whereas buoyancy ratio factor, bio-convective Rayleigh number, and magnetic force have inverse relationship with velocity profile. The presence of radiations and Brownian motion parameter boost energy transfer while it diminishes for higher Prandtl number values and mixed convection factor. Concentration intensifies for larger Prandtl number, activation energy, and thermophoresis parameters whereas it decreases for increasing temperature difference, Brownian motion, Schmidt number, and mixed convection factor. Bio-convective Peclet number, Lewis number, and microorganism concentration gradient factor, all depreciate microorganism concentration panel.

Investigation of Melting Heat Transfer in Viscous Nanofluid Flow Including Micro-Organisms and Entropy Generation Due to an Inclined Exponentially Stretching Sheet

This study investigates melting heat transfer and entropy production in viscous nanofluid flow consisting of micro-organisms over an inclined exponentially stretching permeable sheet. The flow is considered via porous medium. Impacts of heat transport characteristics are invoked in the energy equation. In concentration equation we have included chemical reaction impact. The regulating PDEs are transformed into nonlinear ODEs in non-dimensional form using adequate similarity transformation relations. The analytical solution of the problem is obtained utilizing HAM. Various plots are drawn to exhibit impacts of the regulating parameters (Prandtl number, Porous medium parameter, Thermal Grashof number, Mass Grashof number, Micro-organism Grashof number, Thermophoresis parameter, Radiation parameter, Bio-convection Levis number, Brownian motion parameter, Chemical reaction parameter, Suction parameter, Peclet number, and Melting parameter) occurred in the problem on relevant fields (flow, temperature and concentration distribution) and entropy production and discussed. Further values of significant physical quantities skin friction coefficient, Nusselt number, Sherwood number, and motile microbes density computed using MATLAB based bvp4c function and HAM are displayed in tabular mode and found in excellent agreement. For validity of the results skin friction coefficient and Nusselt number values are compared to prior research, apparently good agreement is found. The effect of melting surface parameter is found to reduce the fluid flow and temperature field. Entropy production lessens with rising values of slip parameters but effects of radiation and porous medium parameters are found to upsurge it. It is also noticed that bioconvection Lewis number and Peclet number reduce the micro-organism density profile. Inclusion of entropy analysis is a novel feature of the study. The solution methodology also enriched the novelty of the investigation. The results of the study may be applied to improve the efficiency of thermal, fluid flow and energy systems. This study may also find applications in bio-nano-coolant systems and heat transfer devices.

Nonlinear Convection Flow of a Micropolar Nanofluid Past a Stretching Sphere with Convective Heat Transfer

An incompressible, steady combined nonlinear convective transport system on a micropolar nanofluid through a stretching sphere with convective heat transfer was investigated. The conservation equations corresponding to momentum, microrotation, thermal energy, and concentration particles have been formulated with suitable boundary constraints. By using the required non-dimensional variables, the conservation equations have been turned into a set of high-order standard differential equations. Then, an implicit finite difference method, also known as the Keller-Box Method (KBM), was used to numerically solve the flow problem. The obtained outcomes are displayed through graphs and tables to explain the impact of various governing variables over velocity, temperature, concentration, number of skin friction, wall coupled stress, Nusselt number, and Sherwood number. The findings demonstrate that increasing the convective heat parameter Bi enhances the factor of skin friction, local Nusselt number, Sherwood number, velocity field, and temperature profile while lowering the wall-coupled stress. It is observed that for high values of the material parameter β, the fluid velocity and the spin of the micro-elements both increase, which causes the dynamic viscosity and microrotation velocity to decrease. In addition, as the rates of magnetic constant Ma, thermophoresis Nt and Brownian movement Nb rise, the thermal distribution and its thickness of boundary layer increase. However, it decline along the enlarging quantities of nonlinear convection parameter λ, Prandtl number Pr, material parameter β, and solutal Grashof number Gm, which agrees to increase fluid density. When the range of thermophoresis Nt surges, it causes an increment in the nanoparticle species, but the opposite behavior have seen in the case of Brownian number Nb, and Lewis number Le. The comparison made with the related published paper achieves a significant agreement. The numerical result is generated through the implementation of the computational software MATLAB R2023a.

Soret effect on stability of Darcy problem in a bidispersive porous medium with an exothermic chemical surface reaction

AbstractWe examine a saturated bidispersive porous medium undergoing an exothermic chemical reaction at its lower boundary. The fluid flow within this medium is modelled using the Darcy approach. While the Dufour effect is disregarded, the influence of the Soret effect is thoroughly explored. This problem represents a complex multiphysical phenomenon that integrates fluid dynamics, heat and mass transfer, chemical kinetics and thermoelectric effects. This problem finds relevance in various scientific and engineering applications, including enhanced oil recovery, chemical engineering, environmental engineering and energy systems. We introduce a complementary energy theory alongside a linear theoretical framework for the model. The Chebyshev collocation method is employed to derive both linear and nonlinear results. Our findings reveal that the effect of enhancing the Soret coefficient on the system's stability is contingent upon the boundary conditions and the Lewis number. Specifically, an increase in the Soret coefficient generally stabilises the system during stationary convection. Conversely, in scenarios where oscillatory convection prevails, a higher Soret coefficient tends to destabilise the system.

Double-diffusive convection of non-newtonian power-law fluids in an inclined porous layer

This paper presents a numerical study of Double-Diffusive convection within an inclined porous medium saturated by a non-Newtonian fluid. The power-law model is utilized for modelling the behavior of the flow in the porous layer. The given statement implies that the long side of the cavity experience thermal and solutal flux rates, whereas the other walls are impermeable and thermally isolated. The issue is characterized by a set of tightly linked non-linear differential equations, termed governing equations, encompassing the mass conservation equation (known as the continuity equation), the momentum equation, the energy equation, and the species equation. The relevant factors that govern the problem being investigated are the Rayleigh number, R_T, the power-law index, n, the angle of inclination, Φ, the cavity aspect ratio, A, the Lewis number, Le, the normalized porosity, ξ, and the buoyancy ratio, N, two types of cavity configuration have been studied: inclined cavity (i.e. Φ≠0°), then we have studied the case of a vertical cavity (i.e. Φ=90°) where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity (N=-1). A semi-analytical solution, valid for an infinite layer (A>>1), is derived on the basis of the parallel flow approximation, A numerical approach utilizing the finite differences method was utilized to resolve the governing equations within the porous medium. It is demonstrated that both the inclination of the layer, Φ, and the power-law index, n, have a strong influence on the strength of the intensity of flow, Ψ_0, the heat transfer rate, Nu, and the mass transfer rate, Sh, within the enclosure. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations.

Enhancement of heat transfer due to nonlinear radiative Burgers nanofluid with triple diffusion and heat source effects

This investigation predicts the assessment of mass and heat transfer due to Burgers nanofluid. The investigation is further supported by triple diffusion flow. Variable thermal conductivity is accounted to endorse the thermal flow. In the heat equation, the extension is suggested by utilizing the external heat source and nonlinear radiated phenomenon. Computations for modeled problems are achieved by the shooting method. The fundamental role of parameters governing flow is noticed which is physically attributed. It is observed that the heat transfer rate is enhanced due to the modified Dufour number. The solutal concentration declined for the regular Lewis number. Furthermore, the nanoparticles concentration reduces due to the nano-Lewis number. The depicted results convey novel applications in chemical processes, cooling control systems, refrigeration, solar energy, extrusion processes, etc.

Modified Reacting Solver: A Simplified Approach for Capturing the Molecular and Flow Diffusivities for the Nonpremixed MILD Flames.

The present study investigates the applicability of the inlet boundary species Lewis number (combined effect of molecular and flow diffusion) for the nonpremixed moderate and intense low oxygen dilution (MILD) flames. A modified reactive solver named modifiedReactingFoam is developed by including the enthalpy flux in the energy equation and using modified model constants in OpenFOAM. The present solver is tested on the delft-jet-in-hot-coflow burner operating under a moderate and intense low oxygen dilution combustion environment. Along with the flame with Reynolds number 4100, eight other jet-in-hot-coflow flames are simulated to test the capability of the present proposed solver. The main aim of the current work is to investigate the efficacy of the proposed solver in predicting the velocity field, temperatures, and flame lift-off height for the considered flames with a significant reduction in computational time. The predictions with the modified eddy dissipation concept model are improved. However, a significant deviation is still observed in the downstream direction of the burner. The numerical simulations are performed with methane Lewis numbers of 0.9-1.14 by keeping the respective constant Lewis numbers for the inlet boundary species. The modifiedReactingFoam predictions at a methane Lewis number of 1.12 are in very close agreement with the experimental results. The maximum deviation in lift-off heights is within ±3% of the experimental results. The present modified solver outperformed the other combustion models in the literature and reduced the computational time up to 10 times with a combination of DLBFoam compared to the inbuilt solver.

Nonlinear stability analysis of Rayleigh-Bénard problem for a Navier-Stokes-Voigt fluid

The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2).

Thermal and flow characteristics of micropolar nanofluid with microorganisms: Insights from the Darcy-Forchheimer relation

The Darcy-Forchheimer relation is a key concept utilized in the analysis of fluid dynamics, specifically in understanding the pressure drop experienced by a fluid as it traverses a porous medium or a conduit with added resistance. This resistance may stem from various factors such as turbulence and viscosity. The Forchheimer coefficient serves as a metric to quantify this resistance and is typically determined through empirical studies or computational modeling. Its value is influenced by parameters like the porosity of the medium and the characteristics of the particles within it. Grasping the intricacies of the Darcy-Forchheimer relation empowers engineers and researchers to make precise predictions regarding pressure differentials and to devise efficient fluid flow systems. This knowledge is particularly vital in sectors such as oil and gas, chemical manufacturing, and environmental management. The aim of this study is to explore the application of the Darcy-Forchheimer relation within the domain of electro-magneto-hydro-dynamics flow of Micropolar nanofluid over a deformable surface. The investigation considers the impact of bio-convection (microorganisms) and the presence of a first-order chemical reaction. The energy equation accounts for phenomena like viscous dissipation, nonlinear thermal radiation, convective heat transfer, and the Soret and Dufour effects. Additionally, the research delves into the stochastic and thermophoretic attributes of the system. The governing equations of the problem were transformed into a dimensionless system and solved using the ND-solve technique. Graphical analyses were conducted to examine fluid flow, microrotation velocity, microorganism distribution, concentration, particle behavior, and temperature in relation to key flow variables. The findings indicate that higher Hartman numbers have a reverse effect on temperature and velocity profiles. An increase in the material variable results in a decrease in microrotation velocity. Temperature is influenced by vector radiation. Concentration shows contrasting trends for random and thermophoresis variables. The presence of motile microorganisms reduces the bioconvection Lewis and Peclet numbers.

Instability of Jeffrey Fluid Throughflow in a Porous Layer Induced by Heat Source and Soret Effect

Abstract In this study, we investigated the instability of thermosolutal convection of Jeffrey fluid in a porous layer with internal heating and the Soret effect. The layer is bounded by two fixed permeable parallel plates which are assumed to be isothermal and isosolutal. An existing initial flow in the vertical direction is passing the layer at a constant speed. The flow fields are adequately presented by PDEs and transformed into dimensionless forms. A small perturbation to the basic flow profiles with linear stability analysis results the problem in an eigenvalue problem. The Runge-Kutta method is used to derive the numerical value of the critical thermal Rayleigh number. The convective instability for asymptotic cases for Le = 1 and Pe = 0 are also examined as special cases. The analysis reveals that for a non-positive Soret parameter, the flow is stable for all Lewis numbers and independent of the heat source. But with a positive Soret parameter in the absence of a heat source, the fluid flow is stable for Le = 3 while the influence of a heat source destabilizes the flow for Le > 2. In high and low shear flows with increasing solutal gradient, the solutal Rayleigh number shows a highly destabilizing nature for all Le. Moreover, smaller relaxation and higher retardation time are the most unstable characteristics of the heat source system. In convective longitudinal rolls, the uni-cellular streamline patterns tend to become bi-cellular by the influence of positive Soret parameters and energy sources.

Non-similar analysis of bio-convective micropolar nanofluid flow including gyrotactic microorganisms across a stretched geometry

This study explores the novel interaction of gyrotactic microorganisms within a two-dimensional bioconvective micropolar nanofluid flow along a stretched surface, employing the Tiwari-Das nanofluid model. Uniquely, blood is modeled as a micropolar fluid incorporating titanium dioxide ( Ti O 2 ) and silver ( Ag ) nanoparticles. The analysis incorporates influential factors such as viscous dissipation, magnetic field, and heat source effects. By converting the control system into dimensionless nonlinear coupled differential equations, a complete understanding of the system is attained through the application of the local non-similarity approach and bvp4c (MATLAB tool). Particularly, the study provides valuable insight into the influence of dimensionless control parameters on key profiles such as velocity, microrotation, temperature, concentration, and microbial profiles. The findings show that temperature, microrotation, and velocity profiles are all improved by raising the values of micropolar parameters. Furthermore, the microbe profile shows an inverse connection with the Lewis number and a positive association with the Peclet number, whereas the concentration profile declines with increasing Schmidt number values. Furthermore, the study provides a quantitative analysis through tables, revealing variations in the drag coefficient and Nusselt number. This innovative exploration sheds light on the unique behavior of micropolar bioconvective nanofluids, offering valuable contributions to the field of fluid dynamics and bioengineering.

Double-diffusive thermosolutal Hadley–Prats flow: stability analysis

ABSTRACT A mathematical model is formulated to study the onset of double-diffusion fluid flow through an infinite permeable channel with internal heat source and viscous dissipation effects under the influence of convection conditions. Numerically, the dimensionless emerging eigenvalue problem is tackled using the fourth-order Runge–Kutta scheme, specifically applied to longitudinal roll disturbances. Critical values of wave number and vertical thermal Rayleigh number are determined. A higher value of Gebhart number is observed to correlate significantly with the destabilizing phenomena in Hadley–Prats flow. Concentration-based internal heat generation also strongly modifies the critical thermal Rayleigh number. Also, it is found that the horizontal mass flow and viscous dissipation exert a substantial influence on the onset of instability in the flow regime. Linear instability analysis indicates that greater values of Lewis number in the porous medium stabilize the convection process for both values of mass diffusion parameter ( C z ) . Enhancing C z from negative to positive values diminishes the critical thermal Rayleigh ( R z ) value and consequently induces instability in the porous medium. Increased concentration-based internal heat generation generates the destabilization process in the flow region.