Lewis Number Research Articles

Impact of rotation on thermal instability of Darcy–Brinkman porous layer filled with a Jeffrey nanofluid

The novelty of this research lies in its investigation of the initiation of thermal instability within a Darcy–Brinkman porous layer containing a Jeffrey nanofluid under the influence of rotation. While non-Newtonian fluids complex flow patterns and heat transfer enhancements due to thermal gradients are known, this study addresses a specific and previously unexplored aspect, the impact of rotation on Darcy–Brinkman porous layer containing a Jeffrey nanofluid. When a fluid is subjected to rotation, it can induce additional forces and flow patterns within the fluid. The linear stability theory and normal mode analysis method are used to analyze the stability of the system analytically and are computed numerically using the software Mathematica version 11.3. The investigation focuses on understanding the influence of various factors, namely, the Taylor number, the Lewis number, the Jeffrey parameter, the modified diffusivity ratio, nanoparticles Rayleigh number, the Darcy–Brinkman number, and medium porosity on the onset of thermal instability in the physical system. This novel perspective can contribute to a deeper understanding of heat transfer processes in non-Newtonian fluids and has potential applications in improving the efficiency of industrial systems, such as cooling systems, heat exchangers, and microfluidic devices where efficient heat transfer is crucial for performance improvement.

Effect of Turbulence and Diffusional–Thermal Instability on Hydrogen‐Rich Syngas Turbulent Premixed Flame

As a kind of fuel with low‐carbon emissions, hydrogen‐rich syngas has a large resource potential and is a promising alternative energy resource. A series of experiments in a constant volume combustion bomb are carried out to investigate the effects of turbulence and diffusional–thermal (DT) instability on a hydrogen‐rich syngas turbulent premixed flame. The flow field in the constant volume combustion bomb is calibrated, and the turbulent flow field's homogeneity and isotropy were investigated. The effects of different speeds of fan (1366–4273 rpm), hydrogen fractions (55%–95%), pressures (1.0–3.0 bar), and equivalence ratios (0.6–1.0) on the hydrogen‐rich syngas turbulent premixed flame are studied. According to the analyses, the flow field in the experimental device exhibits good homogeneous and isotropic characteristics. With the increase of turbulence intensity, equivalence ratio, hydrogen fraction, or pressure, the turbulent flame propagation speed increases gradually. As the hydrogen fraction increases or the equivalence ratio decreases, the effective Lewis number decreases, and the effect of DT instability on the flame increases. The research in this article is crucial for the clean and efficient utilization of hydrogen‐rich syngas and the design of related burners.

Multiple-Relaxation-Time Lattice Boltzmann Simulation of Soret and Dufour Effects on the Thermosolutal Natural Convection of a Nanofluid in a U-Shaped Porous Enclosure

This article reports an investigation of the Soret and Dufour effects on the double-diffusive natural convection of Al2O3-H2O nanofluids in a U-shaped porous enclosure. Numerical problems were resolved using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). The indented part of the U-shape was cold, and the right and left walls were heated, while the bottom and upper walls were adiabatic. The experimental data-based temperature and nanoparticle size-dependent correlations for the Al2O3-water nanofluids are used here. The benchmark results thoroughly validate the graphics process unit (GPU) based in-house compute unified device architecture (CUDA) C/C++ code. Numeral simulations were performed for a variety of dimensionless variables, including the Rayleigh number, (Ra = 104,105,106), the Darcy number, (Da = 10−2,10−3,10−4), the Soret number, (Sr = 0.0,0.1,0.2), the Dufour number, (Df = 0.0,0.1,0.2), the buoyancy ratio, (−2≤Br≤2), the Lewis number, (Le = 1,3,5), the volume fraction, (0≤ϕ≤0.04), and the porosity, ϵ = (0.2−0.8), and the Prandtl number, Pr = 6.2 (water) is fixed to represent the base fluid. The numerical results are presented in terms of streamlines, isotherms, isoconcentrations, temperature, velocity, mean Nusselt number, mean Sherwood number, entropy generation, and statistical analysis using a response surface methodology (RSM). The investigation found that fluid mobility was enhanced as the Ra number and buoyancy force increased. The isoconcentrations and isotherm density close to the heated wall increased when the buoyancy force shifted from a negative magnitude to a positive one. The local Nu increased as the Rayleigh number increased but reduced as the volume fraction augmented. Furthermore, the mean Nu (Nu¯) decreased by 3.12% and 6.81% and the Sh¯ increased by 83.17% and 117.91% with rising Lewis number for (Ra=105 and Da=10−3) and (Ra=106 and Da=10−4), respectively. Finally, the Br and Sr demonstrated positive sensitivity, and the Ra and ϕ showed negative sensitivity only for higher values of ϕ based on the RSM.

MHD nanofluid flow through Darcy medium with thermal radiation and heat source

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter [Formula: see text] while opposite behavior is observed in case of R.

Magneto-double-diffusive natural convection and irreversibility analysis of a nanofluid flowing in an annular concentric space

In the present article, magneto-double-diffusive density driven convection accompanied by an entropy optimization analysis of Al2O3-water nanofluid filled in a horizontal coaxial annular space is numerically addressed. The double-diffusive natural nanofluid flow which is produced due to the maintaining of constant and different temperature and solute on the inner and outer cylinders is affected by a uniform vertical magnetic field. Dimensionless governed equations which are developed through law of conservation of mass, momentum, and energy are numerically solved via finite volume approach, and parametric control analysis is developed. By using Corcione empirical correlations considering the Brownian diffusion of 4% of Al2O3 nanoparticles in water, the thermal conductivity and viscosity of the mixture nanofluid are determined. Results are performed and interpreted in detail for wide range of relevant variables: Rayleigh (102 ≤ Ra ≤ 105), Hartmann (0 ≤ Ha ≤ 30), Lewis numbers (0 ≤ Le ≤ 10), and Buoyancy ratio (−4 ≤ N ≤ 4) to evaluate the double-diffusive convective nanofluid flow, heat and solute transfer rates as well as entropies produced in the system.

A new hybrid approach to study heat and mass transfer in porous medium influenced by imprecisely defined parameters

The present work discusses a hybrid approach of Successive Overrelaxation (SOR) with Finite Element Method (FEM) in presence of non-probabilistic uncertainties. In order to address the heat and mass transfer problem in porous media with fuzzy environment, the proposed SOR FFEM has been applied. Here, the imprecise parameters have taken in terms of TFNs and the convergence analysis of the proposed technique is performed. The parameters viz. Rayleigh number (Ra), Radiation parameter (Rd) and Lewis's number (Le) are considered as uncertain and discussed in case study. Different combinations of uncertain parameters are considered for investigation and the sensitivity analysis of the same is observed. It is noted that the stream function (ψ‾) is sensitive when Ra is fuzzy. Similarly, the stream function (ψ‾) and temperature (T‾) both are exhibiting sensitivity when Rd is fuzzy. Additionally, the stream function (ψ‾) is sensitive when Le is fuzzy. As comparing all the cases, it is observed that, stream function (ψ‾) is more sensitive in all three circumstances that is a small change in value can be affect more.

Thermogravitational Convection in a Controlled Rotating Darcy-Brinkman Nanofluids Layer Saturated in an Anisotropic Porous Medium Subjected to Internal Heat Source

Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.

Nonlinear magnetoconvection of a Maxwell fluid in a porous layer with chemical reaction

ABSTRACT In this paper, the linear and nonlinear instability of magnetoconvection in a Darcy-Benard setup saturated by a Maxwell fluid with chemical reactions is studied. The governing non-dimension equations are solved using the normal modes, and we obtain the expressions for steady and oscillatory thermal Rayleigh numbers. The effects of different physical parameters such as the Damkohler number (), Hartmann number (), Solute Rayleigh number (), relaxation parameter (), Magnetic Prandtl number (), Lewis number () on stationary and oscillatory critical thermal Rayleigh numbers are presented and described. Enhancing the values of the Solute Rayleigh number and Lewis number makes the system unstable. Also, the Hartmann number and Damkohler number have a contrasting effect on stationary and oscillatory convection. Enhancing the value of the relaxation parameter makes the system more stable. In order to study heat transport by convection, the well-known equation, the Landau-Ginzburg equation, is derived.

Effect of near-wall blockage on the magnetohydrodynamics-based double-diffusive convection in rectangular cavities

This research work reports the numerical investigation of magnetohydrodynamics (MHD) characteristics around the near-wall blockage for various separation distances owing to double-diffusive convection (DDC) in a rectangular cavity. The distance between the bottom wall of the cavity and the lower wall of blockage is called separation distance and it has varied from where H is the height of the cavity. The working fluid is considered as liquid metal - Sodium-Potassium alloy (). The numerical computations are conducted by using an in-house developed lattice Boltzmann method solver. The simulations are conducted for the steady-state, laminar, incompressible, and Newtonian fluid flow. The effect of NWB has been explored for a range of parameters, such as Rayleigh number and Lewis number buoyancy ratio and Hartmann number The variation and contour plots show the higher heat and mass transfer (HMT) rates for at constant Ra. As increases, HMT rates enhance. The increase in Ra, N, and Le induces multiple-cell formation inside the cavity for a given As Ha augments HMT rates get decreased monotonically. For negligible or slight variation was observed in the rate of HMT. As the obstruction between the bottom wall of the blockage and the adiabatic bottom wall of the cavity increases, shear force occurs, and the buoyancy-driven flow decreases. The outcomes of the numerical investigation are summarized in the form of empirical correlation of for Ra = and at various separation distances, which might be utilized for probable design purposes.

Flash-back, blow-off, and symmetry breaking of premixed conical flames

Hydrodynamic and thermal-diffusive effects subject premixed flames to intrinsic instabilities that strongly influence their shape and propagation/stabilization characteristics. However, the interaction and coupling of intrinsic flame dynamics with background flow gradients and boundary conditions remain poorly understood. This paper presents a global nonlinear bifurcation analysis of burner-stabilized laminar premixed conical flames with varying reaction rates and reactant diffusivities, respectively parameterized by the Damköhler number Da and the Lewis number Le. Using a dimensionless formulation of the reacting, weakly-compressible Navier–Stokes equations, the dynamics of flash-back, blow-off, and cellular instability are explored in a fully-coupled framework. Our analysis identifies steady conical flame states over a finite range of Da and Le, limited by saddle–node bifurcations corresponding to spontaneous blow-off of the axisymmetric flame below a Le-dependent lower critical Da value and spontaneous boundary-layer flash-back beyond a higher critical Da value. Furthermore, the analysis reveals that the conical flame loses its axisymmetry via circle–pitchfork bifurcations as Le or Da decrease or increase beyond respective critical values. These bifurcations are shown to correspond to stationary three-dimensional global modes describing steady polyhedral or tilted flame structures, each associated with distinct azimuthal periodicities. Statement of SignificanceThis work presents a bifurcation analysis of laminar premixed conical flames within a fully-coupled flame/flow model. By considering variations in reaction rate and reactant diffusivity, the analysis identifies saddle–node bifurcations corresponding to spontaneous flash-back and blow-off of the axisymmetric flame. It also identifies axisymmetry breaking bifurcations associated with transitions to steady three-dimensional polyhedral and tilted flame states. These global instabilities indicate that hydrodynamic and thermal-diffusive effects strongly influence a flame’s steady structure in the azimuthal dimension even when no instabilities appear in the plane of symmetry. As such, future analyses of flame dynamics should rule out symmetry-breaking behaviors before adopting a two-dimensional computational framework.

Magneto-Ternary Hybrid Nanofluid Flow About Stretching Cylinder in a Porous Medium with Gyrotactic Microorganism

The diluted suspension of nanoparticles in base liquids has been found in extensive applications in various industrial processes like nanomedicines, cooling of microsystems, and energy conversion. The idea of tri-hybrid nanofluid have been developed which shows the impact of three nanoparticles at the same time in a single fluid. This newly developed tri-hybrid mixture model getting more attention and performed better than hybrid and nanofluid. Owing to its important applications an attempt has made in this article to investigate the Casson ternary hybrid nanofluids flow along a stretching cylinder through porous medium subject to the influence of microorganism in the modeled equations. The strength of magnetic field has employed in upward direction of the flow system, and Activation Energy effect is addressed. The main equations of fluid motion have been converted to dimensionless format using set of suitable variables. In this work it has noticed that, growth in permeability parameter, Casson and magnetic factors result in more resistive force to fluid motion that declines the velocity characteristics. Moreover, the temperature distribution has grown up while the concentration characteristics have declined with growing values of Brownian factor. Furthermore, microorganism characteristics decay with growth in bio-convection Lewis and Peclet numbers. The impact of these parameters upon heat, mass and motile transfer rates has been evaluated in the tabular form.

Thermal analysis of bioconvective nanofluid flow over a sphere in presence of multiple diffusions and a periodic magnetic field

The current work intends to describe the heat and mass transfer in the mixed bioconvective flow of nanofluid along the sphere. This analysis also takes into account the influences of a periodic magnetic field and the diffusions of species concentrations such as liquid ammonia and liquid hydrogen. The physical problem is represented as a collection of connected nonlinear partial differential equations with appropriate boundary constraints using the Boussinesq approximation. The Buongiorno two-phase model is utilized to examine the nanoparticle's effect on the fluid. The governing equations are represented in the dimensionless form by using nonsimilar transformations. Further, the implicit finite difference scheme and the technique of quasilinearization are employed for numerical computation. Graphs are used to discuss the findings. The skin friction coefficient increases by about 27%, and the heat transfer rate to the fluid from the surface decreases by about 30% when the periodic magnetic field escalates from 0 to 1. The nanoparticle's mass transfer rate increases by about 35% when the Lewis number grows from 5 to 10. Higher Peclet numbers are favorable to the skin friction coefficient and heat transfer rate, but not the microorganism's density number. The present numerical results obtained in this analysis were compared to earlier published work and found to be in excellent agreement.

Weakly nonlinear instability analysis of triple diffusive convection under internal heat generator and modulated boundaries

A nonlinear instability analysis of triple diffusive convection under the time-dependent heat and mass transfer boundary conditions in the presence of internal heat source is evaluated in this study. On various physical parameters, the momentary behavior of both Sherwood and Nusselt number profiles is examined. In the geometry, we have considered two parallel infinite horizontal plates acting gravity vertically downward z-direction. By using the weakly nonlinear analysis, the Ginzburg–Landau equation is generated for the rate of heat and mass transport. Here, we have considered the temperature and concentration of two solutes. The temperature and first concentration of the solute at the lower plate are higher than the upper plate, while the second concentration of the solute at the upper plate is higher compared to that of the lower plate. According to the different modulation, we have considered four cases based on the phase angle of the modulations. The convective heat and mass transports are measured as a function of the Nusselt number (Nu) and Sherwood number (Sh1 and Sh2) for both the concentration. From the results, it is found that the first Lewis number increases all the considered profiles, while Ri increases the Nusselt number profile only. The principal discovery elucidated by this article resides in the observation that the internal heat source, subject to modulated boundaries, maintains the convective instability if different solutes are used from both ends.

The Effect of Methane–Ammonia and Methane–Hydrogen Blends on Ignition and Light-Around in an Annular Combustor

Abstract The use of hydrogen and ammonia in gas turbines, either alone or blended with natural gas, poses various technical challenges for combustion systems, including ignition. Depending on the fuel composition, the laminar flame speed and the ratio of unburned to burned gas density (dilatation ratio) of hydrogen and ammonia flames can be well outside the range seen in natural gas flames. Previous studies in annular combustion chambers have provided evidence of the importance of these properties in determining the ignition dynamics including light-around times. So far, these studies have mostly considered hydrocarbon fuels, have been limited to only a few runs, and have not yet systematically investigated variations in the dilatation ratio and the flame speed but rather have considered them as a lumped parameter. To investigate these effects in more detail, experiments characterizing the light-around times were carried out on an atmospheric annular combustor in which the dilatation ratio and the laminar flame speed was independently varied. This was achieved by varying the equivalence ratio and employing a variety of different hydrocarbon fuels (ethylene, propane, and methane) and fuel blends of methane–ammonia and methane–hydrogen. Light-around times were evaluated from global chemiluminescence measurements obtained using an azimuthal array of photomultipliers placed round the combustor chamber as well as high speed imaging. To improve statistical certainty, more than 3000 ignition and light-around times were measured with 30 repetitions obtained for each operating condition. To provide some insight into the light-around dynamics in specific cases, 900 of the 3000 sets included high-speed OH* chemiluminescence images. Light-around times for premixed pure hydrocarbon flames showed a similar dependence on the laminar flame speed as reported in previous studies. For the range of ammonia fuel blends investigated, an increase in laminar flame speed leads to a predictable increase in the flame propagation speed, as in the case of hydrocarbon fuel. Furthermore, collapse of this dependence for all blends could be achieved when corrected for an effective Lewis number, noting that all Lewis numbers for these blends were above unity. However, for hydrogen fuel blends, a decrease in dilatation ratio was found to decrease the light-around time counter to existing experimental results on the ignition of hydrocarbon fuels for which we currently do not have an explanation.

Propagation and extinction of premixed H2[sbnd]O2[sbnd]N2 edge-flames

The effects of equivalence ratio (ϕ), global strain rate (σ) and mixture strength on the shapes and propagation rates (Uedge) of premixed edge-flames in H2O2N2 mixtures were investigated experimentally using a counterflow slot-jet apparatus. Results are presented for both single (premixed gas against cold inert gas) and twin (premixed gas against premixed gas) configurations. Both advancing (Uedge > 0) and retreating edge-flames (Uedge < 0) were characterized. Flame images show that for lean mixtures where H2 is the deficient species and thus the effective Lewis number (Leeff) is less than unity, the leading edge-flame has a stronger burning intensity than the trailing strained premixed flame. For mixtures with low ϕ (thus low Leeff) at near-extinction conditions corresponding to sufficiently high or low σ, transitions from continuous to broken structures were observed due to diffusive-thermal instabilities. Such transitions enable flames to survive under conditions where extinction would have occurred without transition. The combined effects of ϕ, adiabatic flame temperature and σ were found to correlate well in terms of the effect of a non-dimensional strain rate (ε) on a scaled propagation rate Ũ.

Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial

In this article, the investigation is made to shed a light on the influence of convective boundary conditions on the boundary layer flow over a linearly stretching flat surface. The equations (partial differential equations) describing the model are transformed into system of nonlinear ordinary differential equations using similarity transformations. Equations contain various non-dimensional flow characterizing numbers viz. Prandtl number Pr, Lewis number Le, Biot number Bi, Brownian motion parameter Nb and thermophoresis parameter Nt. The influence of these parameters on thermal boundary layer, concentration distribution and temperature are analyzed in detail, by solving the equations using novel Shifted Chebyshev collocation method. The computed results, reduced Nusselt number, reduced Sherwood number, surface temperature and concentration profiles as functions of dimensionless numbers are validated by comparing the predicted results with available earlier findings (using other methods). To assert the convergence and stability of the scheme used (for much larger, but moderate, parameters values), predicted results are presented in various tabular forms. For presenting finer details of the computed values some results are also given graphically. The innovative semi-numerical scheme is robust and efficient compared with other conventional methods, used in previous studies and enables the analysis of the complex problem adequately.

The Upshot of Nonlinear Thermal Emission on a Conducting Jeffrey Nanofluid Flow over a Stretching Sheet: A Lie Group Approach

The upshot of nonlinear thermal radiation of steady state MHD heat transfer of Jeffrey nanofluid together with prescribed boundary conditions of interest was studied. Essential fluid properties, dimensionless switch parameters with the assistance of the Lie group method were used to transform the convenient partial differential equations that describe the present model into a system of ordinary differential equations. The generalized flow of the present model incorporates Jeffrey parameters and nonlinear thermal radiation. The Mathematical model is first renovated into ordinary differential equations by Lie symmetry group alteration. The renovated equations were solved numerically using a bvp4c MATLAB solver. The Jeffrey parameter serves as a stabilizer on the velocity of the fluid while thermal radiation parameter and heat source-sink parameter improves the flow temperature. Lewis number, chemical reaction parameter diminished the mass transfer flow. Equally skin friction, Sherwood number and Nusselt number were expanded.

Effective Lewis number and burning speed for flames propagating in small-scale spatio-temporal periodic flows

Propagation of premixed flames having thick reaction zones in rapidly-varying, small-scale, zero-mean, spatio-temporal periodic flows is considered. Techniques of large activation energy asymptotics and homogenization theory are used to determine the effective Lewis number Leeff and the effective burning speed ratio ST/SL, which are influenced by the flow through flow-enhanced diffusion. The resultant effective diffusivity matrix is, in general, neither a scalar nor a diagonal matrix and therefore induces anisotropic effects on the propagation of multi-dimensional flames. As the flow Peclet number Pe becomes large, the flow-enhanced fuel diffusion coefficient and the thermal diffusivity behave respectively like (PeLe)σ and Peσ, where Le is the Lewis number and σ≤2 is a constant which depends on the flow and the direction of flame propagation. The maximal value σ=2 is achieved for steady, unidirectional, spatially periodic shear flows, while for steady two-dimensional square vortices, we have σ=1/2. In general, the constant σ is determined by solving a linear partial differential equation. The scaling laws for the diffusion coefficients lead to corresponding scaling laws for the effective Lewis number and the effective burning speed ratio of the form Leeff≃Le1−σ and ST/SL∼(Pe/Le)σ/2. Effects of thermal expansion and volumetric heat loss on the flame are also briefly discussed. In particular, it is shown that the quenching limit is enlarged by a factor 1/Leσ for Le<1 and diminished by the same factor for Le>1, due to the flow-enhanced diffusion. The potential implications of the results to better understand turbulent combustion are discussed. A special emphasis is placed on the dependence of the flame on Le in the presence of high-intensity, small-scale flows. In particular, it is shown that this dependence is intimately linked to the flow through Taylor-dispersion like enhanced diffusion, rather than through the traditional molecular diffusion coupled with curvature effects. The flow-dependent effective Lewis number identified may also provide an explanation to the peculiar experimental observation that turbulence appears to facilitate ignition in Le>1 mixtures and to inhibit it in Le<1 mixtures. Novelty and significance statementAn original study, combining asymptotic analysis and homogenization theory, is applied to describe flame propagation in small-scale, spatio-temporal periodic flow fields. Scaling laws are derived for the effective burning speed and the effective Lewis number for high-intensity small-scale flows, which are useful to better understand the behaviour of turbulent premixed flames in the distributed reaction zone regime. The formula for the flow-dependent effective Lewis number identified herein may explain the peculiar experimental observation that turbulence appears to facilitate ignition in Le>1 mixtures and to inhibit it in Le<1 mixtures. The high-intensity small-scale flows are shown to increase the quenching limit due to volumetric heat losses in Le<1 mixtures and decrease it in Le>1 mixtures

Effects of Stefan blowing on mixed convection heat transfer in a nanofluid flow with Thompson and Troian slip

The combined effects of Stefan blowing and Thompson–Troian slip on mixed convection flow of a nanoliquid over a flat plate with first-order compound response are examined. In several industries and engineering sectors, nanofluid plays a vital role in augmenting heat transport properties. Moreover, nanoliquids are used in chemical manufacturing, cooling of electronic machinery, and biomedical disciplines. The fluids with slip consequences have a wide variety of applications. As the Thompson–Troian slip model permits the alteration of the amounts of slip close to the areas of elevated shear speed and shear anxiety, the effects of this slip model are examined in this article. Using appropriate transformations, the partial differential equations (PDEs) of the model are changed to ordinary differential equations (ODEs), and the reduced ODEs are numerically solved. This study has noteworthy effects on the flow, the heat transfer, and the accumulation transport characteristics. With a rise in the slip velocity and the critical shear rate, the fluid velocity increases, while the temperature field decreases for a rise in the velocity slip. It is also observed that when the Lewis number increases its value from 0.3 to 0.4, the heat transfer rate at the plate increases by almost 30.88%, and the accumulation velocity transport at the plate rises by 56.92%. Interestingly, dual solutions exist for some specific range of values of the relevant parameters. The results of this study will be of use to scientists and engineers to understand better the flow and heat transfer characteristics.

Study the Soret effects on Bioconvective induced magneto-hydrodynamics flow in presence of multiple slip and thermal radiation

The study deals with the bio-convective induced magneto-hydrodynamics (MHD) flow of non-Newtonian fluids with the simultaneous effect of multiple slips, heat source/sink, and linear thermal radiation, along with the Soret effect. The novelty of the present study is to analyze the impact of linear thermal radiation, bio-convection Lewis number and Soret parameter on velocity, induced magnetic field, and concentration. For this the flow for Maxwell and Casson fluids were considered and discussed separately, whereas a single governing momentum conservation equation was constructed by combining these two flow models. The governing equations were transformed by using similarity transformation. The transformed equation was solved by using MATLAB “BVP4C” solver. The transformation contributed various parameters such as the Soret parameter, Bioconvective Lewis number, Peclet Number, Radiation parameter, and Schmidt number. The effect of such parameters on momentum, induced magnetic field (i.m.f), temperature, and concentration were studied. The results depicted that the rise in the value of Nr, the temperature of the fluid were increased. However, the concentration of the microorganism declined with the rising value of chemical reaction parameter in both the Maxwell and Casson fluid. The observation also revealed that the velocity optimizes with the rising value of Sr, due to the hike in the concentration of the fluid.