Presence Of Reaction Research Articles

The Effects of Thermal Stratification on Flow Past an Infinite Vertical Plate in Presence of Chemical Reaction

This study examines how thermal stratification affect the movement of a fluid in presence of first order chemical reaction past an infinite vertical plate. To solve the non-dimensional governing equations in closed form for Pr = 1, the Laplace’s transform system is applied. Significant findings resulting from stratification are compared to the case of no stratification. The effects of many parameters, including S, K, Gr, Gc, Sc and time on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are explored and graphically displayed. It is shown that the steady state is attained at shorter times as a result of the application of stratification on the flow.

Unveiling the Behavior of MHD Mixed Convective Nanofluid Slip Flow over a Moving Vertical Plate with Radiation, Chemical Reaction, and Viscous Dissipation

The effects of chemical reactions on heat and mass transfer with radiation are extremely important in hydrometallurgical industries and chemical technology, such as polymer synthesis and food processing. A mathematical model for a viscous, incompressible, mixed convective, and MHD slip flow over a moving vertical plate is proposed in the present research. On account of physical relevance, the combined effect of radiation and chemical reaction on MHD nanofluid is studied. Using the similarity transformation method, the governing equations are converted into a system of ODEs. The transformed equations are then numerically solved by the Galerkin finite element method (GFEM). To analyse the characteristics of flow and heat transfer, a number of parameters are examined, including the slip, magnetic, radiation, and chemical reaction parameters, as well as the Schmidt, Grashof, Eckert, and Prandtl numbers. The coefficient of skin friction, Nusselt number, and Sherwood numbers for selected parameters are numerically presented. Graphs are used to determine and study the effects of magnetic fields, slip conditions, radiation, and chemical reactions on the temperature, concentration, and velocity profiles of nanofluids. This study shows that the presence of chemical reactions and radiation causes an increase in the velocity profile and temperature profile, respectively. Additionally, it is discovered that the temperature profile grows with increasing velocity slip, and concentration increases with increasing thermal slip. The current work has broad applications in various fields and can lead to the development of more efficient and effective systems in different industries, such as heat exchangers, energy production, environmental engineering, and biomedical engineering.

Thin liquid films on a slippery vertical cylinder in presence of chemical reaction

In industrial settings, chemical reactions often affect thin liquid films that flow down vertical cylinders. However, the effect of non-isothermal reactions on the dynamics of these films is not fully comprehended. To address this issue, this study investigates the behavior and stability of thin film flows on uniformly heated vertical cylinders that exhibit wall slippage when subjected to a pseudo-zero-order exothermic or endothermic chemical reaction. A reduced model is developed for thin liquid films flowing down vertical cylinders in the presence of exothermic or endothermic chemical reactions, assuming the film thickness is much smaller than the cylinder radius. The heat from the reaction and/or wall heating initiates a thermocapillary Marangoni effect, which is further enhanced by wall slippage, directly affecting the dynamics of the free surface. Linear and weakly nonlinear stability analyses show that wall slip amplifies the instability, while exothermic reactions stabilize the system and endothermic reactions destabilize it. It is also found that chemical reactions significantly influence the supercritical stable, subcritical unstable, unconditional stable, and explosive zones of the thin film. A direct numerical simulation confirms the results of linear and weakly nonlinear analyses.

Dissolution‐driven convection of a power‐law fluid in a porous medium in the presence of chemical reaction

AbstractThe flow through porous medium accounts for numerous applications in various fields namely, agriculture, geothermal sciences, and engineering. Furthermore, dissolution‐driven convection in porous media has grabbed great attention in recent years due to its practical applications in long‐term geological storage of carbon dioxide, in the production of mineral deposits, and other industrial applications. In this regard, the current numerical analysis focuses on addressing the thermal instability of dissolution‐driven convective phenomena of a power‐law fluid through a porous horizontal domain with a first‐order chemical reaction. For linear stability analysis, the method of normal modes has been employed to solve governing dimensionless equations which give rise to an eigenvalue problem. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for the onset of convection. The impact of Damköhler number, Péclet number, and power‐law index on the onset of convection has been investigated. The role of these critical parameters is found to be highly significant in stabilizing the system. An increase in the power‐law index causes stabilization or destabilization in the system, depending on the Péclet number. An enhancement in the magnitude of Damköhler number makes the system stable for all values of the Péclet number. Also, Damköhler and critical Rayleigh number are inter‐related, that is, an increment in Damköhler number results in the enhancement of critical Rayleigh numbers, which in turn leads to stabilization of the system. The critical wave number is observed to have a remarkable influence on Damköhler number as well as power‐law index.

Numerical solution to flow of Casson fluid via stretched permeable wedge with chemical reaction and mass transfer effects

The purpose of this research is to discuss a two-dimensional (2D), laminar, continuous flow of Casson liquid through a stretched porous wedge in the presence of chemical reaction and buoyancy effects over wedge. This research is aimed at analyzing chemically reacting flow of Casson model over a heated porous wedge in order to understand the features of dynamic wedge. The governing equations and involved parameters are nondimensionalized using transformations. Bvp4c, a numerical tool in Matlab is employed to assess the solution. Significant findings of the major dimensionless parameters on state profiles of velocity, temperature and concentration are drawn graphically. The principal results indicate the impacts of Casson parameter, Eckert and Prandtl number, R stretching parameter, [Formula: see text] chemical parameter, Sc Schmidt number, C mass transfer parameter, m wedge angle parameter on concentration, velocity and temperature field. The Sherwood, Nusselt number and skin friction numerical values are presented in tabular form. Major findings show that drag force at wedge declines for greater [Formula: see text]. Nusselt number shrinks for larger behavior for [Formula: see text]. Sherwood number upsurges for greater performance for chemical reaction parameter [Formula: see text]. Moreover, [Formula: see text] upsurges the temperature slowly but the impacts of [Formula: see text] on concentration show a decreasing behavior.

Effect of TiO2 nanoparticles on the thermal energy storage of HITEC salt for concentrated solar power applications

Thermal energy storage materials are substantial in concentrated solar power (CSP) plants as they absorb solar thermal energy and store it to be used for electricity production. Enhancing the thermophysical properties of these materials will positively affect the efficiency of the CSP plant system and lower electricity price. This research synthesized a novel composite of Titanium Dioxide (TiO2) nanoparticles and the ternary nitrate molten salt (HITEC) at different nanoparticle concentrations. The nano-enhanced molten salt (NEMS) samples were characterized for compatibility and nanostructure analysis. Also, the thermophysical properties and thermal cycling behaviour of the NEMS samples were evaluated. The results indicate that 0.1 wt% can enhance the specific heat capacity of HITEC by 5.5 %, latent heat by 78 %, and upper working temperature by 5 %. The morphological analysis of the 0.1 wt% NEMS sample revealed a good dispersion of nanoparticles in HITEC and the formation of nanostructures. The FT-IR analysis showed the chemical stability of the nanofluid with no presence of chemical reaction between its components. The thermal cycling test of the optimum sample showed the chemical stability of the nanocomposite and the thermal cycling stability of the enhanced thermophysical properties.

Heat and mass transport behavior in bio-convective reactive flow of nanomaterials with Soret and Dufour characteristics

The main of this article is to analyze magnetohydrodynamic bioconvective flow of Sutterby nanoliquid. Gyrotactic microorganism in presence of chemical reaction is addressed. Thermophoretic, magnetic field, random motion heat generation and radiation are discussed. Furthermore, Dufour and Soret behaviors are taken into account. Thermal conduction augmentation performance is discussed by utilization Boungiorno's model. Nonlinear PDE's (partial differential equations) are changed to ordinary system through appropriate variables. To developed computational solutions, we used the ND-solve technique. Results for temperature, microorganism field, liquid flow, and concentration are exhibited through different emerging variables. The physical quantities like Nusselt number, microorganism density number and solutal transport rate for various sundry variables are presented. Summary of main results re highlighted in the conclusions. Velocity reduces against magnetic field, while reverse trend seen for buoyancy ratio variable. Thermal distribution has an enhancing trend for magnetic and radiation variables. An enhancement in concentration distribution is seen for Soret number.

Unsteady magneto-hydro-dynamics flow of Jeffrey fluid through porous media with thermal radiation, Hall current and Soret effects

In the present paper, Hall current and Soret reaction effects on unsteady natural convection MHD flow with viscous, incompressible, and electrically conducting fluid through a porous medium in the presence of chemical reaction and thermal radiation have been studied. The fluid has considered non-Newtonian fluid, which is Jeffrey fluid. The non-dimensional flow governing equations are solved analytically through the perturbation method, and obtained results of velocity, concentration, and temperature have been analyzed with the help of graphs drawn for different parameters. The numerical values of skin friction, Nusselt number, and Sherwood number have been tabulated. The study's results may find applications related to solar physics dealing with the solar cycle, Magnetohydrodynamics sensors, rotating MHD induction machine energy generators, sunspot development, the structure of rotating magnetic stars, etc. The velocity profiles are observed to increase with an increase in Hall parameters, but reverse effects are found with an increase in viscosity ratio and chemical reaction parameter. The thermal radiation parameter is to increase the temperature profiles, but the reverse effect is observed with an increase in the frequency of oscillations. Further, the concentration is decreased with an increase in the Schmidt number and increased with an increase in the chemical reaction parameter.

Anodic Behaviour of Ni42Fe38Cu20 Electrode in Molten Fluoride Salts

The anodic behaviour of Ni42Fe38Cu20 alloy at different sodium-potassium-cryolite-based electrolyte compositions was examined by chronopotentiometry, chronoamperometry, and linear sweep voltammetry at 1098 K for different electrolyte compositions. Steady-state anodic polarisation curves show that the anodic overpotential in electrolytes with molar ratio CR = (NaF+KF)/AlF3 = 1.4 is significantly less than in electrolyte with CR = 1.3. Short-term galvanostatic polarisation curves indicate that the potential difference between the anode and reference electrode (Al) was stable in electrolytes with CR = 1.4 and potassium ratio KR = KF/(KF + NaF) = 0.3 and CR = 1.4 KR = 0.35. The linear sweep voltammetry method indicates the presence of a diffusion-controlled reaction at a potential below the onset of oxygen evolution, which can be attributed to oxide formation. Tafel curves indicate the presence of the reactions below the potential of oxygen evolution but show a similar overpotential level for the oxygen-evolving reaction as for carbon anodes. Furthermore, the effect of pre-oxidation and influence of consistent polarisation on the anode performance was explored. Pre-oxidised anodes have better stability and lower exchange current density in similar experimental conditions compared to untreated anodes. It was also observed that leaving anodes unpolarised could lead to their instability and fluoridation of both types of anodes, with less severe effect on the pre-oxidised anode.

Darcy-Forchheimer hybrid nanofluid flow over the rotating Riga disk in the presence of chemical reaction: Artificial neural network approach

The aim of present study is to examine the augmentation of thermal energy transfer in hybrid nanofluid flow caused by a rotating Riga disk in the presence of thermal radiation and chemical reaction. The silver and aluminium oxide nanoparticles are used to examine the thermal effect of water base fluid. The Darcy-Forchheimer model is considered to endorse the inertial and porous media effects and makes the model more realistic from the physical scenario. Levenberg-Marquardt backpropagation algorithm is considered to analyze the hybrid nanofluid’s properties. Using scaling group transformations, the governing partial differential equations are transformed into a system of ordinary differential equations. Resulting ordinary differential equations are solved numerically by applying a suitable shooting technique by MATLAB. The results obtained for the governing differential equations have been incorporated into a dataset on which the neural network has been trained. The effects of physical parameters have been analyzed for velocity, temperature, and concentration profiles. The determination, designing, convergence, verification, and stability of the Levenberg-Marquardt backpropagation neural network algorithm are validated on the assessment of achieved accuracy through performance, fit, regression, and error histogram plots for the discussed hybrid nanofluid. It is observed that fluid velocity reduces for enhanced Darcy-Forchheimer number, magnetic parameters and boosted for enhanced modified Hartmann number. Temperature profile increases by increasing the Brownian motion and thermophoresis parameters.

Homotopy Perturbation Method for MHD Heat and Mass Transfer Flow of Convective Fluid through a Vertical Porous Plate in the Presence of Chemical Reaction and Inclined Magnetic Field

The present work is devoted to study a viscous, incompressible, and electrically conducting fluid on an MHD fluid flowing past a semi-infinite porous plate in the presence of chemical reaction and inclined magnetic parameter. The governing equations are expressed in non-dimensional form and the resulting nonlinear equations are solved employing the Homotopy perturbation method for the nondimensional velocity, temperature, and concentration profiles. The effects of various controlling parameters such as Casson parameter, Hartmann number, inclined magnetic parameter, porosity parameter, Grashof number, angle of inclination, Prandtl number, Eckert number, radiation parameter, Schmidt number and thermal radiation parameters are presented graphically and discussed in detail. It was found that, velocity profile is enhanced in the presence of Casson, magnetic field and inclined angle parameters whereas it declined with positive increase in the porosity, Grashof and inclined angle numbers. Similarly, increase in Prandtl, Eckert, radiation and inclined angle numbers lead to increase in the temperature distribution of the fluid, while it deceased as the magnetic field parameter increased. The effect of increased thermal radiation parameter is proportional to the concentration profile, whereas it declines for increase in values of Schmidt number.

Homotopy Perturbation Method for MHD Heat and Mass Transfer Flow of Convective Fluid through a Vertical Porous Plate in the Presence of Chemical Reaction and Inclined Magnetic Field

The present work is devoted to study a viscous, incompressible, and electrically conducting fluid on an MHD fluid flowing past a semi-infinite porous plate in the presence of chemical reaction and inclined magnetic parameter. The governing equations are expressed in non-dimensional form and the resulting nonlinear equations are solved employing the Homotopy perturbation method for the nondimensional velocity, temperature, and concentration profiles. The effects of various controlling parameters such as Casson parameter, Hartmann number, inclined magnetic parameter, porosity parameter, Grashof number, angle of inclination, Prandtl number, Eckert number, radiation parameter, Schmidt number and thermal radiation parameters are presented graphically and discussed in detail. It was found that, velocity profile is enhanced in the presence of Casson, magnetic field and inclined angle parameters whereas it declined with positive increase in the porosity, Grashof and inclined angle numbers. Similarly, increase in Prandtl, Eckert, radiation and inclined angle numbers lead to increase in the temperature distribution of the fluid, while it deceased as the magnetic field parameter increased. The effect of increased thermal radiation parameter is proportional to the concentration profile, whereas it declines for increase in values of Schmidt number.

Semi-Numerical Investigation of Boundary Layer Flow and Heat Transfer of Magnetohydrodynamics Nano-Fluid Flow in Presence of Chemical Reaction Over a Non-Isothermal Porous Medium

Abstract The technical brief presents, analysis of boundary layer flow and heat transfer in nanofluids under the influence of magnetic field, thermal radiation and chemical reaction over non-isothermal stretching surface through permeable porous medium. The self-similarity equations obtained from governing equations are solved using shifted Chebyshev and Haar wavelet collocation methods. The prescribed surface temperature, prescribed heat flux cases and impact of various flow governing parameters are discussed in detail. The established results are compared with earlier results and are comparable.

Simulating bulk viscosity in neutron stars. I. Formalism

The faithful inclusion of the effects of bulk viscosity induced by the presence of chemical reactions is an important issue for simulations of core-collapse supernovae, binary neutron star mergers, and neutron star oscillations, where particle abundances are locally pushed out of chemical equilibrium by rarefaction and compression of the fluid elements. In this work, we discuss three different approaches that can be used to implement bulk viscosity in general relativistic hydrodynamic simulations of neutron stars: the exact multi-component reacting fluid, and two M\"uller-Israel-Stewart theories, namely the second order Hiscock-Lindblom model and its linear limit, the Maxwell-Cattaneo model. After discussing the theory behind the three approaches, we specialize their dynamics equations to spherical symmetry in the radial gauge-polar slicing (i.e., Schwarzschild) coordinates. We also discuss a particular choice for the equation of state of the fluid and the associated neutrino emission rates, which are used in a companion paper for the numerical comparison of the three frameworks, and we obtain the effective sound speed for the Hiscock-Lindblom theory in the non-linear regime.

Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman–Kac Approach

We derive, through subordination techniques, a generalized Feynman–Kac equation in the form of a time fractional Schrödinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through a stochastic treatment how this generalized Feynman–Kac equation describes subdiffusive processes with reactions. In this interpretation, the subordinated local time represents the number of times a specific spatial point is reached, with the amount of time spent there being immaterial. This distinction provides a practical advance due to the potential long waiting time nature of subdiffusive processes. The subordinated local time is used to formulate a probabilistic understanding of subdiffusion with reactions, leading to the well known radiation boundary condition. We demonstrate the equivalence between the generalized Feynman–Kac equation with a reflecting boundary and the fractional diffusion equation with a radiation boundary. We solve the former and find the first-reaction probability density in analytic form in the time domain, in terms of the Wright function. We are also able to find the survival probability and subordinated local time density analytically. These results are validated by stochastic simulations that use the subordinated local time description of subdiffusion in the presence of reactions.

Transient MHD Free Convection Flow, Heat and Mass Transfer in Darcy–Forchheimer Porous Medium in the Presence of Chemical Reaction and Heat Absorption with Soret and Dufour Effects: Element-Free Galerkin Modelling

Transient MHD Free Convection Flow, Heat and Mass Transfer in Darcy–Forchheimer Porous Medium in the Presence of Chemical Reaction and Heat Absorption with Soret and Dufour Effects: Element-Free Galerkin Modelling

Study of Heat and Mass Transfer of an Unsteady Magnetohydrodynamic (MHD) Nanofluid Flow Past a Vertical Porous Plate in the Presence of Chemical Reaction, Radiation and Soret Effects

This paper investigates the heat and mass transfer of an unsteady, MHD incompressible water-based nanofluid (Cu and TiO2) flow over a stretching sheet in a transverse magnetic field with thermal radiation Soret effects. The governing differential equations are transformed into a set of non-linear ordinary differential equations and solved using a regular perturbation technique with appropriate boundary conditions for various physical parameters. The effects of different physical parameters on the dimensionless velocity, temperature, and concentration profiles are depicted graphically and analyzed in detail. Favourable comparisons with previously published work on various exceptional cases of the problem are obtained. Finally, numerical values of the physical quantities, such as the local skin-friction coefficient, the local Nusselt number and the local Sherwood number, are presented in tabular form. Results describe that the velocity and temperature diminish with enhancing the thermal radiation. Concentration decreases with improving the chemical reaction. Both velocity and concentration are enhanced with increases of soret parameter. And also, water–based TiO2 nanofluids possess higher velocity than water-based Cu nanofluids.

Solute dispersion phenomena in a free and forced convective flow with boundary reactions

The applications of solute dispersion in a free and forced convective flow are highly important in the diversified fields of chemical industries, nuclear power plants, etc. In the present work, the dispersion of tracers between two parallel plates in a combined free and force convective flow under the effect of wall absorption and bulk chemical reaction is explored using Mei’s multi-scale homogenization method. A uniform temperature variation is considered along both the plates. The main focus of this study is to investigate the effect of the Grashof number not only on Taylor diffusivity but also on the longitudinal and transverse concentration distribution. The effects of the boundary absorption and bulk chemical reaction in presence of the Grashof number are analyzed. The most interesting fact of this study is that the Taylor dispersivity is equal for both the positive and negative Grashof number i.e. for heating and cooling respectively. Also, the longitudinal concentration of solute reduces when both the process of cooling and heating increases. But the opposite scenario arises in the case of transverse concentration distribution. The results of the present study may be applied to waste management systems in chemical industries.

Three Dimensional Modelling of Magnetohydrodynamic Bio-Convective Casson Nanofluid Flow with Buoyancy Effects Over Exponential Stretching Sheet Along with Heat Source & Gyrotactic Micro-Organisms

In current analysis, influence of buoyancy forces in MHD bioconvective non-Newtonian nanofluids over three dimensional exponential sheet has been studied numerically. Additionally, impact of heat source parameter along with convective conditions has been incorporated. Moreover, nanofluid flow with gyrotactic microorganisms has been analyzed in presence of chemical reaction. Initially similarity variables are used for the conversion of partial differential equations into highly non-linear differential equations. Thusly, non-linear behavior of equations makes typical solutions which are not solved analytically. So, computational MATLAB software is used to calculate results and graphs by following shooting algorithm with Runge Kutta Fehlberg technique using ODE45 solver. Present modeling investigates the influence of crucial fluid parameters especially; magnetic M (0.1 ≤ M ≤ 0.9), Casson parameter β (0.09 ≤ β ≤ 0.13), permeability parameter Bθ, Brownian motion Nb (0.5 ≤ Nb ≤ 5.0), thermophoresis Nt (0.2 ≤ Nt ≤ 2.0), thermal Biot number Bt (0.3 ≤ Bt ≤ 0.7), heat generation parameter Q (0.1 ≤ Q ≤ 0.5), Prandtl number Pr (0.1 ≤ Pr ≤ 0.9), concentration Biot number Bc (0.1 ≤ Bc ≤ 0.9), Lewis number Le (1 ≤ Le ≤ 5), chemical reaction parameter Ch (0.1 ≤ Ch ≤ 0.9), bioconvective Lewis number Lb (0.1 ≤ Lb ≤ 2), Peclet number Pe (0.1 ≤ Pe ≤ 5), gyrotactic Biot number Bn (0.1 ≤ Bn ≤ 0.5), stretching ratio parameter c (0.1 ≤ c ≤ 0.3) and microorganism concentration difference parameter Ω (0.1 ≤ Ω ≤ 5.0). Final results are compared for Prandtl number and stretching ratio parameter along with residual errors. It is inferred that motile concentration declines for larger bioconvective Lewis number whereas rises for motile gyrotactic microorganism Biot number.

Modified Buongiorno's model for the analysis of chemically reacting jet flow of ternary hybrid nanofluid under the influence of activation energy and bio‐active mixers

AbstractIn the modern era, the heat transfer is the basic need in every field of sciences and engineering. To augment the energy transfer, the ternary hybrid nanofluid (Thnf) has been used. After the successful nanofluid working performance, the researchers used this idea in many physical situations. Later on, the researchers tried to further improve the performance of nanofluid with high stability. Motivated from the unique practical applications of hybrid nanofluid, in the present analysis, we have considered ternary nanoliquid, which is obtained by the suspension of three nano particulates in base fluids. The aim of the present research is to highlight the thermal applications of ternary nanofluid in the vertical stretching wall jet flow. The suspension of three different nano solid particles is considered in a base liquid water a jet flow over a vertical extending sheet is addressed. In addition to this, the presence of chemical reaction in the concentration, thermophoresis effect in the energy equation and heat source is also addressed. To model the present phenomena of flow using the modified Buongiorno's model, that highlights the impact of Brownian motion and thermophoresis effect. The present flow problem is modelled in terms of PDE's. To transform the obtained model, we use appropriate similarity variables. The transform model is then solved numerically, using the fast convergence numerical PCM approach (parametric continuation method). The solution obtained is shown through graphical representation by indicating the impact of pertinent flow parameters. Finally, from the present results, we obtained that the performance of Thnf is effective in water as compared to hybrid nanoliquid and mono nanofluid. Furthermore, the motile gyrotactic microbes profile gets lower with the varying values of bioconvection Lewis number and Peclet number.