Heat and Mass Flux Effects on a Moving Vertical Cylinder with Chemically Reactive Species Diffusion

This paper presents the development of the free convection boundary layer flow of a viscous and incompressible fluid past an impulsively started semi-infinite vertical cylinder with uniform heat and mass fluxes and chemically reactive species. The governing coupled nonlinear partial differential equations have been solved numerically using the finite-difference scheme of Crank–Nicolson type. Graphical results for the velocity, temperature, concentration, local and average skin friction, Nusselt number and Sherwood number profiles are illustrated and discussed for various physical parametric values. It is noted that due to the presence of first-order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter     

Unsteady Flow of Radiating and Chemically Reacting MHD Micropolar Fluid in Slip-Flow Regime with Heat Generation

An analytical study of the problem of unsteady free convection with thermal radiation and heat generation on MHD micropolar fluid flow through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime has been presented. The Rosseland diffusion approximation is used to describe the radiation heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted for in the mass diffusion equation. A uniform magnetic field acts perpendicular on the porous surface absorbing micropolar fluid with a suction velocity varying with time. A perturbation technique is applied to obtain the expressions for the velocity, microrotation, temperature, and concentration distributions. Expressions for the skin-friction, Nusselt number, and Sherwood number are also obtained. The results are discussed graphically for different values of the parameters entered into the equations of the problem.     

Magnetohydrodynamics Nanofluid Flow Containing Gyrotactic Microorganisms Propagating Over a Stretching Surface by Successive Taylor Series Linearization Method

Nanofluid dynamics with magnetohydrodynamics has tremendously contributed in industrial applications recently since presence of nanoparticle in base fluids enhances the specific chemical and physical properties. Owing to the relevance of nanofluid dynamics, we analyze the nanofluid flow in the presence of gyrotactic microorganism and magnetohydrodynamics through a stretching/shrinking plate. The impacts of chemical reaction and thermal radiation on flow characteristics are also studied. To simplify the governing equations of microorganisms, velocity, concentration and temperature, the similarity transformations are employed. The couple governing equations are numerically solved using Successive Taylor Series Linearization Method (STSLM). The velocity profile, motile microorganism density profile, concentration profile, temperature profile as well as Nusselt number, skin friction coefficient, Sherwood number and density number of motile microorganisms are discussed using tables and graphs against all the sundry parameters. A numerical comparison is also given for Nusselt number, Sherwood number, skin friction, and density number of motile microorganisms with previously published results to validate the present model. The results show that Nusselt number, Sherwood number and density number diminish with increasing the magnetic field effects.     

On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species

Finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with constant heat flux and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The concentration profiles are compared with the exact solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction, the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Estimation of magnetohydrodynamic radiative nanofluid flow over a porous non‐linear stretching surface: application in biomedical research

The present study investigates the effects of thermal radiation and chemical reaction on magnetohydrodynamic flow, heat, and mass transfer characteristics of nanofluids such as Cu–water and Ag–water over a non‐linear porous stretching surface in the presence of viscous dissipation and heat generation. Using similarity transformation, the governing boundary layer equations of the problem are transformed into non‐linear ordinary differential equations and solved numerically by the shooting method along with the Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme. The influences of various parameters on velocity, temperature, and concentration profiles of the flow field are analysed and the results are plotted graphically. A backpropagation neural network is applied to predict the skin friction coefficient, Nusselt number, and Sherwood number and these results are presented through graphs. The present numerical results are compared with the existing results and are found to be in good agreement. The results of artificial neural network and the obtained numerical values agree well with an error <5%.Inspec keywords: silver, copper, transforms, nanofluidics, friction, backpropagation, heat radiation, water, external flows, partial differential equations, nonlinear differential equations, boundary layers, Runge‐Kutta methods, mass transfer, flow through porous media, magnetohydrodynamicsOther keywords: magnetohydrodynamic radiative nanofluid flow, nonlinear stretching surface, biomedical research, thermal radiation, chemical reaction, magnetohydrodynamic flow, nonlinear porous stretching surface, viscous dissipation, similarity transformation, governing boundary layer equations, nonlinear ordinary differential equations, shooting method, Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme, flow field, backpropagation neural network, Cu–water nanofluid, Ag–water nanofluid, skin friction coefficient, Nusselt number, Sherwood number, artificial neural network, Ag‐H₂ O, Cu‐H₂ O     

Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface

Summary The effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The velocity profiles are compared with previously published works and are found to be in good agreement. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite element method. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first-order chemical reaction the concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Heat and mass transfer on a stretching sheet with a magnetic field in a visco-elastic fluid flow through a porous medium with heat source or sink

A mathematical model will be analyzed in order to study the role of an applied magnetic field on heat and mass transfer in a visco-elastic fluid flow through a porous medium with a stretching sheet in the presence of such effect as heat generation or absorption. A similarity transformation is used to reduce the governing partial differential equations into ordinary ones, which are solved numerically by shooting method. Numerical results for the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Unsteady three-dimensional combined heat and mass free convective flow over a stretching surface with time-dependent chemical reaction

Summary This paper investigates the combined effects of the free convective heat and mass transfer on the unsteady three-dimensional laminar boundary layer flow over a stretching surface. The stretching rates of the surface are assumed to vary as a reciprocal of a linear function of time. Generation or consumption of the diffusing species due to a homogeneous chemical reaction is considered. The chemical reaction rate is assumed to vary with time according to a power law. With appropriate similarity transformation, the boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying a fifth-order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Prandtl number Pr, Schmidt number Sc, the unsteadiness parameter λ, the chemical reaction parameter γ₀ and the reaction order n are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various values of the parameters. A comparison is made between the present work and previous results.     

Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium

The free convection phase change heat transfer of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous space is theoretically addressed. The core of the nanoparticles is made of a phase change material and encapsulated in a thin shell. Hence, the core of the nanoparticles of the suspension undergoes a phase change at its fusion temperature and release/store large amounts of latent heat. The phase change of nanoparticles is modeled using a sine shape temperature-dependent heat capacity function. Darcy-Brinkman model is used to model the flow in the porous medium. The governing equations including the conservation of mass, momentum, and heat are transformed into a non-dimensional form before being solved by the finite element method in a structured non-uniform mesh. The influence of the porosity, Darcy number, Rayleigh number, fusion temperature of nanoparticles, and the unsteady time-periodic boundary conditions on the thermal behavior of the porous medium in the presence of NEPCM particles is investigated. The results show that the presence of NEPCM particles improves the heat transfer. The increase of porosity improves the heat transfer when the volumetric concentrations of NEPCM particles are higher than 3%. There exists an optimal dimensionless fusion temperature of NEPCM nanoparticles for the interval [0.25; 0.75].     

Kinetics of silicon–metal alloy infiltration into porous carbon

The kinetics of infiltration of Si and its alloys into porous carbon has been investigated theoretically using a modified Washburn model. The effect of alloy composition and temperature on infiltration has been quantified. The resulting characteristics depend on the type of alloy and the composition of the secondary metallic phase. Aluminum generally suppresses infiltration rate while the influence of Cu depends on composition. Infiltration is enhanced for low Cu concentration below a threshold value, and attenuated for higher concentration. Increasing the temperature enhances both the infiltration capacity and reaction rate.     

MHD 3D free convective flow of nanofluid over an exponentially stretching sheet with chemical reaction

This paper deals with a problem where the effect of variable magnetic field and chemical reaction on free convective flow of an electrically conducting incompressible water based nanofluid over an exponentially stretching sheet has been investigated. In the present study, Buongiorno model associated with Brownian motion and thermophoretic diffusion is employed to describe the heat transfer enhancement of nanofluids. Some suitable similarity transformations reduced the governing boundary layer non-linear partial differential equations into a set of ordinary non-linear differential equations. The transformed equations are then solved numerically using fourth order Runga-Kutta method along with Shooting technique. The major outcomes of the present study is that the magnetic field impedes the fluid motion while thermal as well as mass buoyancy forces accelerate it, the thermophoretic diffusion enhances dimensionless fluid temperature as well as concentration leading to thicker thermal and concentration boundary layers. On the other hand, concentration exponent, Brownian motion parameter and chemical reaction parameter exhibit reverse trend on temperature and concentration. In addition, the presence of magnetic field under the influence of thermal as well as mass buoyancies supports to reduce the rate of heat transfer as well as wall shear stress while the first order chemical reaction develops a thinner concentration boundary layer.     

Synthesis and processing of ceramic–metal composites by reactive metal penetration

Molten aluminum reduces and penetrates silicate ceramics to produce a metal–ceramic composite which yields an Al₂O₃ skeleton infiltrated with a solidified Al–Si alloy. Penetration experiments have been used to study the influence of p(O₂), temperature and substrate composition on penetration kinetics and composite microstructure. The limiting kinetic step for Al penetration is the chemical reaction between Al and the ceramic. For dense substrates the maximum reaction rates are observed between 1000–1200°C and are independent of p(O₂). For porous substrates it is necessary to reach a critical temperature or p(O₂), before infiltration starts. Increasing the Si concentration in the molten Al results in the reduction of the reaction rates.     

Transport and fate of volatile organic chemicals in unsaturated, nonisothermal, salty porous media: 1. Theoretical development.

A wide variety of volatile organic chemicals (VOC) have been applied to agricultural land or buried in chemical waste sites. The fate of these chemicals depends upon several mechanisms such as sorption, degradation, and transport in liquid and gaseous phases. Understanding the transport mechanisms affecting the volatile chemicals can lead to better management strategies. A theory describing inorganic solute transport, water and heat transfer, and the fate and transport of VOC in porous media has been developed. This theory includes matric water pressure head, solution osmotic pressure head, gravity pressure head, temperature, inorganic solute concentration, and VOC concentration gradients as driving forces for heat and mass transfer. The effect of surface tension, as a function of VOC concentration and temperature, on the matric water pressure head is included. The VOC can be associated with gas, liquid, and solid phases of the porous media. The gas and liquid phases are mobile, but the solid phase is immobile. The transfer of VOC across the gas/liquid, liquid/solid, and gas/solid interfaces is included using sorption-equilibrium assumptions at the interfaces. The VOC can degrade. This degradation is described by a first-order decay rate. The theory can be used to predict spatial and temporal variations of water content, temperature, inorganic concentration and the total concentration of VOC within a porous medium. The concentration of VOC in each phase can be predicted also.     

Effects of suction on heat and mass transfer along a moving vertical surface in the presence of chemical reaction

Heat and mass transfer effects on a continuously moving vertical surface with chemical reaction of first order is considered. The velocity and concentration profiles are studied for different parameters like Schmidt number, Prandtl number and Chemical reaction parameter. It is observed that the velocity and concentration increases during generative reaction and decreases in destructive reaction.     

Numerical Simulation for Magneto Nanofluid Flow Through a Porous Space with Melting Heat Transfer

Melting heat transfer and non-Darcy porous medium effects in MHD stagnation point flow toward a stretching surface of variable thickness are addressed. Brownian motion and thermophoresis in nanofluid modeling are retained. Zero mass flux condition for concentration at surface is imposed. The problem of ordinary differential system are analyzed numerically through shooting technique. Graphically results of various physical variables on the velocity, temperature and concentration are studied. Skin friction coefficient local Nusselt number and Sherwood number are also addressed through tabulated values. The results described here illustrate that the velocity field is higher via larger melting parameter. However reverse situation is examined for Hartman number. Moreover the influence of thermophoresis parameter on temperature and concentration is noted similar.     

Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy

An analysis is performed to study the combined effects of nonlinear thermal radiation, Arrhenius activation energy, chemical reaction and heat generation/absorption on the steady three-dimensional magnetohydrodynamic flow of Eyring-Powell nanofluid flow over a slendering stretchable sheet with velocity, thermal and solutal slips. The prevailing partial differential equations are transmuted into coupled non-linear ordinary differential equations via with the suitable similarity transformations. The resultant non-linear coupled differential equations are solved numerically by using the R-K 4^th order method along with shooting scheme. The results are calculated to measure the influence of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient are presented graphically and in tabular form. It is noticed that the temperature is more impactable for higher values of radiative heat transport. The local Sherwood number decays exponentially for all the values of the chemical reaction parameter. We compared the present results for the limiting cases with previously published results, which has shown reliability and efficiency.     

接枝聚乙二醇单甲醚侧链制备聚酰亚胺多孔微球

以3,5-二氨基苯甲酸与线性低聚物聚乙二醇单甲醚在催化剂存在的条件下发生酯化反应,得到了接枝单体。以接枝单体、3,5-二氨基苯甲酸以及均苯四甲酸二酐在非水乳液体系中发生聚合反应,经过两步亚胺化及热处理得到了多孔聚酰亚胺微球。通过实验确定了接枝单体的最优反应条件:酸醇摩尔比为1.3,催化剂、携水剂的用量与醇的质量比分别为4%、130%,反应时间为6h。实验结果表明,随着接枝单体在聚酰亚胺中浓度从20%～40%,粒径逐渐增大,粒径范围为9.5～15.7μm;而玻璃化温度从210℃降至178℃;同时在接枝单体浓度为40%时得到了孔结构,比表面积为148cm3/g;通过控制热处理时气体压力可以控制孔结构大小。     

Computational simulation of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper primarily deals with the computational aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. After the dimensionless governing partial differential equations of the non‐isothermal chemical dissolution‐front instability problem are briefly described, the formulation of a computational procedure, which contains a combination of using the finite difference and finite element method, is derived for simulating the morphological evolution of chemical dissolution fronts in the non‐isothermal chemical dissolution system within two‐dimensional fluid‐saturated porous media. To ensure the correctness and accuracy of the numerical solutions, the proposed computational procedure is verified through comparing the numerical solutions with the analytical solutions for a benchmark problem. As an application example, the verified computational procedure is then used to simulate the morphological evolution of chemical dissolution fronts in the supercritical non‐isothermal chemical dissolution system. The related numerical results have demonstrated the following: (1) the proposed computational procedure can produce accurate numerical solutions for the planar chemical dissolution‐front propagation problem in the non‐isothermal chemical dissolution system consisting of a fluid‐saturated porous medium; (2) the Zhao number has a significant effect not only on the dimensionless propagation speed of the chemical dissolution front but also on the distribution patterns of the dimensionless temperature, dimensionless pore‐fluid pressure, and dimensionless chemical‐species concentration in a non‐isothermal chemical dissolution system; (3) once the finger penetrates the whole computational domain, the dimensionless pore‐fluid pressure decreases drastically in the non‐isothermal chemical dissolution system.     

Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction

An exact solution to the flow due to impulsive motion of an infinite vertical plate in its own plane in the presence of i) species concentration ii) constant heat flux at the plate iii) chemical reaction of first order, has been derived by the Laplace-transform technique. Velocity and concentration profiles are shown on graphs. It is observed that due to the presence of first order chemical reaction, the velocity decreases but the skin-friction being positive at large values of the chemical reaction parameter, there may not occur separation of the flow near the plate.     

Optical metal ion sensor based on diffusion followed by an immobilizing reaction. Quantitative analysis by a mesoporous monolith containing functional groups

A new optical metal ion sensor based on diffusion followed by an immobilizing reaction has been developed. The current sensor is based on a model that unifies two fundamental processes which a metal analyte undergoes when it is exposed to a porous, ligand-grafted monolith: (a) diffusion of metal ions to the binding sites and (b) metal-ligand (ML(n)) complexation. A slow diffusion of the metal ions is followed by their fast immobilizing reaction with the ligands in the monolith to give a complex. Inside the region where the ligands have been saturated, the diffusion of the metal ions reaches a steady state with a constant external metal ion concentration (C(0)). If the complex ML(n) could be observed spectroscopically, the absorbance of the product A(p) follows: A(p) = Kt(1/2), K = 2epsilon(p)(L(0)C(0)D)(1/2). D = diffusion constant of the metal ions inside the porous solid; L(0) = concentration of the ligands grafted in the monolith; and t = time. This equation is straightforward to use, and the K vs C(0)(1/2) plot provides the correlations with the concentrations (C(0)) of the metal ions. This is a rare optical sensor for quantitative metal ion analysis. The use of the model in a mesoporous sol-gel monolith containing grafted amine ligands for quantitative Cu(2+) sensing is demonstrated. This model may also be used in other chemical sensors that depend on diffusion of analytes followed by immobilizing reactions in porous sensors containing grafted/encapsulated functional groups/molecules.