Non-dimensional Concentration Research Articles

Investigating the effect of an inclined magnetic fieldon heat and mass transmission in turbulent squeeze flowof UCM fluid between parallel plates

This paper investigates the effects of an inclined magnetic field on heat and mass transfer in turbulent squeeze flow of a viscoelastic fluid with an upper-convected Maxwell model. Squeezing flow is an important phenomenon in various industrial and mechanical processes related to flows between parallel surfaces. Mathematical modelling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. The study employs a system of partial differential equations to describe the flow issue. Governing nonlinear partial equations are reduced into nonlinear ordinary differential equations. The modelled equations are then solved numerically by utilizing the efficient Adams-Moulton method of the fourth order based on the shooting technique using the Fortran programming language. Numerical results are compared with another numerical approach and an excellent agreement is observed. The effects of various factors on the non-dimensional velocity, temperature, and concentration patterns are presented using graphs, while tables are used to assess the numerical values of the skin friction, Nusselt and Sherwood numbers. It is found that the temperature profile decreases as the compression parameter increases but increases with an increase in the Eckert number. The results of this study could be useful in designing heat and mass transfer equipment for applications in viscoelastic fluid flows under an inclined magnetic field.

DUFOUR, SORET AND DISSIPATION EFFECTS ON MAGNETOHYDRODYNAMIC FLOW PAST A STRETCHING PERMEABLE SHEET WITH RADIATIVE CHEMICAL REACTION ANDHEAT SOURCE

Present investigation explores the numerical solution of Magnetohydrodynamic laminar steady gray fluid flow with heat and mass transfer past a stretching permeable sheet, incorporating several factors such as heat source, viscous and joules dissipation effects, thermal radiation, chemical reactions, Soret and Dufour effects. The governing nonlinear PDEs are simplified into ODEs with the help of similarity transformations. Momentum equation is solved analytically. Non-Dimensional temperature and concentration calculated with the help of RK- shooting method with Nachtsheim-Swigert iteration method. Key results include the calculation of heat and mass transfer rates and Co-efficient of skin friction. The effects of various parameters such as magnetic field strength, suction, radiation, chemical reactions, internal heat generation and dissipative effects on the flow characteristics and other physical parameters are thoroughly investigated, highlighting their impact on the thermal and concentration profiles in the system. This comprehensive analysis provides insights into the behaviour of the fluid flow under the specified conditions, which can be useful for applications in engineering and industrial processes.

Heat and Mass Transport Aspects of Nanofluid Flow towards a Vertical Flat Surface influenced by Electrified Nanoparticles and Electric Reynolds Number

This study examines the heat and mass transfer aspects of the natural convective flow of a nanofluid along a vertical flat surface, incorporating electrified nanoparticles and electric Reynolds number. While conventional nanofluid models like Buongiorno’s model overlook the nanoparticle electrification and electric Reynolds number mechanisms, this study addresses the nanoparticle electrification and electric Reynolds number mechanisms by justifying its relevance, particularly when tribo-electrification results from Brownian motion. This incorporation of the electric Reynold number and nanoparticle electrification mechanism is a unique aspect of this investigation. Using the similarity method and nondimensionalization, the governing partial differential equations of the flow are transformed into a set of locally similar equations. MATLAB's bvp4c solver is employed to solve this set of equations, along with the boundary conditions. The obtained results are validated by comparison with those from previously published works. Graphical representations are provided for the numerical outcomes of non-dimensional velocity, concentration and temperature concerning the nanoparticle electrification parameter and electric Reynolds number. The combined effects of the nanoparticle electrification parameter and the electric Reynolds number on non-dimensional heat and mass transfer coefficients are examined in tabular form. Furthermore, the impact of the nanoparticle electrification parameter on both heat and mass transfer for varying values of the Brownian motion parameter is explored graphically. The primary finding of this investigation indicates that the electrification mechanism of nanoparticles quickens the transfer of heat and mass from a flat surface to nanofluid, suggesting promising prospects for utilization in cooling systems and biomedical applications.

Magneto-Micropolar Nanofluid Flow Over a Convectively Heated Sheet with Nonlinear Radiation, Chemical Reaction, and Viscous Dissipation

A mathematical model is presented for analyzing the flow of magneto-micropolar nanofluid above a convectively heated permeable stretching sheet with nonlinear radiation, chemical reaction, and viscous dissipation. Similarity transformation is utilized to change the governing partial differential equations to the system of nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is sorted out mathematically by utilizing the shooting method with the Adams-Moulton method of fourth order, and the obtained mathematical outcomes are compared with published results. The obtained numerical results reflect very good agreement with those from open literature. Numerical values of physical quantities like skin friction coefficient, Sherwood number, and Nusselt number for emerging parameters such as Pr , Nb , Nt , Le , etc. are also computed and discussed in this work. The impact of pertinent flow parameters on nondimensional velocity, temperature, and concentration profiles is illustrated via tables and graphs.

Heat and Mass Transfer in Unsteady Radiating MHD Flow of a Maxwell Fluid with a Porous Vertically Stretching Sheet in the Presence of Activation Energy and Thermal Diffusion Effects

The aim of this study is to analyze the effects of activation energy and thermal diffusion an unsteady MHD reactive Maxwell fluid flow past a porous stretching sheet in the presence of Brownian motion, Thermophoresis and nonlinear thermal. The non-linear partial differential equations that govern the fluid flow have been transformed into a two-point boundary value problem using similarity variables and then solved numerically by fourth order Runge–Kutta method with shooting technique. Graphical results are discussed for non-dimensional velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system. The present study is compared with the previous literature and found to be in good agreement.

Lie group and stability analysis of tangent hyperbolic fluid flow driven by a shrinking sheet

This study elaborates on the mathematical modeling of tangent hyperbolic fluid flow driven by a shrinking sheet in a porous medium. The roles of Soret-Dufour and thermal radiation are considered to model the energy and concentration equations. The primary objective is to find an appropriate similarity transformation through Lie group analysis, which helps to produce the self-similar equations from the governing nonlinear partial systems. The similarity solutions are calculated numerically using the “bvp4c” solver in Matlab. Additionally, adequate suction is required to obtain the similarity solutions. As expected, dual solutions are found within a certain range of the suction parameter. The skin friction coefficient, heat, and mass transfer rates at the sheet are observed for pertinent flow constraints of physical interest. It reveals that the dual solutions bifurcate from a critical point, and beyond this point, no solution exists. Furthermore, the branches of dual solutions on the nondimensional velocity, temperature, and concentration profiles depict different characteristics. Thus, a linear temporal stability analysis has been employed to test the flow stability, revealing that the upper branch is physically reliable. The heat transfer rate increases by 7.69% and 9.55% in the upper and lower branches, respectively, for Soret parameter changes from 0.6 to 0.9. Meanwhile, the mass transfer rate decreases by 85.30% and 324.60% in the upper and lower branches, respectively. The consequences of Weissenberg and suction parameters show an opposite character on the velocity, temperature, and concentration profiles in the upper branch.

Chemical reaction effect across the moving flat plate with heat generation and MHD flow of Maxwell fluid with viscous dissipation

In this paper, the investigation centered on examining a Maxwell fluid’s convective double diffusive flow carefully considers factors such as chemical reactions, radiation, and the presence of a permeable moving flat plate. Additionally, the study encompassed the effects of heat generation and magnetohydrodynamics (MHD). The governing equations, initially expressed as partial differential equations, were converted into ordinary differential equations using a similarity transformation technique to facilitate the analysis. The computational power of MATLAB’s BVP4C software was harnessed to solve this resultant system of ODEs efficiently. The outcomes of this investigation were presented in the form of graphical representations that vividly depicted the behavior of the flow field, energy conservation, and concentration profiles under various parameter combinations. The research findings were thoughtfully summarized in a table, offering a comprehensive overview of temperature, velocity, and mass profiles across various parameters. These parameters included the Deborah number, chemical reaction rate, Eckert number, Lewis number, Prandtl number, porosity parameter, and MHD parameter. A notable discovery emerging from this study was the inverse relationship observed between nondimensional concentration contours and the magnitude of the chemical reaction rate. Simultaneously, it was observed that higher values of the Maxwell fluid led to a rise in the thickness of the temperature boundary layer. These findings offer valuable insights into the intricate interplay of physical and chemical phenomena in convective flows involving complex fluid properties and boundary conditions. The temperature outline diminishes as the heat generation rate increases, while the concentration profile declines with an elevation in the chemical reaction rate.

EFFECT OF RADIATION AND INJECTION ON A NEWTONIAN FLUID FLOW DUE TO POROUS SHRINKING SHEET WITH BRINKMAN MODEL

This paper is centered on an analytical solution of radiation and injection effects on a Newtonian fluid flow due to a porous shrinking sheet with the Brinkman model. For the momentum equations, the Brinkman model is employed. In addition, the effects of radiation and injection factors on temperature and concentration are considered. Consideration is given to the cross-diffusion relationship between temperature and concentration. By using a similarity transformation, the flow and heat transfer-related coupled partial differential equations are transformed into coupled ordinary differential equations that are non-linear. The exact solutions are obtained for the governing equations analytically. Energy, as well as concentration equations, are solved using the Euler-Cauchy equation method. The accuracy of the method is verified with the existing results, and they are found to be in good agreement. The effect of various physical parameters such as the Darcy number, shrinking parameter, radiation, Soret, and Dufour numbers on non-dimensional velocity, temperature, and concentration profiles have been graphically interpreted. It is found that the velocity profile decreases as the porous parameter increases asymptotically. The temperature increases with an increase in the parameter value of the radiation. The shear stress profile improves when the inverse Darcy value is raised, but it degrades when the suction parameter is moved. Heat transfer rate increases with an increasing Soret number for small values of Dufour number, but it slightly decreases with an increasing Soret number for larger values of Dufour number, and the mass transfer rate reacts in the opposite direction.

Behavior of a sessile droplet over dielectric infused hydrophobic surface under direct current electric field

The manipulation of sessile droplets on hydrophobic surfaces with high controllability, accuracy, and flexibility is vital for various applications of engineering sciences and technology. In this research, the combined effects of a uniform electric field, dielectric infused surface (DIS), and surfactants were investigated for the manipulation and control of sessile droplets on hydrophobic substrates. DIS reduced surface adhesion and enabled the action of electrohydrodynamic and electrophoretic forces. Experimental analysis revealed three different modes of droplet behavior on DIS under varying electro-physical conditions: elongation without motion, elongation with motion, or dispersion. These modes were observed for surfactant concentrations below the critical micelle concentration (CCMC), while elongation leading to restricted spreading of droplet occurred above CCMC. The modes were mapped in the parametric space of electric capillary number (Cae) vs. non-dimensional surfactant concentration (C* = Cs /CCMC), with Cae representing the ratio of interfacial electric to capillary stresses and Cs representing the surfactant concentration. A simple theoretical analysis based on interfacial electric and capillary stress balance distinguished between the stable and unstable configurations. This research contributes to advancing the understanding of droplet manipulation and control, which are critical in emerging microfluidic or biological applications.

Study of the smoke toxicity characteristics in an inclined tunnel

Fire smoke is one of the most important factors causing casualties, but also has the potential to bring some harm to the surrounding environment. In this work, the longitudinal temperature profile and the pollutant toxicity of a ceiling jet induced by a wall-attached fire with different tunnel slopes, were numerically and experimentally investigated by using a 1:8 reduced-scale inclined tunnel. The results show that for a given heat release rate (HRR), the flame extension is longer and the temperature decay is slower in ceiling jets induced by a wall-attached fire than for similar free-burning fires, because the air entrainment is restricted by the tunnel side walls. Further, the uphill pollutant toxicity was found to be higher with greater HRR and lower tunnel slope. Finally, a correlation between the non-dimensional longitudinal smoke temperature and CO concentration could be established for the inclined tunnel fire.

Enhanced thermal and mass transfer of harnessing microbial mediation in electrically conducting Oldroyd-B nanofluid flow: Eukaryotes microorganisms in biological applications

In bioremediation, pollutants are broken down or detached from an atmosphere using microorganisms like bacteria or fungus. These bacteria can either ingest contaminants or be enzymatically converted into innocuous molecules. Bioremediation can be enhanced by several techniques, such as bioaugmentation (the introduction of specific microorganisms), biostimulator (the provision of nutrients to stimulate microbial activity), and bioventing (the provision of air or oxygen to encourage microbial growth). The creation and dissipation of heat in a convective non-Newtonian Oldroyd-B fluid flow across a nonlinear stretching sheet in a three-dimensional boundary layer is examined in this study. The boundary layer flow's highly nonlinear partial differential equations are transformed into ordinary differential equations in the study via similarity transformations. The bvp4c technique of MATLAB is then used to resolve these equations. The study looks at some variables, including as temperature, concentration, the presence of microorganisms, velocity, heat transfer rate, and shear stress. These parameters are evaluated graphically and presented in tabular form, with a focus on the local Deborah numbers (β₁ and β₂), the local buoyancy parameters (λ₁ and λ₂), the Prandtl number (Pr), the Schmidt number (Sc), the Bio-convection Schmidt number (Sb), and the Peclet number (Pe). The results show that raising the local buoyancy parameter improves the boundary layer flow's velocity field and rate of heat transfer. Visual representations of the effects of non-dimensional factors on non-dimensional velocity, concentration, motile microorganism, and temperature profiles help to comprehend the underlying physical properties clearly.

A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure

This paper proposes a modified artificial intelligence (AI) approach based on the gradient-enhanced physics-informed neural network (gPINN) with a novel structure for the generalized coupled non-Fickian/non-Fourierian diffusion-thermoelasticity analysis. Previous successful application of gPINN in function approximation and single partial differential equation (PDE) problems gave us enough motivation to develop its application with a novel structure for solving a system of coupled PDEs. The governing equations are formulated for a copper-made strip based upon the Lord-Shulman theory of the generalized coupled thermoelasticity. In order to shed light on the capacity of the gPINN-based approach, three examples with different boundary conditions for a one-dimensional half-space are presented, as well as an example for a two-dimensional half-space. The primary goal is to investigate the transient behavior of field variables (i.e., non-dimensional molar concentration, non-dimensional displacement, and non-dimensional temperature). Variations of dimensionless stress are also examined in depth. Performance comparisons between the gPINN-based method and commonly used approaches support the efficacy of the gPINN with a novel structure. Detailed sensitivity analyses are provided to sufficiently explore the impact of neural network hyperparameters. Moreover, the effect of relaxation time on the behavior of mass concentration is addressed in a single scenario. Overall, the proposed gPINN-based method with a novel structure yields consistently encouraging and satisfactory results, and this approach entails the capability to be applied to more complicated problems. Numerical results underline the importance of the weights assigned to the derivatives of the loss terms to achieve more accurate predictions. Nonparametric statistical tests offer further evidence for exceptional agreement between gPINN solutions with certain weights and outcomes derived by commonly used analytical techniques.

Bioconvective surface-catalyzed Casson hybrid nanofluid flow analysis by using thermodynamics heat transfer law on a vertical cone

The main finding of this research is to describe the numerical analysis of MHD bioconvective base Casson nanomaterials (hybrid nanofluid) flow via a non-Darcy permeable medium confined in a vertical cone with homogeneous-heterogeneous reactions. Feature of hybrid nanofluid which containing nanoparticles like Ag and MgO with water as a working fluid is discussed. Viscous dissipation, thermal stratification, and non-uniform heat source/sink are also investigated as heat transport mechanisms. The 2nd law of thermodynamics is used to determine a total entropy rate, which is based on three different forms of irreversibility’s heat transfer, fluid friction, and the Darcy-Forchheimer relation. To get numerical solutions of the flow model is transformed into system of couple nonlinear equations, which is solved by implementing shooting approach. The influence of the evolving parameters on non-dimensional velocity, temperature, concentration, microorganism, and entropy generation distribution is graphically examined. It is worth interesting to see that a stronger value of Casson fluid parameters improves the fluid velocity, whereas fluid velocity reduces by the growth of porosity parameter, the reason behind the reduction of velocity is that greater porosity parameter, contained more nanoparticles, which produce more resistance to the fluid velocity. Further, it is observed that higher estimation of local Rayleigh number improves the entropy generation, because heat production boosts up due to strong values of Rayleigh number.

Controlling release from encapsulated drug-loaded devices: insights from modeling the dissolution front propagation.

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug. However, the interplay between these two competing processes in the context of drug delivery is not as well understood as it is for other mass transfer problems, particularly for practical controlled-release considerations such as an encapsulant layer around the drug delivery device. To address this gap, this work presents a mathematical model that describes controlled release from a drug-loaded device surrounded by a passive porous layer. A solution for the drug concentration distribution is derived using the method of eigenfunction expansion. The model is able to track the dissolution front propagation, and predict the drug release curve during the dissolution process. The utility of the model is demonstrated through comparison against experimental data representing drug release from a cylindrical drug-loaded orthopedic fixation pin, where the model is shown to capture the data very well. Analysis presented here reveals how the various geometrical and physicochemical parameters influence drug dissolution and, ultimately, the drug release profile. It is found that the non-dimensional initial concentration plays a key role in determining whether the problem is diffusion-limited or dissolution-limited, whereas the nature of the problem is largely independent of other parameters including diffusion coefficient and encapsulant thickness. We expect the model will prove to be a useful tool for those designing encapsulated drug delivery devices, in terms of optimizing the design of the device to achieve a desired drug release profile.

Non-Newtonian Flow with Heat and Mass Transfer Over a Porous Stretching Sheet Under the Effects of Space Dependent and TGD Heat Sink, Non-Uniform Heat Source and Dissipation of Energy and CGD Mass Diffusion with Suction/Blowing

In the present paper, an analytical study of visco - elastic fluid flow with heat and mass transfer characteristics over a porous stretching sheet has been examined. Heat balance is maintained with space dependent and temperature gradient dependent heat sink/source, viscous dissipation, and non-uniform heat source on the non-Newtonian Walter’s liquid B' model. The mass balance is maintained with chemically reactive species of order I, variable mass diffusivity and concentration gradient dependent mass diffusion. Using similarity transformation technique on the highly non-linear differential equations, several closed form analytical solutions are obtained for non-dimensional temperature and concentration in both PST and PHF cases in the form of confluent hypergeometric (Kummar’s) functions. The effect of permeability parameter, viscoelastic parameter, suction parameter on velocity profiles and various physical fluid situations with different degrees of viscoelasticity, Prandtl number, Eckert number, heat source- sink strength, temperature field are discussed in detail and presented through graphs. Similarly in the mass transfer field the effects of Schmidt number, reaction rate parameters are discussed in detail and presented through graphs.

Consequences of mass transpiration and thermal radiation on Jeffery fluid with nanofluid

The present work is focused on the stagnation point flow over a Jeffery fluid flow through a stretching/shrinking sheet. The nanoparticles namely Cu are considered by exploiting water-based fluid. The governing nonlinear system of partial differential equations is converted into a system of highly nonlinear ordinary differential equations via a similarity transformation. Therefore, it is quite significant to assimilate the analytical extension of heat transfer and mass transfer fluid in the presence of porous under the influence of slip velocity. The analytical solution available for nondimensional momentum, heat transfer, and concentration profiles across the boundary layer is examination is done by checking the various values of physical parameters viz., Prandtl number, Radiation parameter, stretching/shrinking parameter, and mass transpiration for the flow and heat transfer which are obtainable through graphs. The present work on nanofluids flowing through stretching/shrinking surfaces has numerous applications in biomedicine, solar energy, cooling, nuclear system cooling, etc.

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.

Radiative transport of MHD stagnation point flow of chemically reacting Carreau nanofluid due to radially stretched sheet

The flow of Carreau nanofluid with generation/absorption and magnetic field can be valuable for modifying solar energy production. In this work, we extended the study of the MHD boundary layer flow of Carreau nanofluid with heat generation/absorption close to a stagnation point over the radially extending plate. Likewise, the features of radiation and magnetic field with convective boundary conditions are considered. Further, keeping in view the importance of chemical reactions, their effect is also incorporated during the modelling process. For motivation, the impact of thermophoresis and Brownian motion has been taken into account. Using appropriate similarity transformation, we converted nonlinear governing partial differential equations of Carreau nanofluid into a couple of nonlinear ODEs. Using a recognized shooting technique and the MATLAB bvp4c solver and Mathematica ND-solve built-in command, we were able to get numerical results for these modeled ODEs. Through graphs and tables, the effects of different physical parameters like magnetic, Weissenberg number, Brownian motion, thermal radiation, thermophoresis, Prandtl number, chemical reaction, and rate of heat generation/absorption on non-dimensional velocity, temperature, and concentration profile are discussed.

Effects of chemical reaction and thermal radiation on MHD free convective flow of micro polar fluid past an infinite moving vertical porous plate with viscous dissipation

AbstractThis article discusses the impact of chemical reaction and radiation on an unstable two‐dimensional laminar flow around a viscous fluid over a semi‐infinite, vertical absorbent surface that moves progressively. The governing classification of partial differentiation was converted into an ordinary differentiation system in this case. To get numerical solutions, the Galerkin finite element technique is applied to nondimensional velocity, micro‐rotation, temperature, and concentration profiles. The consequences of skin friction, the combined pressure quantity, the mass, and heat assignments at the boundary are formed using different fluid properties and flow conditions. Physical quantities and their effects Graphs depict the radiation parameter R, thermal conductivity k, Eckert number Ec, and other velocities, micro‐rotation, temperature, and concentration factors. The main findings of this current problem is showing the chemical reaction effects on velocity and concentration. It is observed that both the velocity and concentration of the fluid decrease when Kr increases.