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10 results on '"UNEQUAL DIFFUSIVITIES"'

1. A significant assessment of two unequal classes of chemical reaction for the incompressible flow

Author

Mumtaz Khan and Dianchen Lu

Subjects
Fractional derivatives, Chemical Reaction, Darcy Medium, Unequal diffusivities, Numerical analysis, Engineering (General). Civil engineering (General), TA1-2040
Abstract

The current article numerically investigates the time-dependent fractional non-Newtonian fluid model on a vertical plane in a Darcy medium. A generalized Scott-Bliar model with heterogeneous and homogeneous interaction is employed to control the flow and mass transfer in the boundary layer region. Chemical reactions in flow are responsible for variable concentration, which causes long-lasting chemical species to better understand the chemical process.The highly nonlinear coupled model is discretized using the finite difference method with the L1 technique. The current analysis shows that the fractional exponent significantly affects the concentration of chemical species. It also revealed during the studies that for maximum values of Kr and δ1 the concentration of chemical species for a reduces. Currently no such result in the literary works for the non-integer fractional Casson model. This analysis is help full to understand the chemical process in fractional Casson fluid model.

Published
2023
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2. Interplay of chemical reacting species in a fractional viscoelastic fluid flow.

Author

Rasheed, Amer and Shoaib Anwar, Muhammad

Subjects
*CHEMICAL reactions, *VISCOELASTIC materials, *PARTIAL differential equations, *NUMERICAL analysis, *FINITE difference method
Abstract

Abstract Fractional MHD viscoelastic fluid flow has been discussed in this study. Two dimensional and two directional unsteady flow field is more critically analyzed via non-integer time derivatives. Three memory parameters are incorporated to explore the viscoelastic characteristics of the model. Variations in concentration occurred due to homogeneous-heterogeneous reactions in the flow domain. Change in concentrations consequently leads to one of the lasting chemical species. Heterogeneous reactions are observed at the boundary while homogeneous reactions are seen in the flowing region. We consider different orders of diffusion coefficients of chemical reacting species to tackle the wider class of physical and chemical processes. Governing equations are nonlinear in nature. Hence a recently established finite difference technique along with " L 1 algorithm" is used for discretization and solution of governing fractional partial differential equations. Presence of chemical reactions in flow process made the simulations valuable for chemical industry. Highlights • Unsteady two dimensional fractional flow is constructed. • Chemical species are considered with unequal diffusivities. • Average Sherwood numbers are plotted for pertinent parameters. • Finite difference algorithm is used for solution of governing equations. [ABSTRACT FROM AUTHOR]

Published
2019
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3. A significant assessment of two unequal classes of chemical reaction for the incompressible flow.

Author

Khan, Mumtaz and Lu, Dianchen

Subjects
CHEMICAL reactions, CHEMICAL species, FINITE difference method, CHEMICAL processes, NON-Newtonian fluids, MASS transfer, INCOMPRESSIBLE flow, NON-Newtonian flow (Fluid dynamics)
Abstract

The current article numerically investigates the time-dependent fractional non-Newtonian fluid model on a vertical plane in a Darcy medium. A generalized Scott-Bliar model with heterogeneous and homogeneous interaction is employed to control the flow and mass transfer in the boundary layer region. Chemical reactions in flow are responsible for variable concentration, which causes long-lasting chemical species to better understand the chemical process.The highly nonlinear coupled model is discretized using the finite difference method with the L 1 technique. The current analysis shows that the fractional exponent significantly affects the concentration of chemical species. It also revealed during the studies that for maximum values of K r and δ 1 the concentration of chemical species for a reduces. Currently no such result in the literary works for the non-integer fractional Casson model. This analysis is help full to understand the chemical process in fractional Casson fluid model. [ABSTRACT FROM AUTHOR]

Published
2023
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4. Scott-Blair model with unequal diffusivities of chemical species through a Forchheimer medium.

Author

Khan, Mumtaz and Rasheed, Amer

Subjects
*CHEMICAL processes, *CHEMICAL species, *BOUNDARY layer equations, *VISCOELASTIC materials, *FINITE difference method, *FINITE differences, *DIFFUSION coefficients, *PRESSURE-sensitive paint
Abstract

• Non-integer derivatives are explored for unequal diffusivity of chemical spices Forchheimer Medium. • Theoretical Error and convergence analysis are carried out. • The Finite Difference method is constructed along with the L1 algorithm. • Average mass transfer rates are analyzed through plots for different physical parameters. Owing to the fact that fractional viscoelastic models contribute significantly with application point of view, a good number of researchers have diverted their attention to this area. In the current study, we have carried out a numerical investigation of the fractional viscoelastic fluid model with unsteady convection, on an inclined plane, via Forchheimer medium. Furthermore, we have presented the generalized Scott-Bliar model to Caput-type fractional derivatives with homogeneous-heterogeneous reactions in the constitutive relations. The viscoelastic features of the proposed model are explored by introducing three memory parameters. The homogeneous-heterogeneous reactions in the flow domain cause variations in the concentration, leading to one of the long-lasting chemical species. One can witness the homogeneous reactions in the flowing region, whereas the heterogeneous reactions occur at the boundary. A broader cluster of physical and chemical processes is tackled by considering diffusion coefficients of a different order. The well-known finite difference technique combined with the " L 1 algorithm" is utilized to discretize the principal nonlinear boundary layer equations. The proposed numerical scheme is being validated by performing error and convergence analysis so that a thorough investigation of the chemical reaction process through the Forchheimer medium in the viscoelastic fluid model may be carried out. The proposed mathematical approach may be regarded as a valuable technique for studying the viscoelastic model and chemical reaction processes in a fluid to formulate schemes dealing with unsteady convection. Resultantly, this model can be utilized in the chemical industry. [ABSTRACT FROM AUTHOR]

Published
2021
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5. Absorption of nitric oxide into aqueous solutions of ferrous chelates accompanied by instantaneous reaction

Subjects
GAS SOLUBILITIES, SALT-SOLUTIONS, MIXED-SOLUTIONS, NITROSYL COMPLEXES, EQUILIBRIUM-CONSTANT, UNEQUAL DIFFUSIVITIES, FE-II-EDTA, NITRILOTRIACETIC ACID, ENHANCEMENT FACTORS, IRON(II) COMPLEXES
Abstract

The absorption of nitric oxide (NO) into aqueous solutions of ferrous chelates of nitrilotriacetic acid (NTA), ethylene diaminetetraacetic acid (EDTA), hydroxyethylenediaminetriacetic acid (HEDTA), and diethylenetriaminepentaacetic acid (DTPA) was studied in a stirred cell reactor. Experimental conditions were as follows: 0.05 less than or equal to CF(IIL) less than or equal to 0.1 kmol/mg(3), 8 less than or equal to P-NO less than or equal to 30 kPa, 3 less than or equal to pH less than or equal to 10 (NTA), or 7 less than or equal to pH less than or equal to 8 (EDTA, HEDTA, DTPA), C-L less than or equal to C-Fe(II) less than or equal to 3C(L) (NTA) or C-L = C-Fe(II) (EDTA, HEDTA, DTPA), and 293 less than or equal to T less than or equal to 333 K (NTA, EDTA, HEDTA) or T = 294 K (DTPA). The absorption leads to stable ferrous NO chelates. Due to the high reaction rate, in combination with the relatively high P-NO applied, the absorption rate is strongly affected by mass transfer limitation only. By applying penetration theory, the ratio of the diffusion coefficients of ferrous chelates and NO was determined: at T = 294 K (D(Fe(II)chelate)/D-NO)(1/2) = 0.44 +/- 0.01, 0.34 +/- 0.01, 0.36 +/- 0.01, and 0.31 +/- 0.015, for the ferrous NTA, HEDTA, EDTA, and DTPA complexes, respectively. At elevated T, (D(Fe(II)chelate)/D-NO)(1/2) decreases due to the unusual T-dt pendency of D-NO. For ferrous NTA, the formation of the ferrous NO chelate is;accompanied by pH effects that can be understood from iron chelate chemistry. In the case of ferrous NTA, pH

Published
1997

6. Absorption of Nitric Oxide into Aqueous Solutions of Ferrous Chelates Accompanied by Instantaneous Reaction

Author

I.C.F. vanGils, Antonie A. C. M. Beenackers, J.F Demmink, Chemical Technology, and Faculty of Science and Engineering

Subjects
Aqueous solution, General Chemical Engineering, Inorganic chemistry, Nitrilotriacetic acid, SALT-SOLUTIONS, MIXED-SOLUTIONS, Ethylenediaminetetraacetic acid, NITROSYL COMPLEXES, General Chemistry, EQUILIBRIUM-CONSTANT, UNEQUAL DIFFUSIVITIES, NITRILOTRIACETIC ACID, ENHANCEMENT FACTORS, Industrial and Manufacturing Engineering, Ferrous, GAS SOLUBILITIES, Reaction rate, chemistry.chemical_compound, chemistry, Chelation, Solubility, FE-II-EDTA, Equilibrium constant, IRON(II) COMPLEXES
Abstract

The absorption of nitric oxide (NO) into aqueous solutions of ferrous chelates of nitrilotriacetic acid (NTA), ethylene diaminetetraacetic acid (EDTA), hydroxyethylenediaminetriacetic acid (HEDTA), and diethylenetriaminepentaacetic acid (DTPA) was studied in a stirred cell reactor. Experimental conditions were as follows: 0.05 less than or equal to CF(IIL) less than or equal to 0.1 kmol/mg(3), 8 less than or equal to P-NO less than or equal to 30 kPa, 3 less than or equal to pH less than or equal to 10 (NTA), or 7 less than or equal to pH less than or equal to 8 (EDTA, HEDTA, DTPA), C-L less than or equal to C-Fe(II) less than or equal to 3C(L) (NTA) or C-L = C-Fe(II) (EDTA, HEDTA, DTPA), and 293 less than or equal to T less than or equal to 333 K (NTA, EDTA, HEDTA) or T = 294 K (DTPA). The absorption leads to stable ferrous NO chelates. Due to the high reaction rate, in combination with the relatively high P-NO applied, the absorption rate is strongly affected by mass transfer limitation only. By applying penetration theory, the ratio of the diffusion coefficients of ferrous chelates and NO was determined: at T = 294 K (D(Fe(II)chelate)/D-NO)(1/2) = 0.44 +/- 0.01, 0.34 +/- 0.01, 0.36 +/- 0.01, and 0.31 +/- 0.015, for the ferrous NTA, HEDTA, EDTA, and DTPA complexes, respectively. At elevated T, (D(Fe(II)chelate)/D-NO)(1/2) decreases due to the unusual T-dt pendency of D-NO. For ferrous NTA, the formation of the ferrous NO chelate is;accompanied by pH effects that can be understood from iron chelate chemistry. In the case of ferrous NTA, pH

Published
1997
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7. Kinetics of the reaction of Fe-II(EDTA) with oxygen in aqueous solutions

Author

Ineke J. Ganzeveld, Francesca Gambardella, Jos G. M. Winkelman, Erik Heeres, Chemical Technology, and Applied Physics

Subjects
MECHANISM, Aqueous solution, Autoxidation, Chemistry, General Chemical Engineering, IRON, Kinetics, Inorganic chemistry, EDTA, chemistry.chemical_element, General Chemistry, CHELATION, GASES, Iron chelate, UNEQUAL DIFFUSIVITIES, OXIDATION, Oxygen, Industrial and Manufacturing Engineering, ENHANCEMENT FACTORS, DIFFUSION, Limiting oxygen concentration, Chelation, Selectivity, AUTOXIDATION
Abstract

The kinetics of the reaction of oxygen with aqueous Fe-II(EDTA) solutions has been determined in a range of process conditions (C-Fe(II)(EDTA) = 15-60 mol/m(3), P-O2 = 5-20 kPa, pH = 5-8, T = 298-328 K, C-NaCl = 0-15 kg/m(3)) using a gas-liquid stirred cell reactor. The oxygen absorption rates were modeled using an expression derived by De Coursey using the penetration theory of mass transfer. Within the range of process conditions applied, the reaction was shown to be first order in oxygen and second order in iron chelate. The temperature dependence of the kinetic constant may be expressed as (pH = 7, no salt addition): k(12) = 5.3 X 10(3) e(-4098/T) m(6)/(mol(2.)s). The kinetic constant is essentially independent of the pH in the range 5

Published
2005
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8. Experimental and modeling studies on the absorption of NO in aqueous ferrous EDTA solutions

Author

Alberts, Hero J. Heeres, Michel S. Alberts, F. Gambardella, Jos Winkelman, Erik Heeres, Stratingh Institute of Chemistry, Engineering and Technology Institute Groningen, Chemical Technology, and Applied Physics

Subjects
REVERSIBLE BINDING, IRON(II), Aqueous solution, Chemistry, General Chemical Engineering, Kinetics, Analytical chemistry, Monoxide, General Chemistry, MONOXIDE, Atmospheric temperature range, EQUILIBRIUM-CONSTANT, GASES, Thermal diffusivity, UNEQUAL DIFFUSIVITIES, Industrial and Manufacturing Engineering, ENHANCEMENT FACTORS, Ferrous, Mass transfer, FE(II)-EDTA, COMPLEXES, Equilibrium constant, KINETICS
Abstract

This work describes an experimental and modeling study on an industrial relevant process (i.e., the absorption of NO in aqueous Fell(EDTA) solutions) to accurately determine the equilibrium constant of the reaction in the temperature range of 299-329 K. The experiments were carried out in a stirred cell contactor using a pH of 7 and an initial Fe-II(EDTA) concentration of 7-9 mol/m(3). A dynamic reactor model was developed to describe the experimental absorption profiles. Mass transfer effects were taken into account using the penetration theory for mass transfer. Excellent fits were obtained between measured and modeled profiles when assuming that the reaction takes place in the instantaneous regime. The following temperature dependence for the K value was obtained: K = exp((4702/T) - 8.534). Dynamic reactor modeling not only allowed calculation of the equilibrium constants of the reaction but also provided accurate values for the ratio of the diffusivity of Fe-II(EDTA) and NO (r(P)) at various temperatures. This ratio is of extreme importance for the design of a reactive NO absorption unit and could be expressed as: r(P) = -1.775 x 10(-4)T(2) + 0.11T - 16.93.

Published
2005

9. Experimental and modeling studies on the absorption of NO in aqueous ferrous EDTA solutions

Author

Gambardella, F, Alberts, MS, Winkelman, JGM, Heeres, EJ, Alberts, Michel S., Heeres, H.J., Gambardella, F, Alberts, MS, Winkelman, JGM, Heeres, EJ, Alberts, Michel S., and Heeres, H.J.

Abstract

This work describes an experimental and modeling study on an industrial relevant process (i.e., the absorption of NO in aqueous Fell(EDTA) solutions) to accurately determine the equilibrium constant of the reaction in the temperature range of 299-329 K. The experiments were carried out in a stirred cell contactor using a pH of 7 and an initial Fe-II(EDTA) concentration of 7-9 mol/m(3). A dynamic reactor model was developed to describe the experimental absorption profiles. Mass transfer effects were taken into account using the penetration theory for mass transfer. Excellent fits were obtained between measured and modeled profiles when assuming that the reaction takes place in the instantaneous regime. The following temperature dependence for the K value was obtained: K = exp((4702/T) - 8.534). Dynamic reactor modeling not only allowed calculation of the equilibrium constants of the reaction but also provided accurate values for the ratio of the diffusivity of Fe-II(EDTA) and NO (r(P)) at various temperatures. This ratio is of extreme importance for the design of a reactive NO absorption unit and could be expressed as: r(P) = -1.775 x 10(-4)T(2) + 0.11T - 16.93.

Published
2005

10. Absorption of nitric oxide into aqueous solutions of ferrous chelates accompanied by instantaneous reaction

Subjects
GAS SOLUBILITIES, SALT-SOLUTIONS, MIXED-SOLUTIONS, NITROSYL COMPLEXES, EQUILIBRIUM-CONSTANT, UNEQUAL DIFFUSIVITIES, FE-II-EDTA, NITRILOTRIACETIC ACID, ENHANCEMENT FACTORS, IRON(II) COMPLEXES
Abstract

The absorption of nitric oxide (NO) into aqueous solutions of ferrous chelates of nitrilotriacetic acid (NTA), ethylene diaminetetraacetic acid (EDTA), hydroxyethylenediaminetriacetic acid (HEDTA), and diethylenetriaminepentaacetic acid (DTPA) was studied in a stirred cell reactor. Experimental conditions were as follows: 0.05 less than or equal to CF(IIL) less than or equal to 0.1 kmol/mg(3), 8 less than or equal to P-NO less than or equal to 30 kPa, 3 less than or equal to pH less than or equal to 10 (NTA), or 7 less than or equal to pH less than or equal to 8 (EDTA, HEDTA, DTPA), C-L less than or equal to C-Fe(II) less than or equal to 3C(L) (NTA) or C-L = C-Fe(II) (EDTA, HEDTA, DTPA), and 293 less than or equal to T less than or equal to 333 K (NTA, EDTA, HEDTA) or T = 294 K (DTPA). The absorption leads to stable ferrous NO chelates. Due to the high reaction rate, in combination with the relatively high P-NO applied, the absorption rate is strongly affected by mass transfer limitation only. By applying penetration theory, the ratio of the diffusion coefficients of ferrous chelates and NO was determined: at T = 294 K (D(Fe(II)chelate)/D-NO)(1/2) = 0.44 +/- 0.01, 0.34 +/- 0.01, 0.36 +/- 0.01, and 0.31 +/- 0.015, for the ferrous NTA, HEDTA, EDTA, and DTPA complexes, respectively. At elevated T, (D(Fe(II)chelate)/D-NO)(1/2) decreases due to the unusual T-dt pendency of D-NO. For ferrous NTA, the formation of the ferrous NO chelate is;accompanied by pH effects that can be understood from iron chelate chemistry. In the case of ferrous NTA, pH

Published
1997

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