scholarly journals A linearized non-isothermal general rate model for studying thermal effects in liquid chromatographic columns

2020 ◽  
pp. 336-336
Author(s):  
Nadia Kiran ◽  
Sadia Perveen ◽  
Seemab Bashir ◽  
Shamsul Qamar
Keyword(s):  
Differential Equations ◽  
Numerical Test ◽  
Fixed Bed ◽  
Packed Bed ◽  
Eigenvalue Decomposition ◽  
Finite Volume Scheme ◽  
Rate Model ◽  
Chromatographic Columns ◽  
Liquid Chromatographic ◽  
The Impact

A linearized non-isothermal general rate model is formulated and analytically solved to quantify the effects of temperature variations in fixed-bed chromatographic columns. The model contains a set of four coupled partial differential equations (PDEs) accounting for energy transfer resistances, inner and outer particle-pore diffusions, and interfacial mass and axial dispersion. The Laplace transform, the eigenvalue-decomposition technique, and a conventional technique for the solutions of ordinary differential equations (ODEs) are jointly employed for the solution of the model equations. A few numerical test studies are considered to assess the impact of system parameters on the performance of packed-bed adsorption columns. To access the range of applicability and to get the scope of the appropriateness of calculated analytical results, the numerical results are also obtained by applying a high resolution finite volume scheme (HR-FVS). The analytical solutions obtained can be used as an invaluable tool for analyzing, optimizing, and upgrading the non-isothermal liquid chromatographic procedures.

scholarly journals Analysis of temperature variations in fixed-bed columns using non-isothermal and non-equilibrium transport model

2020 ◽  
pp. 192-192
Author(s):  
Shireen Zafar ◽  
Sadia Perveen ◽  
Asad Cheema ◽  
Shamsul Qamar
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Fixed Bed ◽  
Solution Technique ◽  
Finite Volume Scheme ◽  
Temperature Variations ◽  
Model Equations ◽  
Energy Balances ◽  
Mass And Energy Balances ◽  
Non Equilibrium

A non-isothermal and non-equilibrium two-component lumped kinetic model (LKM) of fixed-bed column liquid chromatography is formulated with the linearized isotherm and solved analytically to study the influence of temperature variations on the process. The model equations constitute a system of convection-diffusion partial differential equations for mass and energy balances in the bulk phase coupled with differential equations for mass and energy balances in the stationary phase. The analytical solutions are derived for Dirichlet boundary conditions by implementing the Laplace transformation, Tschirnhaus-Vieta approach, the linear decomposition technique and an elementary solution technique of ordinary differential equations. An efficient and accurate numerical Laplace inversion technique is applied to bring back the solution in the actual time domain. In order to validate the derived analytical solutions for concentration and temperature fronts, the high-resolution upwind finite volume scheme is applied to approximate the model equations numerically. Various case studies are carried out assuming realistic model parameters. The results obtained will be beneficial for interpreting mass and energy profiles in non-equilibrium and non-isothermal liquid chromatographic columns and provide deeper insight into the sensitivity of the separation process without performing costly and time-consuming laboratory experiments.

Design of a continuous flow immobilized-cell reactor for biosynthetical production of L-aspartic acid

1985 ◽  
Vol 50 (10) ◽  
pp. 2122-2133 ◽  
Author(s):  
Jindřich Zahradník ◽  
Marie Fialová ◽  
Jan Škoda ◽  
Helena Škodová
Keyword(s):  
Aspartic Acid ◽  
Continuous Flow ◽  
Immobilized Cells ◽  
Scale Up ◽  
Fixed Bed ◽  
Packed Bed ◽  
Fixed Bed Reactor ◽  
Experimental Program ◽  
Design Parameters ◽  
Immobilized Cell

An experimental study was carried out aimed at establishing a data base for an optimum design of a continuous flow fixed-bed reactor for biotransformation of ammonium fumarate to L-aspartic acid catalyzed by immobilized cells of the strain Escherichia alcalescens dispar group. The experimental program included studies of the effect of reactor geometry, catalytic particle size, and packed bed arrangement on reactor hydrodynamics and on the rate of substrate conversion. An expression for the effective reaction rate was derived including the effect of mass transfer and conditions of the safe conversion-data scale-up were defined. Suggestions for the design of a pilot plant reactor (100 t/year) were formulated and decisive design parameters of such reactor were estimated for several variants of problem formulation.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

scholarly journals Effect of Ni(NO3)2 Pretreatment on the Pyrolysis of Organsolv Lignin Derived from Corncob Residue

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 23
Author(s):  
Wenli Wang ◽  
Yichen Liu ◽  
Yue Wang ◽  
Longfei Liu ◽  
Changwei Hu
Keyword(s):  
Sustainable Development ◽  
Fixed Bed ◽  
Value Added ◽  
Bio Oil ◽  
Fuels And Chemicals ◽  
Gas Products ◽  
Work Samples ◽  
Nickel Species ◽  
The Impact ◽  
Selective Formation

The thermal degradation of lignin for value-added fuels and chemicals is important for environment improvement and sustainable development. The impact of pretreatment and catalysis of Ni(NO3)2 on the pyrolysis behavior of organsolv lignin were studied in the present work. Samples were pyrolyzed at 500 ∘C with an upward fixed bed, and the characteristics of bio-oil were determined. After pretreatment by Ni(NO3)2, the yield of monophenols increased from 23.3 wt.% to 30.2 wt.% in “Ni-washed” and decreased slightly from 23.3 wt.% to 20.3 wt.% in “Ni-unwashed”. Meanwhile, the selective formation of vinyl-monophenols was promoted in “Ni-unwashed”, which indicated that the existence of nickel species promoted the dehydration of C-OH and breakage of C-C in pyrolysis. In comparison with “Water”, HHV of bio-oil derived from “Ni-unwashed” slightly increased from 27.94 mJ/kg to 28.46 mJ/kg, suggesting that the lowering of oxygen content in bio-oil is associated with improved quality. Furthermore, the content of H2 in gas products dramatically increased from 2.0% to 7.6% and 17.1%, respectively.

Probing the impact of material properties of core-shell SiO2@TiO2 spheres on the plasma-catalytic CO2 dissociation using a packed bed DBD plasma reactor

2021 ◽  
Vol 46 ◽  
pp. 101468
Author(s):  
Periyasamy Kaliyappan ◽  
Andreas Paulus ◽  
Jan D’Haen ◽  
Pieter Samyn ◽  
Yannick Uytdenhouwen ◽  
...  
Keyword(s):  
Material Properties ◽  
Plasma Reactor ◽  
Packed Bed ◽  
Core Shell ◽  
Dbd Plasma ◽  
The Impact

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

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