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1

Impacts of chemical reactions on inclined isothermal vertical plate

Sundar Raj M., Nagarajan G., Murugan V. P., Muthucumaraswamy R.

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 2

64--76

EN

An accurate parameterization of an irregular surge across a continuously propelled circulation through an endless isothermal inclined plate has been investigated in the presence of a first-degree uniform chemical reaction. Both the plate’s temperature and the proximal intensity are increased systematically. To evaluate non-dimensional equations, the Laplace transform is utilized. The effect of velocity components on a range of physical parameters is investigated which include Sc, Pr, Gr, Gc, α, K and t. A proportionate increase of velocity with Gr and Gc was prominent. τ and Sh were mathematically determined.

2

Mathematical analysis of mass and heat transfer through arterial stenosis

Hussain Azad, Sarwar Luba, Akbar Sobia, Malik M. Y.

Journal of Power Technologies

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2022

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Vol. 102, nr 3

88--95

EN

The article investigates the steady state flow of an incompressible fluid which is treated as a Williamson fluid through a stenoised region in the shape of cosine constriction. Blood is taken as a Williamson fluid. Mathematical formulation leads us to nonlinear compatibility and energy equations, which are then deciphered by the shooting technique to obtain the numerical solution. Suitable resemblance transformations are used to change partial differential equations into an embellished form of ordinary differential equations. Further, the consequences of the different parameters involved are shown by graphs and a conclusion is presented. Velocity and temperature fields are canvassed graphically for the distinct values of emerging parameters and discussed in tabular form. Skin friction and the coefficient of heat transfer are also covered in the discussion. The resulting Nusselt number curve exhibits negative deflection for variational values of λ and height of the stenosis δ.

3

Review on the numerical investigations of mass transfer from drug eluting stent

Song Jianfei, Kouidri Smaine, Bakir Farid

Biocybernetics and Biomedical Engineering

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2021

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Vol. 41, no. 3

1057--1070

EN

Drug-eluting stent (DES) as the newly developed treatment for the cardiovascular disease has been the preferred treatment option for most of the patients with significant reduction of restenosis incidents. However, the follow-up complications such as late thrombosis after stent implantation limit the further widespread use of DES which has caused extensive attention from the researchers. Numerical method has been widely employed to predict the DES performance in human body during the past decades, contributing to the stent design optimization and a better understanding of drug release mechanisms in a cost-effective way compared to the experiments. Among the existing numerical investigations, different modelling methods of DES inside artery can be found to study the drug transport process, and adopting the proper models physically and mathematically plays a key role to obtain the results well fitting with the practical case. Therefore, in this review article, the existing numerical researches regarding DES mainly in the last two decades have been focused and summarized including the established modeling methods and the controlling parameters investigations related to drug release from DES. In addition, the common results obtained have been discussed collectively aiming to guide the following researches.

4

The four-sided lid driven square cavity using stream function-vorticity formulation

Bagai Shobha, Kumar Manoj, Patel Arvind

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 2

17--30

EN

In this paper, an unsteady 2-D incompressible fluid flow with heat and mass transfer in a four-sided lid driven square cavity is investigated numerically. The top, bottom, left, and right walls of the square cavity move to the right, left, downward and upward respectively. All four sides of the cavity move with a uniform velocity. The flow variables are simulated below the critical Reynolds numbers with isothermal and mass-transfer conditions in the square cavity. We have used a streamfunction-vorticity (ψ - ξ) formulation to investigate the fluid flow in terms of flow variables ψ, ξ, T and C at low Reynolds numbers (Re). The Prandtl number (Pr) and Schmidt number (Sc) have been chosen as 6:62 and 10, 50, 100, 150 respectively, in order to calculate the numerical solutions of T and C. The matrix method has been used to evaluate the stability and convergence of the numerical scheme. The conditions obtained from the matrix method have been used to arrive at the numerical solutions with desired accuracy.

5

Effects of radiation and Eckert number on MHD flow with heat transfer rate near a stagnation point over a non-linear vertical stretching sheet

Fenuga O. J., Hassan A. R., Olanrewaju P. O.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

27--36

EN

This work investigates the effects of radiation and Eckert number on an MHD flow with heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the sixth order Runge-Kutta method with shooting technique. Tabular and graphical results are provided to examine the physical nature of the problem. Heat transfer rate at the surface decreases with radiation, Eckert number and as radiation increases, the flow temperature also increases for velocity ratio parameters […].

6

The improvement of the rheological model for controlling the stress-strain state and humidity in the materials of museum pieces: zener thermodiffusion model for capillary-porous bodies

Dovhaliuk V. B., Chovnyuk Y. V., Ivanov E. A., Shyshyna M. O.

Zeszyty Naukowe. Quality. Production. Improvement

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2019

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No. 2 (11)

51--71

EN

The drying and humidifying processes of capillary-porous (colloid) bodies occur during the production of various materials for the consumer goods industry, building materials, storage of museum pieces, etc. It is known that the main linkage forms of the moisture and colloid capillary-porous bodies (CCPBs), namely adsorption, capillary condensation and capillary linkage of the free moisture in the cavities of the above bodies, depend on the temperature and relative humidity of drying/humidifying agent. It means that the CCPBs behave in a peculiar way depending on the temperature and humidity fields. The problems of CCPBs drying (or humidifying) process include the issue of the heat and humidity transfer both in the middle of the body and in the boundary layer on the interface of phases “body (object of drying/humidifying process) – environment”. The drying/humidifying intensity is at its maximum when the possibilities of the heat and mass transfer in the boundary layer correspond to the possibilities of moisture and heat moving inside the object of drying/humidifying process. The properties of the CCPB as material possessing specific elastic-viscous properties are described within the framework of O.Y. Ishlinskiy - O.R. Rzhanitsin generalized elastic-viscous body theory. A comparative analysis of the above mentioned CCPB’s properties from the point of view of Zener thermodiffusion theory is conducted. The mechanism of moisture transferring from the CCPBs’ central layers (as object of drying/humidifying process) up to their surfaces is developed. The theoretical researches examined the drying/humidifying phenomena for both the entire volume of the CCPB and three structural directions. It is noted that drying/humidifying of CCPBs is a complicated heat and mass transfer process accompanied by mechanisms of molecular nature determining the kinetics of their running. It is shown that the appropriate equations’ solution of molecular-molar heat and moisture transfer under the appropriate boundary (limit) conditions allows to describe the fields, i.e. the distribution of transfer potentials (the temperature and moisture content in the CCPB as object of drying/humidifying) at any time of the appropriate process. The drying/humidifying curves (“drying/humidifying rate versus CCPB humidity”) and the temperature curves (“CCPB temperatures versus CCPB humidity”) reflect the nature of the drying/humidifying processes. In the framework of the proposed generalized rheological model of CCPB, the residual deformations of bodies for various load types (the time-varying stress applied to the CCPB) is estimated.

7

Analysis of a chemically reactive MHD flow with heat and mass transfer over a permeable surface

Fenuga O. J., Aroloye S. J., Popoola A. O.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 1

53--66

EN

This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

8

A numerical method for viscous flow in a driven cavity with heat and concentration sources placed on its side wall

Ambethkar V., Basumatary L. R.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

17--30

EN

This paper proposes a method to numerically study viscous incompressible two-dimensional steady flow in a driven square cavity with heat and concentration sources placed on its side wall. The method proposed here is based on streamfunction-vorticity (Ψ-ξ) formulation. We have modified this formulation in such a way that it suits to solve the continuity, x and y-momentum, energy and mass transfer equations which are the governing equations of the problem under investigation in this study. No-slip and slip wall boundary conditions for velocity, temperature and concentration are defined on walls of a driven square cavity. In order to numerically compute the streamfunction Ψ, vorticityfunction ξ , temperature θ, concentration C and pressure P at different low, moderate and high Reynolds numbers, a general algorithm was proposed. The sequence of steps involved in this general algorithm are executed in a computer code, developed and run in a C compiler. We propose that, with the help of this code, one can easily compute the numerical solutions of the flow variables such as velocity, pressure, temperature, concentration, streamfunction, vorticityfunction and thereby depict and analyze streamlines, vortex lines, isotherms and isobars, in the driven square cavity for low, moderate and high Reynolds numbers. We have chosen suitable Prandtl and Schmidt numbers that enables us to define the average Nusselt and Sherwood numbers to study the heat ad mass transfer rates from the left wall of the cavity. The stability criterion of the numerical method used for solving the Poisson, vorticity transportation, energy and mass transfer has been given. Based on this criterion, we ought to choose appropriate time and space steps in numerical computations and thereby, we may obtain the desired accurate numerical solutions. The nature of the steady state solutions of the flow variables along the horizontal and vertical lines through the geometric center of the square cavity has been discussed and analyzed. To check the validity of the computer code used and corresponding numerical solutions of the flow variables obtained from this study, we have to compare these with established steady state solutions existing in the literature and they have to be found in good agreement.

9

Experimental evaluation of a helical laboratory photobioreactor for cultivation of thermophilic cyanobacteria – hydrodynamics and mass transfer studies

Gluszcz P., Klepacz-Smółka A., Ledakowicz S.

Chemical and Process Engineering

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2018

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Vol. 39, nr 4

457-–473

EN

The aim of the paper is to present the hydrodynamic, mass transfer and illumination characteristics of a laboratory helical-tube photobioreactor Biostat PBR-2S, commercially available and used in many laboratories in Poland and worldwide. The investigated hydrodynamics parameters were: mean liquid circulation rate, liquid velocity/residence time in the tubular part of the apparatus and mixing time, measured in the wide range of rotary speed of the circulation pump. The influence of the aeration intensity on these parameters was also checked. The volumetric oxygen and carbon dioxide transfer coefficients in the liquid phase and their dependency on the liquid circulation rate and gas inflow rate were determined. The experiments were performed in tap water and then in a real three-phase cultivation broth at the end of thermophilic cyanobacteria T. synechococus growth. For the final evaluation of the tested PBR there were series of test cultivations run under different conditions of illumination. The highest final concentration of the biomass of tested cyanobacteria reached the relatively high value of 4.38 g/dm3 of the dry biomass, although the process conditions were not fully optimized. The laboratory photobioreactor PBR-2S proved to be a good tool for investigations of microalgae cultivation processes. The presented results and practical observations may help to analyze and understand the mutual influence of the specific process parameters in the described PBR, especially during autotrophic organism cultivations.

10

Influence of rotating magnetic field on gas-liquid volumetric mass transfer coefficient

Rakoczy R., Konopacki M., Kordas M.

Chemical and Process Engineering

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2017

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Vol. 38, nr 3

423--432

EN

The main objective of these experiments was to study the oxygen mass transfer rate through the volumetric mass transfer coefficient (kLa) for an experimental set-up equipped with a rotating magnetic field (RMF) generator and various liquids. The experimental results indicated that kLa increased along the magnetic strength and the superficial gas velocity. Mathematical correlations defining the influence of the considered factors on kLa were proposed.

11

Energetic Efficiency of Mixing and Mass Transfer in Single Phase and Two-Phase Systems

Bałdyga J., Jasińska M.

Chemical and Process Engineering

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2017

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Vol. 38, nr 1

79--96

EN

In this work a concept of energetic efficiency of mixing is presented and discussed; a classical definition of mixing efficiency is modified to include effects of the Schmidt number and the Reynolds number. Generalization to turbulent flows is presented as well. It is shown how the energetic efficiency of mixing as well as efficiencies of drop breakage and mass transfer in twophase liquid-liquid systems can be identified using mathematical models and test chemical reactions. New expressions for analyzing efficiency problem are applied to identify the energetic efficiency of mixing in a stirred tank, a rotor stator mixer and a microreactor. Published experimental data and new results obtained using new systems of test reactions are applied. It has been shown that the efficiency of mixing is small in popular types of reactors and mixers and thus there is some space for improvement.

12

Application of new chemical test reactions to study mass transfer from shrinking droplets and micromixing in the rotor-stator mixer

Bałdyga J., Kotowicz M.

Chemical and Process Engineering

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2017

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Vol. 38, nr 3

477--489

EN

A pair of fast competitive reactions, neutralization and 2,2-dimetoxypropane (DMP) hydrolysis, has been applied do study mass transfer and micromixing in a T 50 Ultra-Turrax® - IKA rotor-stator device. In experiments the dispersed organic phase containing p-Toluenesulfonic acid (pTsOH) dissolved in diisopropyl ether, whereas the continuous phase was represented by the aqueous solution of sodium hydroxide, 2,2-dimetoxypropane (DMP) and ethanol. During mixing a fast mass transfer of a solute (pTsOH) from organic phase droplets, which were shrinking due to fast dissolution of the organic solvent, was followed by micromixing and chemical reactions in the continuous phase. Measured hydrolysis yields were applied to express effects of mixing on the course of chemical reactions. Modeling was based on application of models describing drop breakup, mass transfer in the liquid-liquid system and micromixing. Combined effects of mass transfer and drop breakage on drop population were expressed using the population balance equations. The model has been used to interpret experimental results, in particular to identify the efficiency of mixing.

13

Determination of a Mass Transfer Area during Metal Melting in a Vacuum Induction Furnace

Golak S., Przylucki R., Barglik J.

Archives of Metallurgy and Materials

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2014

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Vol. 59, iss. 1

287--292

EN

In the paper, a simulation model that allows for determination of the actual surface area of inductively stirred liquid metal and the value of metal near-surface velocity during its melting is presented. Also, the effects of induction furnace working frequency on both parameters are demonstrated. The simulation was performed for copper and liquid steel that were melted in two different induction furnaces. The calculation results were also used for determination of coefficients of copper mass transfer in liquid steel and of antimony mass transfer in liquid copper during their stirring in the discussed furnace.

PL

W pracy przedstawiono model symulacyjny pozwalający na wyznaczenie wartości rzeczywistej powierzchni ciekłego metalu mieszanego indukcyjnie jak i wartości prędkości przypowierzchniowej metalu w trakcie jego topienia Wykazano jednocześnie wpływ częstotliwości roboczej pieca indukcyjnego na obydwie wielkości. Symulacji dokonano dla miedzi i ciekłej stali topionych w dwóch różnych piecach indukcyjnych. Wyniki obliczeń posłużyły także do wyznaczenia wartości współczynników transportu masy miedzi w ciekłej stali i antymonu w ciekłej miedzi w przypadku ich mieszania w omawianym agregacie.

14

Modelling of mass transport in watercourses considering mass transfer between phases in unsteady states. Part I. Mass transfer process for periodic and aperiodic changes of concentration

Bielski A.

Environment Protection Engineering

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2011

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Vol. 37, nr 2

35-51

EN

A model most often used for the description of the processes of mass transport through phase boundaries is the model of Whitman. Results of calculations obtained using this model may occasionally considerably differ from the results obtained using diffusion models. Thus an attempt has been made to correct the model proposed by Whitman. The dynamics of the processes of mass transport from a liquid phase (river water) to a solid phase (layer of material in the river bottom) has been analysed. Several equations have been derived describing the rate of absorption with a chemical reaction and periodical changes of the concentration of the analysed substance. An attempt has been made to determine the relation between the concentration gradient and concentration at the phase boundary. In dynamic conditions, the concentration gradient at the phase boundary can be approximated by means of time dependence of a linear combination of concentration, delayed concentration, and concentration derivative at the phase boundary. Analysis of the dynamics of the absorption process with the chemical reaction enabled one to derive an equation describing the stream of the substance penetrating to the inside of the solid phase. Such equations may be used to determine the error generated by the film model of Whitman for the process of mass penetration.

15

Mass transfer enhancement in Newtonian and non-Newtonian liquids flowing in channels of the sinusoidal shape

Broniarz-Press L., Bednarz J., Różański J.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no spec

93-98

EN

The aim of the present work was the study of flow phenomena of chosen Stokes fluids in the plate and sinusoidal shape channels of two various types. The first of them had the regular shape and the second one was characterized by the opponent walls displaced in the phase. The constructions of this type can be applied in processing and biotechnology where the media very often have the non-Newtonian character and the laminar flow is required. Mass transfer coefficients in modified channels observed were greater than these ones measured in the plate exchanger. The best effect was obtained for the sinusoidal channel of symmetric construction.