Transport of a reactive solute in a pulsatile non-Newtonian liquid flowing through an annular pipe

Debnath, Sudip; Saha, Apu Kumar; Mazumder, B. S.; Roy, Ashis Kumar

doi:10.1007/s10665-019-09999-1

Cited by 26 publications

(19 citation statements)

References 56 publications

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“…The numerical solutions of Eqs. (25) and (26) subjected to the boundary conditions (Eq. 29) are computed using the finite difference method.…”

Section: Resultsmentioning

confidence: 99%

“…Reddy et al 24 investigated the concept of unsteady MHD flow over a contract cylinder of the non-linear radiative heat transfer of Casson liquid. Debnath et al 25 discussed a pulsatile non-Newtonian fluid flow through a pipe. Khan et al 26 studied the heat convection of a Casson fluid over a moving vertical plate in a porous medium with MHD effects and chemical reaction.…”

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confidence: 99%

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Impact of Lorentz force on the pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law: a numerical study

Ali

Farooq

Abbas

et al. 2020

Sci Rep

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The present paper examines the flow behavior and separation region of a non-Newtonian electrically conducting Casson fluid through a two-dimensional porous channel by using Darcy's law for the steady and pulsatile flows. The vorticity-stream function approach is employed for the numerical solution of the flow equations. The effects of various emerging parameters on wall shear stress and stream-wise velocity are displayed through graphs and discussed in detail. It is noticed the increasing values of the magnetic field parameter (Hartman number) cause vanishing of the flow separation region and flattening of the stream-wise velocity component. The study also reveals that the non-Newtonian character of Casson fluid bears the potential of controlling the flow separation region in both steady and pulsating flow conditions. Non-Newtonian fluids have earned a lot of attention because of a wide range of their applications in science and engineering. Various models such as Jeffery fluid, elastic fluid, micro-polar fluid, and Casson fluid are termed as non-Newtonian fluids. The mechanics of non-Newtonian fluids pose challenges for scientists, engineers, and mathematicians because of their versatility 1-3. Casson fluid is a non-Newtonian fluid introduced by Casson 4. Casson fluid is a shear-thinning liquid that is supposed to have an infinite viscosity at zero shear rate, yield stress below which there is no flow and zero viscosity at an infinite shear rate 5. This means that if the shear stress is lower than the yield stress, it acts like a solid. However, Casson fluid tends to flow as the shear stress surpasses the yield stress. Some examples of Casson fluid are Jelly, salt solutions, ketchup, paints, shampoo, tomato sauce, honey, soup, concentrated fruit juices, etc. Human blood is assumed to have low electric conduction. It is remarkably affected by a magnetic field 6. The phenomenon of blood flow through narrow vessels at low shear rates can be described precisely as a Casson fluid. Numerous studies have been performed regarding blood flow with varying hematocrits, blood temperature, and blood behavior as a Casson fluid 7-9. The findings of such analyses help in the development of models such as for the blood oxygenators and haemodialysers. Sarifuddin 9 analyzed the effects of stenosis and mass transfer on arterial flow. Siddiqui et al. 10 studied blood pulsation within the stenotic artery by modeling blood as a Casson fluid and discussed how the blood flow is affected by the pulsation, stenosis, and non-Newtonian behavior. Priyadharshini and Ponalagusamy 11 studied the influence of MHD on blood parameters with magnetic nanoparticles in a stenosed artery. Fredrickson 12 discussed the steady flow of a Casson fluid. Dash et al. 5 investigated Casson fluid moving in a porous vessel. Mustafa et al. 13 analyzed an unsteady boundary layer flow and heat transfer of a Casson fluid. They used the Homotopy Analysis Method in the study. Hayat et al. 14 studied non-Newtonian fluid boundary layer flows caused by a stretching sheet....

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“…The numerical solutions of Eqs. (25) and (26) subjected to the boundary conditions (Eq. 29) are computed using the finite difference method.…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Impact of Lorentz force on the pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law: a numerical study

Ali

Farooq

Abbas

et al. 2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In this section we discuss about stability analysis of an equivalent system of equations to the stabilized formulation (19). From the above derivation it can be easily observed that ( 19) is equivalent to the following system of equations: for given…”

Section: Stability Analysismentioning

confidence: 99%

“…For simplifying the notations we denote the spaces L ∞ (0, T ; L 2 (Ω)) L 2 (0, T ; H 1 (Ω)) and L 2 (0, T ; L 2 (Ω)) by M and N respectively. (19), assume dt is sufficiently small and positive, and the coefficients satisfy the assumptions (i)-(ii). Then there exists a constant C, depending upon u, p, c such that…”

Section: Apriori Error Estimationmentioning

confidence: 99%

“…Importance of studying transportation of non-Newtonian fluids lies in its wide range of applications in the fields of chemical engineering ( [2], [19], [20]), biomedical engineering ( [18], [23], [30], [33], [38]), fluid mechanics ( [31], [32], [34], [37]), petroleum engineering [39], environmental sciences etc. in modeling various contemporary real life based problems.…”

Section: Introductionmentioning

confidence: 99%

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Subgrid multiscale stabilized finite element analysis of non-Newtonian Power-law model fully coupled with Advection-Diffusion-Reaction equations

Chowdhury,

Kumar

2021

Preprint

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This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction (V ADR) equation. Considering the highly non-linear viscosity coefficient as solute concentration dependent makes the coupling two way. The stabilized formulation of the transient coupled system is developed based upon time dependent subscales, which ensures inherent consistency of the method. The proposed algebraic expressions of the stabilization parameters appropriately shape up the apriori and aposteriori error estimates. Both the shear thinning and shear thickening properties, indicated by different power-law indices are properly highlighted in theoretical derivations as well as in numerical validations. The numerical experiments carried out for different combinations of small and large Reynolds numbers and power-law indices establish far better performance of time dependent ASGS method in approximating the solution of this coupled system for all the cases over the other well known stabilized finite element methods.

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Transient solute dispersion in electro‐osmotic viscoplastic flow in a microchannel

2023

Self Cite

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The transport of a neutral solute in incompressible electro-osmotic flow of Bingham plastic non-Newtonian liquid flowing through a microchannel is studied theoretically. The flow is driven by a constant axially applied electric field. The non-dimensional conservation equations with associated boundary conditions are solved with Gill's series expansion technique. The whole transport process is analyzed using three transport coefficients, namely, advection coefficient, dispersion coefficient and the apparent asymmetry coefficient, respectively. The mean concentration distribution of the solute is calculated via a third-order approximation of the series expansion. The study investigates the collective effects of yield stress and electric double layer (EDL) thickness (inverse Debye length) on the transport of solute. The long-term behaviour of mean concentration distribution is shown to be accurately predicted by second-order approximations; however, utilizing third or higher order approximations in Gill's series expansion enables a more refined analysis of the small and moderate time behavior of transport coefficients. The present analysis is relevant to emerging applications in bio-microfluidics exploiting electroviscous fluent media.

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Transport of a reactive solute in a pulsatile non-Newtonian liquid flowing through an annular pipe

Cited by 26 publications

References 56 publications

Impact of Lorentz force on the pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law: a numerical study

Impact of Lorentz force on the pulsatile flow of a non-Newtonian Casson fluid in a constricted channel using Darcy’s law: a numerical study

Subgrid multiscale stabilized finite element analysis of non-Newtonian Power-law model fully coupled with Advection-Diffusion-Reaction equations

Transient solute dispersion in electro‐osmotic viscoplastic flow in a microchannel

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