Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Filters

2019 - 201912020 - 20245

Settings

Author: search.filters.author.Tiwari, AshishSubject: search.filters.subject.Variable viscosity

Search Results

Now showing 1 - 6 of 6
  • No Thumbnail Available
    Item
    Solute dispersion in non-Newtonian fluids flow through small blood vessels: A varying viscosity approach
    (Elsevier, 2022) Tiwari, Ashish
    Present work concerns the combined effect of Jeffrey fluid parameter and varying nature of viscosity on the solute dispersion in non-Newtonian fluids flow through small blood vessels. The generalized dispersion model of Sankarasubramanian and Gill (1973) has been considered. The objective of the present work is to understand the solute dispersion in non-Newtonian fluids flow through microvessels with absorbing walls under varying viscosity assumption. For more realistic modeling of blood flow in microvessels, Jeffrey and Herschel–Bulkley fluids model have been considered for a comparative study due to its low shear rate flow in small blood vessels such as arterioles, venules and capillaries. The whole solute dispersion analysis has been done for two alternative non-Newtonian fluids (Herschel–Bulkley and Jeffrey fluids) owing to their physiological importance. The present model has been validated by reducing it to previously studied specific cases of Newtonian, Bingham-plastic and Power-law fluids with constant/varying viscosities. It is perceived that the mean concentration, convection and axial dispersion coefficients are significantly affected by varying viscosity and Jeffrey fluid parameters. A noteworthy observation is that an increase in ratio of relaxation to retardation times (Jeffrey fluid parameter) enhanced the values of the transport coefficients. The outcome of the present study shows the diffusion of drugs to the physiological system through small blood vessels is significantly affected by the varying nature of viscosity and Jeffrey fluid parameters.
  • No Thumbnail Available
    Item
    Homogeneous reactive mass transport in a four layer model of KL-Newtonian fluids flowing through biporous layered microvessels
    (Elsevier, 2024-05) Tiwari, Ashish
    The present work is an effort to investigate the dispersion process of reactive mass transport in human blood vessels for varying viscosity and permeability. Considering a four-layer model of Luo and Kuang (KL)-Newtonian fluids flowing through a biporous layered microvessel, the current research focuses on unsteady mass transport under the first-order chemical reaction. A two-fluid model is adopted where the core region contains the KL fluid, depicting the flow of blood cells, and the coaxial peripheral region represents the plasma region. The outer plasma layer containing Newtonian fluid is segregated into three sublayers, where adjacent to the KL fluid is the non-porous plasma region. The outer two regions, the Brinkman and the Brinkman-Forchheimer regions exhibit radially varying permeability and viscosity characteristics. Analyzing the impact of the Froude number on the solute dispersion process necessitates incorporating an additional body force into the analysis. The porous medium equations are solved using regular and singular perturbation techniques to obtain closed-form solutions. Nevertheless, analytical solutions for the KL fluid and non-porous plasma layer have been derived. The analytical solution of mass distribution due to advection and diffusion is obtained through the Gill and Sankarasubramanian (1970) approach with the aid of Hankel transformation. The effect of various parameters such as Darcy's number, Forchheimer number, Reynolds number, Froude number, permeability parameters , and viscosity parameters on the transport coefficients and mean concentration are discussed graphically. Higher Froude numbers caused weaker dispersion, while the parameters of the Brinkman-Forchheimer region have a significant effect on mass transport compared to the parameters of the Brinkman region. The findings of the current study may assist physiologists in developing a more nuanced understanding of these complex processes, ultimately leading to improved clinical outcomes.
  • No Thumbnail Available
    Item
    Effect of varying viscosity on two-fluid model of pulsatile blood flow through porous blood vessels: A comparative study
    (Elsevier, 2019-05) Tiwari, Ashish
    Present work concerns the pulsatile blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity. Blood is modeled as two-phase fluid model consisting a core region by non-Newtonian (Herschel-Bulkley) fluid and a plasma region modeled as Newtonian fluid. No slip condition has been used on wall and pressure gradient is taken as periodic function of time. Up to first order approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in flow resistance between our model and previously studied single and two-fluid models without porous layer near wall has also been done. The wall of the blood vessel is composed by a thin Brinkman (porous) layer. The stress jump condition has been imposed on fluid-porous interface. Analytical expressions for the velocity profile, flow rate, wall shear stress and flow resistance have been obtained for different regions and the effect of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the flow variables are pictorially discussed. It is perceived that values of flow rate for two-fluid model with porous region near wall is higher in comparison to two-fluid model without porous region near wall. Present study reveals a significant impact of glycocalyx layer on blood flow through blood vessels with a porous layer near wall.
  • No Thumbnail Available
    Item
    Solute dispersion in two-fluid flowing through tubes with a porous layer near the absorbing wall: Model for dispersion phenomenon in microvessels
    (Elsevier, 2020-10) Tiwari, Ashish
    Present study concerns the solute dispersion analysis in a two-fluid model of blood flow through tubes with a thin porous layer near the absorbing wall. A thin porous layer near the wall represents an endothelial glycocalyx layer the composition of which may be attributed to the accumulation of carbohydrates, absorbed plasma proteins and macromolecules in a layer at the wall that affects the plasma flow (Secomb et al., 1998. A model for red blood cell motion in glycocalyx-lined capillaries. Am. J. Physiol. 274 (Heart Circ. Physiol. 43), H1016-H1022; Pries et al., 2000. The endothelial surface layer. Eur. J. Physiol. 440, 653–666). Two-fluid model for blood flow is considered in which the central region of the blood vessel is occupied by Herschel-Bulkley fluid with variable viscosity and a peripheral region of plasma surrounded over the central region is occupied by a Newtonian fluid with constant viscosity. Governing equations are solved analytically for all the regions (central, intermediate and porous regions) and the approach of Sankarasubramanian and Gill (Sankarasubramanian, R, Gill, W N, 1973. Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. London Ser. A 333, 115–132) is followed to solve the diffusion equation by series expansion method. The impact of porous layer (and hence the porous layer parameters), varying viscosity, plasma layer and wall absorption parameters on the diffusion process like convective, dispersion and mean concentration have been analyzed. A comparative investigation of solute dispersion between Newtonian and non-Newtonian fluids has also been discussed. It is perceived that the presence of such a layer reduces the convective and axial dispersion for a highly reactive wall. A remarkable observation is that a reduced porosity near the wall contributes towards reduced average concentration of the solvent. The analysis of the porous layer inside the arterial wall may be used to understand the diffusion process for flow through arteries with a deposition of a porous layer near the absorbing wall.
  • No Thumbnail Available
    Item
    Unsteady solute dispersion in two-fluid flowing through narrow tubes: A temperature-dependent viscosity approach
    (Elsevier, 2021-03) Tiwari, Ashish
    The drug delivery or transportation of nutrients to our body involves the solute dispersion process through physiological systems and hence affected by the varying nature of viscosity, heat transfer and other factors. The majority of the previous works involving the solute dispersion in fluid flow through microvessels assumed the constant blood viscosity but in treatments involving temperature variations, the blood viscosity will be affected by the change in temperature and hence it is interesting to analyze its effect on the diffusion process. The motivation of the present work is to analyze the simultaneous impact of temperature-dependent viscosity and heat transfer on the solute dispersion in a two-fluid model of blood flow through narrow tubes by adopting the solution technique proposed by Sankarasubramanian and Gill (1973). Blood is considered as Herschel-Bulkley fluid with temperature-dependent viscosity filled up in a central region of the blood vessel and an outer cell free layer of plasma encircled over the central region consists of Newtonian fluid with constant viscosity. The desired flow related information using heat transfer aspect are obtained analytically for varying viscosity model and these expressions for velocity are then used to compute the diffusion coefficients and mean concentration. The entire dispersion process described by the three main diffusion coefficients known as exchange, convective and dispersion coefficients. An important observation is that the whole diffusion process (asymptotic convection, asymptotic dispersion coefficients and mean concentration) isaffected by the temperature-dependent viscosity with temperature parameters and same observation persist for three different types of fluids like Newtonian fluid (NF), Bingham-plastic fluid (BP), Power-law fluid (PL) which are specific cases of our model. A noteworthy observation is that an enhancement in viscosity index (and hence decay in viscosity of the core region fluid) affects the fluid flow velocity and hence affects the diffusion coefficients. Further, the dominance of thermal buoyancy forces expedite the diffusion process. The outcome of the results reveal the dependence of the solute dispersion on temperature-dependent viscosity and heat transfer. The study may be applicable to drug delivery through bloodstreams in the treatments involving the temperature variations such as chemotherapy.
  • No Thumbnail Available
    Item
    Creeping flow of Jeffrey fluid through a swarm of porous cylindrical particles: Brinkman–Forchheimer model
    (Elsevier, 2021-12) Tiwari, Ashish
    The majority of the previous studies analyzed the flow of fluids with constant viscosity through membranes composed of porous cylindrical particles using the particle-in-cell approach with the Brinkman equation governing the flow through porous media. However, a slight variation in temperature affects the viscosity of the fluids and hence affects the filtration process of fluids through membranes. The motivation of this problem came from the fact that viscosity is concentration dependent due to presence of impurities and contaminants in the fluids and hence can be taken as function of position or temperature. The present work is a theoretical attempt to investigate the impact of temperature-dependent viscosity on the creeping flow of Jeffrey fluid through membrane consisting of the aggregates of the porous cylindrical particles. The flow pattern of the Jeffrey fluid is taken along the axial direction of the cylindrical particles, and the cell model approach is utilized to formulate the governing equations driven by a constant pressure gradient. The flow regime is divided into two-layer form, one is inside the porous cylindrical particle enclosing a solid core, which is governed by the Brinkman–Forchheimer equation, and another one is outside of the porous cylindrical particle, which is governed by the Stokes equation. Being a nonlinear equation, an analytical solution of the Brinkman–Forchheimer equation is intractable. To overcome this difficulty, the regular and singular perturbation methods have been employed to solve the Brinkman–Forchheimer equation under the assumption of temperature-dependent viscosity for small and large permeability of the porous medium, respectively; however, an analytical approach is utilized to solve the Stokes equation.