Department of Mathematics
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Item Analytical study of micropolar fluid flow through porous layered microvessels with heat transfer approach(Springer, 2020-02) Tiwari, AshishThe transport theory of three-layered fluid flow and heat transfer aspects in porous layered tubes is considered in the present work to study the flow of microlevel fluids through porous layered microvessels. The transportation of energy through porous media and the applications associated with heat transfer in physiological aspects are analyzed. Blood is considered as three-layered liquid model in which the core and peripheral regions of the tube are occupied by micropolar and Newtonian fluids, respectively. A thin glycocalyx layer near the wall is considered that represents the porous region due to the deposition of carbohydrates, fibrous tissues or macromolecules inside the interior surface of the tube wall. Analytical expressions for the various flow quantities like velocity, temperature profile, flow rate, flow impedance and additional quantities like hematocrit and Fahraeus effect are obtained and the impacts of various parameters like heat transfer and porous layer parameters are analyzed pictorially for two different formulations (no-spin and no-couple stress conditions). A noteworthy observation is that the impact of no-couple stress condition is relatively more significant in flow quantities, hematocrit and Fahraeus effect than the no-spin condition at the interface. The motivational work of the blood flow through porous blood vessels by selecting the micropolar fluid for the microlevel effects of the molecules may leave a significant impact in the treatment of the various diseases in medical sciences.Item Solute dispersion in micropolar-Newtonian fluid flowing through porous layered tubes with absorbing walls(Elsevier, 2020-12) Tiwari, AshishThe physical mechanism of heat and mass transfer in solute dispersion in a two-fluid model of the blood flow through porous layered tubes with absorbing walls has been studied in the present work. For a more realistic representation of the blood flow in microvessels, the two-fluid approach is employed by considering the fluid in which the blood particles like RBCs, WBCs, and platelets are suspended as a micropolar fluid in the core region and the cell-free layer of plasma as Newtonian fluid in the peripheral region. A thin Brinkman layer mathematically governed by the Brinkman equation replicates the mechanical aspects of the porous layer near the tube wall. Either no-spin or no-couple stress condition at the micropolar-Newtonian fluid interface has been taken in to account to compare our findings with previous studies and the stress-jump condition of Ochoa-Tapia and Whitaker (J.A. Ochoa-Tapia and S. Whitaker, Int. J. Heat Mass Transfer 38 (1995) 2635–2646) is employed at the fluid-porous interface. A uniform magnetic field has also been applied in the transverse direction of the flow pattern to understand some of the clinically relevant aspects of blood flow in the cardiovascular system.Item Unsteady solute dispersion in two-fluid flowing through narrow tubes: A temperature-dependent viscosity approach(Elsevier, 2021-03) Tiwari, AshishThe 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.Item Creeping flow of Jeffrey fluid through a swarm of porous cylindrical particles: Brinkman–Forchheimer model(Elsevier, 2021-12) Tiwari, AshishThe 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.