Department of Mathematics
Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920
Browse
12 results
Search Results
Item Heat transfer in micro devices packaged in partial vacuum(IOP, 2012) Rana, AnirudhThe influence of rarefaction effects on technical processes is studied numerically for a heat transfer problem in a rarefied gas, a box with bottom heated plate. Solutions obtained from several macroscopic models, in particular the classical Navier-Stokes-Fourier equations with jump and slip boundary conditions, and the regularized 13 moment (R13) equations [Struchtrup & Torrilhon, Phys. Fluids 15, 2003] are compared. The R13 results show significant flow patterns which are not present in the classical hydrodynamic description.Item A numerical study of the heat transfer through a rarefied gas confined in a microcavity(Springer, 2014-07) Rana, AnirudhFlow and heat transfer in a bottom-heated square cavity in a moderately rarefied gas is investigated using the R13 equations and the Navier–Stokes–Fourier equations. The results obtained are compared with those from the direct simulation Monte Carlo (DSMC) method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results—including flow patterns in fair agreement with DSMC—in the transition regime, which the conventional Navier–Stokes–Fourier equations are not able to capture.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.Item Analytical investigation of the hydromagnetic flow in a porous medium due to periodically heated oscillating plate(International Journal of Applied Mechanics and Engineering, 2000) Sharma, Bhupendra KumarThe Stokes second problem in the presence of a magnetic field in a porous medium is considered. The flow is due to an oscillating plate at the bottom of the porous medium of finite thickness and fully saturated with the viscous incompressible liquid. The plate is kept at oscillating temperature and a transverse uniform magnetic field is applied normal to the plate. It is assumed that the flow in the porous medium is governed by the Brinkman equations. The flows at the interface (porous medium-clear fluid boundary) are matched by the conditions suggested by Ochao-Tapia and Whittaker. Approximate solutions for velocity, temperature field, skin-friction and rate of heat transfer are calculated and effects of various parameters upon them are examined.Item Numerical investigation of the entropy generation analysis for radiative MHD power-law fluid flow of blood through a curved artery with Hall effect(Taylor & Francis, 2023-06) Sharma, Bhupendra KumarIn the last few decades, mortality rate due to blood vessel diseases has hiked rapidly and it is almost one-third of total mortalities. Identifying the vascular geometry and hemodynamic blood flow inside the artery is essential for preventing vascular disease progression. By motivating vascular diseases effects on the human body, a mathematical model has been developed to discuss the blood flow phenomena and entropy estimation in the stenosed curved artery in the presence of a magnetic field and the Hall effect. The patient-specific condition of elliptic shape stenosis has been considered at the arterial wall. Blood is considered in the artery as two-phases; core and plasma region. Power-law fluid has been considered for core region fluid, while, Newtonian fluid is considered in the plasma region. The non-dimensional governing equations have been discretized using the second-order central difference method. Then, Stone's strongly implicit scheme is used in the ‘MATLAB’ software to solve a system of nonlinear partial differential equations (PDEs). A computing error tolerance of 10−6 has been set for each iteration step throughout the computing process. The influence of various parameters such Hall parameter (m), Brinkman number (Br), flow behavior index (q), Radiation parameter (N), magnetic field (M), arterial curvature, etc., have been discussed graphically. The present study concludes that the heat transfer rate enhances with the increase in the Hall parameter values while wall shear stress reduces with it. In addition, the chances of stenosis deposition rise for highly curvature arteries, and also blood produces more entropy with the increase in viscous heating and thermal radiation intensity. Results from the current computational study will aid clinical researchers in making more accurate predictions about the prevalence of vascular diseases.Item The effect of suction on magnetohydrodynamic forced flow of a viscous electrically conducting fluid through a porous medium induced by a rotating disk(Interdisciplinary Centre for Mathematical and Computational Modelling, 2012) Sharma, Bhupendra KumarThe present paper investigates the steady MHD forced flow of an incompressible viscous electrically conducting fluid, due to an infinite rotating disk bounded by a porous medium. A uniform suction is applied on the upper disk. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium by Brinkman equations. Flows in the two regions are matched at the interface by assuming that the velocity and stress components are continuous at it. At the interface (porous medium-clear fluid boundary), a modified set of boundary conditions suggested by Ochao-Tapia and Whittaker is applied. Assuming constant suction at the disk surface, analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined.Item Fluctuating hydromagnetic natural convection flow past a magnetized vertical surface in the presence of thermal radiation(Thermal Science, 2012) Sharma, Bhupendra KumarThe effect of radiation on fluctuating hydro-magnetic natural convection flow of viscous, incompressible, electrically conducting fluid past a magnetized vertical plate is studied; when the magnetic field and surface temperature oscillates in magnitude about a constant non zero mean. The numerical solutions have been obtained for different values of radiation parameter (Rd) magnetic Prandtl number (Pm) magnetic force parameter (S) Prandtl number (Pr) and surface temperature ( w θ ) in terms of amplitude and phase angle of coefficients of skin friction, rate of heat transfer and current density at the surface of the plate. Moreover, the effects of these parameters on transient coefficients of skin friction, rate of heat transfer and current density have been discussed. The finite difference method for primitive variable transformation and asymptotic series solution for stream function formulation has been used to obtain the numerical solution of the boundary layer flow field