Department of Mathematics

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    Entropy generation optimization for casson hybrid nanofluid flow along a curved surface with bioconvection mechanism and exothermic/endothermic catalytic reaction
    (Wiley, 2025-03) Sharma, Bhupendra Kumar
    This article deals with the heat and mass transfer analysis of Casson hybrid nanofluid flow over a curved Riga surface with slip conditions in the presence of gyrotactic microorganisms. The mechanism of Soret and Dufour effects, exothermic/endothermic catalytic reaction, and an exponential heat source are also investigated. The mixture of aluminum oxide and multi-walled carbon nanotubes with Therminol-VPI fluid is assumed as the hybrid nanofluid. Boundary layer assumptions are taken in the mathematical modeling of governing equations. Transformation variables are introduced to get the dimensionless governing equations. Numerical simulation of the transformed equations is done with the help of the Matlab computational tool using the Cash and Carp numerical method. Numerical results corresponding to the influential factors are plotted in graphs for velocity profile, temperature profile, concentration profile, drag coefficient, Nusselt number, Sherwood number, and entropy generation. It is observed that the fluid velocity diminishes with an enhancement in the curvature parameter, and fluid velocity enhances with an improvement in the suction parameter. Thermal profile improves for enhancing modified magnetic field parameter and drops with an increase in exponential index parameter. The microorganisms respond to temperature and concentration gradients, affecting the overall heat and mass transfer dynamics. This research aims to reveal the coupled effects of heat transfer, diffusion, and microorganism behavior in computational simulations, which have various applications in different sectors like electronics, chemical engineering, and material science.
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    Entropy generation optimization of EMHD mixed convective flow with higher order chemical reaction: Sensitivity analysis
    (Elsevier, 2024-02) Sharma, Bhupendra Kumar
    This investigation deals with the sensitivity analysis of the unsteady, incompressible fluid flow past a vertical elongating surface using the Response Surface Methodology. The impact of Joule heating, viscous dissipation, non-uniform heat source, and higher-order chemical reaction are encountered under the influence of external electric and magnetic fields. The governing equations are modeled by the boundary layer assumptions with slip conditions, which are changed to dimensionless form by incorporation of the transformation variables. The dimensionless equations are higher-order ordinary differential equations. These ordinary differential equations are numerically simulated by the application of iterative shooting technique with Runga Kutta 4th-order numerical method. Outcomes corresponding to the fluid velocity, temperature, and concentration profile are presented in the graphs, surface plots, and contours for different influential parameters like Eckert number, electric field parameter, Prandtl number, and chemical reaction parameter. It is observed that the Nusselt number escalates with an increment in the electric field parameter and Hartmann number. The entropy formation rate is greater along the higher Hartmann number values and lesser along the higher electric field parameter values. Findings of this attempt are helpful in heat storage systems, pharmaceuticals, biological engineering, medication delivery, safer cooling surgery, cooling reactors, biosensors, magnetic cell isolation, and military fields.
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    Three-Dimensional Unsteady Mixed Convection and Mass Transfer Flow with Periodic Temperature
    (Dirasat, 2008) Sharma, Bhupendra Kumar
    This research investigates the effect of periodic heat flux and mass flux on unsteady convection flow bounded by an infinite vertical flat porous plate. The porous infinite surface is subjected to a slightly sinusoidal transverse suction velocity distribution. The problem becomes three dimensional, due to the periodic suction velocity variation in space. Assuming the free stream velocity to be uniform, the approximate solutions for velocity, temperature, concentration, skin friction and rate of heat transfer are obtained using multi-parameter perturbation technique. The dependence of solution on Pr(Prandtl number), Gr(Grashof number), Gc(modified Grashof number), Sc(Schmidt number), ω(frequency parameter) and Re(Reynold number) is investigated with the help of graphs and tables.
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    Flow characteristics of MHD oscillatory two-phase blood flow through a stenosed artery with heat and mass transfer
    (ARXIV, 2017-05) Sharma, Bhupendra Kumar
    In blood, the concentration of red blood cells varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the center of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non-uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. The present article analyzes the heat and mass transfer effects on the two-phase model of the unsteady pulsatile blood flow when it flows through the stenosed artery under the effects of radiation and chemical reaction. The direction of the artery is assumed to be vertical and the magnetic field is applied along the radial direction of the artery. We assume that the value of the shear stress is high enough so that nature of blood can be modeled as Newtonian in both erythrocytes suspended core region as well as RBC-depleted plasma region. We derive a mathematical model for the mixed convection problem of two-phase blood flow as nonlinear partial differential equations and get the exact solutions for the velocity, temperature and concentration profiles. Further, a comparative study is carried out between the single-phase and two-phase model of the blood flow, and it is observed that the two-phase model fits the experimental data more accurately than the single phase model. Subsequently, to measure two-phase blood flow behavior under the effects of applied magnetic field and thermal radiation, we demonstrate the graphs of wall shear stress, impedance, and total flow rate under the effect of applied magnetic field and thermal radiation via simulations
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    Role of Slip Velocity in a Magneto-Micropolar Fluid Flow from a Radiative Surface with Variable Permeability: A Numerical Study
    (De Gruyter, 2017-09) Sharma, Bhupendra Kumar
    An analysis is presented to describe the hydromagnetic mixed convection flow of an elec trically conductingmicropolar fluid past a vertical plate through a porous medium with radiation and slip flow regime. A uniformmagnetic field has been considered in the study which absorbs the micropolar fluid with a varying suctionvelocity and acts perpendicular to th e porous surface of the above plate.The governing non-linear partialdifferential equations have been transformed into linear partial differential equations, which are solvednumerically by applying the explicit finite difference method. The numerical results are presented graphically inthe form of velocity, micro-rotation, concentration and temperature profiles, the skin-friction coefficient, thecouple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters
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    In uence of periodic temperature and concentration on unsteady free convective viscous incompressible ow and heat transfer past a vertical plate in slip- ow regime
    (CORE, 2005) Sharma, Bhupendra Kumar
    The e ect of combined heat and mass transfer on unsteady free convective, viscous incompressible ow past a vertical at plate in slip- ow regime is studied. Assuming variable suction at the plate, approximate solutions are obtained for velocity, skin-friction, temperature, heat transfer and concentration. During the course of discussion, the e ects of Gr (Grashof number based on temperature), Gc (modi ed Grashof number based on concentration di erence), A (suction parameter) and ! (frequency parameter) for carbon dioxide (Sc = 0:94) in air (Pr = 0:71) are presented and discussed graphically
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    Heat Source and Soret Effects on Megneto-Micropolar Fluid Flow with Variable Permeability and Chemical Reaction
    (Global Journal of Pure and Applied Mathematics, 2017) Sharma, Bhupendra Kumar
    Present paper deals with the effects of heat source on the hydromagnetic mixed convection flow of an electrically conducting micropolar fluid past a vertical plate through porous medium with Soret effect, taking into account the homogeneous chemical reaction of first order. A uniform magnetic field has also been considered in the study which absorbs the micropolar fluid with a varying suction velocity and acts perpendicular to the porous surface of the above plate. The governing non-linear partial differential equations have been transformed in to linear partial differential equations, which are solved numerically by applying explicit finite difference method. The numerical results are presented graphically in the form of velocity, microrotation, concentration and temperature profiles for different material parameters
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    Computational biomedical simulations of hybrid nanoparticles (Au-Al2O3/ blood-mediated) transport in a stenosed and aneurysmal curved artery with heat and mass transfer: Hematocrit dependent viscosity approach
    (Elsevier, 2022-08) Sharma, Bhupendra Kumar
    In the present study, effects of hybrid nanoparticles () on hemodynamical characteristics of unsteady blood flow through a curved artery with stenosis and aneurysm have been analysed. Blood viscosity is assumed as hematocrit-dependent viscosity. The Crank-Nicolson method is applied to solve governing equations with tolerance in each iteration. The acquired results for both stenotic and aneurysm segments are presented graphically and have been examined for various physical parameters. It is noted that with an increment in volume fraction of gold (Au) nanoparticles, the velocity profile rises, while, reverse effect is noticed for the volume fraction of Aluminium Oxide () nanoparticles. It is also observed that hybrid nanoparticles may help to control the blood velocity and temperature, which allow the surgeons to readjust it as and when required. The current findings are in good agreement with recent outcomes in previous research studies. The motive of this research is to provide a mathematical analysis of some diseases conditions, which can be helpful in the process of diagnosis and treatment related to the problems of plaque deposition and aneurysm in cardiovascular disorders without surgery, reduction in medical expenses, and minimizing post-surgical effects. Present study also has various applications in the treatment of a variety of pathological conditions such as tumors, removal of blood clots, brain aneurysms, infections. It can be utilized for controlling the blood flow rate, resistance to flow, wall shear stress, and heating effect during surgical processes by varying the strength of the applied magnetic field, the volume fraction of nanoparticles, radiation effect, etc.
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    Influence of heat and mass transfer on MHD two-phase blood flow with radiation
    (AIP, 2018-06) Sharma, Bhupendra Kumar
    The article presents the study of heat and mass transfer effects on the two-phase model of the blood flow through a stenosed artery. The blood flow is considered as Newtonian fluid in both phases, i.e., the core and the plasma region. The coupled nonlinear differential equations are modeled for momentum, energy and concentration of the blood flow in the central core and plasma regions. Since the study takes care of radiation and magnetic effects on blood flow, major characteristics of the blood flow such as flow resistance, total flow rate and wall shear stress are calculated for different values of magnetic field and radiation parameter. The study reveals that increasing the magnetic field intensity and radiation effect leads to decreased velocity and temperature profiles of the blood flow. It is pointed out here that the concentration of the blood flow in core and plasma regions increases as values of the Schmidt number increase. Streamlines in stenosed, narrowed artery are demonstrated for the case of 20%, 40% and 50% of the arterial blockage.
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    Hemodynamical analysis of MHD two phase blood flow through a curved permeable artery having variable viscosity with heat and mass transfer
    (Springer, 2022-02) Sharma, Bhupendra Kumar
    A numerical investigation of MHD blood flow through a stenosed permeable curved artery has been done in this study. Blood flow is considered in two-phases; core and plasma region, respectively. Viscosity of the core region is considered as temperature-dependent, while constant viscosity is considered in plasma region. The governing equations of the proposed two-phase blood flow model are considered in the toroidal coordinate system. The second-order finite difference method is adopted to solve governing equations with 10−6 tolerance in the iteration process. A comparative study of Darcy number (Da) is performed to understand the influence of permeable and impermeable wall conditions. The effect of various physical parameters such as magnetic field (M), viscosity variation parameter (λ1), Darcy number (Da), heat source (H) and chemical reaction parameter (ξ) is displayed graphically on the flow velocity, temperature, concentration, wall shear stress and frictional resistance profiles. A comparison with published work has also been displayed through the graph to validate the present model, and it is in fair agreement with the existing work. The present study suggested that the curvature and permeability of the arterial wall raise the risk of atherosclerosis formation, while the implication of heat source on the blood flow lower this risk.