Department of Mathematics

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Author: search.filters.author.Sharma, Bhupendra KumarSubject: search.filters.subject.Variable viscosity

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Now showing 1 - 7 of 7
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    Optimization of heat transfer nanofluid blood flow through a stenosed artery in the presence of Hall effect and hematocrit dependent viscosity
    (Elsevier, 2023-07) Sharma, Bhupendra Kumar
    The heat transfer rate of the MHD nanofluid blood flow through a stenosed composite artery with hematocrit-dependent viscosity and Hall effect is optimized by using the response surface methodology (RSM). An experimental design and sensitivity analysis based on RSM are employed to examine the impact of different physical parameters and how changes to these parameters affect the response factors of interest. RSM is utilized in the process of constructing the model dependencies between the output response variables, such as the skin friction coefficient and the local Nusselt number, and the independent input parameters, such as the magnetic field parameter, the Hall parameter, and the Brinkman number. These model dependencies are used to determine the relationship between the output response variables and the independent input parameters. For medical applications, the effects of the aforementioned parameters on the velocity and temperature along the radial axis have been examined and physically interpreted. Shear stress and Nusselt number are analyzed using graphs for several physical factors in addition to stenosis height. The increases in the hematocrit parameter are accompanied with a decrease in velocity profile, as it enhances the fluid viscosity that reduces the fluid motion. The sensitivity of (Nusselt number) and (shear stress profile) are positive for , while negative for M and Be. In addition, current research may be helpful in biomedical by detecting the abnormalities in the artery with the help of the artery image, also known as magnetic resonance angiography (MRA).
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    Radiation effect on MHD copper suspended nanofluid flow through a stenosed artery with temperature-dependent viscosity
    (IJNAA, 2022-08) Sharma, Bhupendra Kumar
    In the present paper, the effects of radiation, variable viscosity, and the inclination of the artery on copper nanofluid through composite stenosis with chemical reaction are discussed. The viscosity of blood is varied with temperature as represented in the Reynolds viscosity model. The coupled nonlinear equations of the nanofluid model are simplified by considering the mild stenosis case. The governing equations are solved numerically by applying the Finite Difference Method. The effects of the physical parameters on the velocity, temperature, and concentration along the radial axis have been studied and are physically interpreted for medical applications. The effect of shear stress along the increasing height of stenosis has been explained with the help of graphs. The proposed work will be beneficial to clinicians, hematologists, and biomedical engineers because they serve as useful approximations, which are capable of throwing some light toward the understanding of the genesis of pathological states, like arteriosclerosis as well as the mechanism of gaseous exchanges that take place within arteries and capillaries.
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    Effect of heat transfer on MHD blood flow through an inclined stenosed porous artery with variable viscosity and heat source
    (Romanian Journal of Biophysics, 2018-05) Sharma, Bhupendra Kumar
    In this article, effects of heat transfer on MHD blood flow through a stenosed inclined porous artery with heat source have been investigated. The viscosity of the blood is assumed to be varying radially with hematocrit throughout the region of the artery. Governing equations have been derived by treating blood as incompressible magnetohydrodynamic (MHD) Newtonian fluid. Momentum and energy equations of the fluid flow are simplified under the assumption of mild stenosis. Homotopy perturbation method (HPM) is used to solve nonlinear differential equations for velocity and temperature profiles of the blood flow. Variation of flow rate and shear stress for different values of inclination angle and hematocrit parameter along the diseased part of artery have been plotted graphically. For having the adequate insight of the flow pattern in the diseased artery, velocity contours have been plotted for different values of the height of the stenosis and for different inclination angles of the artery.
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    Entropy Analysis for MHD Flow Subject to Temperature-Dependent Viscosity and Thermal Conductivity
    (Springer, 2022-10) Sharma, Bhupendra Kumar
    This research aimed to figure out how to optimise the entropy of MHD flow past a continuously stretching surface. The effect of temperature-dependent variables viscosity and electric conductivity has been taken into account. The fluid region is subjected to a uniform magnetic field. By using similarity analysis, the governing coupled partial differential equations (PDEs) that describe the model are turned into non-linear ordinary differential equations and then computed by employing “BVP4C” in MATLAB software. The effect of various pertinent parameters like Magnetic field parameter M, radiation parameter R, Grashof number Gr, Brinkman number Br, Reynold number Re, and a variation of variables viscosity ϵ1 and electric conductivity ϵ2 is analysed and presented graphically on velocity, temperature, entropy, and concentration profile. The comparison is based on previously published studies, and there is a considerable deal of agreement.
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    Mathematical analysis of two-phase blood flow through a stenosed curved artery with hematocrit and temperature dependent viscosity
    (IOP, 2021) Sharma, Bhupendra Kumar
    Atwo-phase blood flow model is considered to analyze the fluid flow and heat transfer in a curved tube with time-variant stenosis. In both core and plasma regions, the variable viscosity model (Hematocrit and non linear temperature-dependent, respectively) is considered. A toroidal coordinate system is considered to describe the governing equations. The perturbation technique in terms of perturbation parameter ε is used to obtain the temperature profile of blood flow. In order to find the velocity, wall shear stress and impedance profiles, a second-order finite difference method is employed with the accuracy of 10−6 in the each iteration. Under the conditions of fully-developed flow and mild stenosis, the significance of various physical parameters on the blood velocity, temperature, wall shear stress (WSS) and impedance are investigated with the help of graphs. A validation of our results has been presented and comparison has been made with the previously published work and present study, and it revels the good agreement with published work. The present mathematical study suggested that arterial curvature increase the fear of deposition of plaque (atherosclerosis), while, the use of thermal radiation in heat therapies lowers this risk. The positive add in the value of λ1 causes to increase in plasma viscosity; as a result, blood flow velocity in the stenosed artery decreases due to the assumption of temperature-dependent viscosity of the plasma region. Clinical researchers and biologists can adopt the present mathematical study to lower the risk of lipid deposition, predict cardiovascular disease risk and current state of disease by understanding the symptomatic spectrum, and then diagnose patients based on the risk.
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    Entropy generation for MHD two phase blood flow through a curved permeable artery having variable viscosity with heat and mass transfer
    (Elsevier, 2022-04) Sharma, Bhupendra Kumar
    Present study deals with the analysis of entropy generation of MHD blood flow through a stenosed permeable curved artery with heat source and chemical reaction. 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), Brinkman number (Br), heat source (H), chemical reaction parameter (ξ) etc. are displayed graphically on the flow velocity, temperature, concentration, wall shear stress (WSS), frictional resistance profile and entropy generation 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. Clinical researchers and biologists can use the current mathematical research to lower the risk of lipid deposition and predict the risk of cardiovascular disease, and then diagnose patients based on risk.
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    Effect of Variable Viscosity on MHD Inclined Arterial Blood Flow with Chemical Reaction
    (Sciendo, 2018-08) Sharma, Bhupendra Kumar
    In this paper, we present the mathematical study of heat and mass transfer effects on an arterial blood flowunder the influence of an applied magnetic field with chemical reaction. A case of mild stenosis is considered in anon-tapered artery which is inclined at an angle  from the axis. The variable viscosity of the blood is consideredvarying with the hematocrit ratio. Governing non-linear differential equations have been solved by using ananalytical scheme, homotopy perturbation method to obtain the solution for the velocity, temperature andconcentration profiles of the blood flow. For having an adequate insight to blood flow behavior through astenosed artery, graphs have been plotted for wall shear stress, velocity, temperature and concentration profileswith varying values of the applied magnetic field, chemical reaction pa rameter and porosity parameter. Theresults show that in an inclined artery, the magnitude of the wall shear stress at stenosis throat increases as valuesof the applied magnetic field increase while it reduces as the values of both the chemical reaction and porosityparameters increase. Contour plots have been plotted to show the variations of the velocity profile of blood flowas the values of the height of the stenosis as well as the influence of the applied magnetic field increase