Department of Mathematics
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Item Three-Dimensional Unsteady Mixed Convection and Mass Transfer Flow with Periodic Temperature(Dirasat, 2008) Sharma, Bhupendra KumarThis 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.Item Flow characteristics of MHD oscillatory two-phase blood flow through a stenosed artery with heat and mass transfer(ARXIV, 2017-05) Sharma, Bhupendra KumarIn 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 simulationsItem 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 KumarAn 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 parametersItem 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 KumarThe 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 graphicallyItem 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 KumarPresent 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 parametersItem Influence of heat and mass transfer on MHD two-phase blood flow with radiation(AIP, 2018-06) Sharma, Bhupendra KumarThe 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.Item Heat and mass transfer in magneto-biofluid flow through a non-Darcian porous medium with Joule effect(Springer, 2013-09) Sharma, Bhupendra KumarIn the present study, a mathematical model for the hydromagnetic non-Newtonian biofluid flow in the non-Darcy porous medium with Joule effect is proposed. A uniform magnetic field acts perpendicularly to the porous surface. The governing nonlinear partial differential equations are transformed into linear ones which are solved numerically by applying the explicit finite difference method. The effects of various parameters, like Reynolds number and hydro-magnetic, Forchheimer, and Darcian parameters, Prandtl, Eckert, and Schmidt numbers, on the velocity, temperature, and concentration are presented graphically. The results of the study can find applications in surgical operations, industrial material processing, and various heat transfer processes.