BITS Faculty Publications

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    Multidimensional HLLI generalized riemann problem solver for conservation laws – the two-dimensional case for structured meshes
    (Elsevier, 2025-10) Bhoriya, Deepak
    The Riemann problem, and the associated generalized Riemann problem (GRP), are increasingly seen as important building blocks for modern higher order Godunov-type schemes. While most solutions of the GRP are specific to a particular hyperbolic law, a general-purpose GRP that can be applied to any hyperbolic conservation law has emerged in the form of the one-dimensional HLLI-GRP. Approximate multidimensional Riemann solvers have also been designed by the first author and his colleagues. However, a multidimensional GRP that is applicable to any hyperbolic conservation law has never been designed until now to the best of our knowledge. It this paper, we accomplish such a task. The study of the multidimensional Riemann problem entails the study of the strongly-interacting state. Starting with the multidimensional HLL-based Riemann solver, we present all the steps for endowing spatial gradients to the strongly-interacting state. This is accomplished through application of Rankine-Hugoniot shock jump conditions to the higher order terms in a Taylor series expansion of the strongly-interacting state. A linearized formulation is also used to obtain the spatial gradients to the strongly-interacting state. With the spatial gradients in hand, it is possible to specify the multidimensional HLL flux as well its time-derivative. This results in a multidimensional HLL-GRP solver. We then utilize intermediate waves to reduce the dissipation of the multidimensional HLL-GRP. This gives us an HLLI-GRP solver which significantly reduces dissipation and is complete in multiple dimensions.
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    Influence of magnetohydrodynamics and chemical reactions on oscillatory free convective flow through a vertical channel in a rotating system with variable permeability
    (World Scientific, 2024) Sharma, Bhupendra Kumar
    This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity Ω. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.
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    Mixed Convection Flow and Heat Transfer Using CNTs across a Vertically Stretching/Shrinking Sheet
    (Springer, 2023-03) Bhattacharyya, Suvanjan
    The current paper examined the influence of an inclined MHD on natural convection, which has been studied analytically in recent articles. The governing equations are simplified to a self-similar third-order highly non-linear ODE with a constant coefficient, which can be solved analytically. SWCNTs and MWCNTs, two forms of CNTs-water nanofluids, are solved by mixed convection. The findings could be used in a variety of ways, such as cooling electronic equipment in computers or creating clouds in the environment. CNTs have a wide range of industrial and biomedical, energy production, and space cooling applications because they can improve the thermal properties of base materials. As a result, the CNTS used in the field are being investigated for their potential in heat transfer applications. The fluid was initially at repose until achieving flow over the linear velocity of the stretching/shrinking sheet. The momentum and energy equations have asymptotic continuous solutions. The present problem of the mixed convective boundary layer flow and heat transfer of CNTs over a stretching/shrinking sheet, also thermal radiation is also considered in the heat transfer characteristics. The effect of several relevant parameters on the velocity profile and temperature distribution is calculated, and the result is that graphical representations are used to depict the effects of the emerging constraints on the profiles. Skin friction and Nusselt number also verified with variety of parameters.
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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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    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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    MHD forced flow of a conducting viscous fluid through a porous medium induced by an imprevious rotating disk
    (Romanian Journal of Biophysics, 2006-08) Sharma, Bhupendra Kumar
    The forced flow of an electrically conducting viscous incompressible fluid, due to an infinite impervious rotating disk bounded by porous medium has been investigated. A uniform magnetic field is applied in the direction normal to the flow. 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. Analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined
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    Effect of MHD on Unsteady Oscillatory Couette Flow Through Porous Media
    (Sciendo, 2022-03) Sharma, Bhupendra Kumar
    This paper describes the effects of a magnetic field on unsteady free convection oscillatory systems. Whentemperature and species concentration fluctuate with time around a non-zero constant, "Couette flow" across aporous medium occurs. The system of non-linear ODEs that governs the flow is solved analytically using theperturbation approach because the amplitude of fluctuations is very tiny. Mean flow and transient velocity, transientconcentration, transient temperature, heat transfer, mean skin friction and phase and amplitude of skin friction. Allhave approximate solutions. The influence of different parameters on flow characteristics has been specified anddiscussed.
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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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    Radiation Effect on MHD Blood Flow Through a Tapered Porous Stenosed Artery with Thermal and Mass Diffusion
    (Sciendo, 2019-06) Sharma, Bhupendra Kumar
    A mathematical model for MHD blood fl ow through a stenosed artery with Soret and Dufour effects in thepresence of thermal radiation has been studied. A uniform magne tic field is applied perpendicular to the poroussurface. The governing non-linear part ial differential equations have been transformed into linear partialdifferential equations, which are solved numerically by applying the explicit finite difference method. Thenumerical results are presented graphically in the form of velocity, temperature and concentration profiles. Theeffects of various parameters such as the Reynolds number, Hartmann num ber, radiation parameter, Schmidtnumber and Prandtl number, Soret and Dufour parameter on the velocity, temperature and concentration havebeen examined with the help of graphs. The present results have an important bearing on the therapeuticprocedure of hyperthermia, particularly in understanding/regulating blood flow and heat transfer in capillaries.
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    Thermal radiation effect on inclined arterial blood flow through a non-Darcian porous medium with magnetic field
    (ASTFE, 2015) Sharma, Bhupendra Kumar
    A theoretical analysis is presented for the hydro-magnetic inclined arterial blood flow through a non-Darcy porous medium with thermal radiation. A uniform magnetic field is applied to the inclined porous surface. The dimensionless governing coupled, non-linear partial differential equations are solved by an efficient, accurate and extensively validated and unconditionally stable finite difference scheme of the Crank-Nicolson type. The effects of the various important parameters entering into the problem like thermal radiation, Reynolds number, hydro-magnetic parameter, Forchheimer parameter, Darcian parameter, Prandtl number, inclined angle and variable viscosity parameter on the velocity and temperature have been examined with the help of graphs.