Browsing by Author "Sivakumar R."

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Development of a high order discretization scheme for solving fully nonlinear magnetohydrodynamic equations
(2018) Abin Rejeesh A.D.; Udhayakumar S.; Sekhar T.V.S.; Sivakumar R.
We have developed fully fourth order accurate compact finite difference discretization scheme for the Navier-Stokes equations coupled with Maxwell�s equations. The implementation is done in cylindrical polar geometry. Due to the full-MHD modeling of physical flow, the modeled equations are fully nonlinear coupled hydrodynamic equations which are again coupled with Maxwells equations. In our computations, we have accounted for the induced magnetic field in the flow of an electrically conducting fluid in an external magnetic field. The code is tested against available experimental and theoretical data where applicable. It is observed that a smaller grid of 64 � 64 is sufficient for weakly nonlinear problems and higher grids up to 512�512 are needed as the degree of nonlinearities grow in the modeled equation. In the absence of magnetic field, a discontinuity of total drag coefficient and separation length is noted for Re = 73 which is in agreement with literature. When the magnetic Reynolds number Rm < 1 separation length decreases linearly with strength of magnetic field on a log-log scale whereas if Rm > 1, it decreases nonlinearly, at a much faster rate. Thermal boundary layer thickness decreases as the strength of magnetic field increases and it forces the thermal convection to take place in a laminar structure as observed from thermal contour lines. Finally, using divided differences, we establish that the accuracy of the proposed numerical scheme is in fact fourth order. � 2018, Wilmington Scientific Publisher. All rights reserved.
Forced convection magnetohydrodynamic flow past a circular cylinder by considering the penetration of magnetic field inside it
(2019) Ghosh S.; Sarkar S.; Sivakumar R.; Sekhar T.V.S.
A numerical investigation is carried out to analyze forced convection heat transfer in magnetohydrodynamic (MHD) flow past a circular cylinder by considering the penetration of magnetic field inside it. The coupled Navier�Stokes and Maxwell equations are solved along with the energy equation using fourth-order compact finite difference scheme. We have found that the actual decrease in the rate of heat transfer upon the increase in magnetic field is almost double than what is presented in earlier studies where magnetic field is not considered to penetrate inside the cylinder. A non-monotonic behavior of local Nusselt number and mean Nusselt number with interaction parameter is observed which is in good agreement with experimental findings. Validity of heat transfer with quasi static MHD (QSMHD) flow suggests that the heat transfer results of QSMHD flow can be reproduced from our full MHD model in the limit of vanishing magnetic Reynolds number. � 2019, � 2019 Taylor & Francis Group, LLC.
Full magnetohydrodynamic flow past a circular cylinder considering the penetration of magnetic field
(2018) Ghosh S.; Sarkar S.; Sivakumar R.; Sekhar T.V.S.
An investigation of steady Full Magnetohydrodynamic (FMHD) flow around a circular cylinder is carried out by considering the penetration of the magnetic field inside it. The governing highly non-linear coupled partial differential equations are solved using a compact finite difference scheme. For the first time, the magnetic field is calculated in the entire domain, that is, both inside the cylinder and within the fluid, with a proper matching on the interface. This feature unfurls the actual mutual interactions between the magnetic field and fluid flow. It is observed that magnetic streamlines bend inwards with an increase in the magnetic Reynolds number (Rm), whereas it straightens with an increase in interaction parameter (N). Vorticity contours get dense with an increase in N or kinematic Reynolds number (Re). Further increase in N results in the contraction of vorticity contours near the middle of the cylinder which gets shifted toward the downstream region for higher values of Rm. The values of viscous and pressure drag coefficients are presented for an extensive range of Rm, N, and Re. Hitherto, all computational FMHD flows past bluff bodies neglected the influence of the magnetic field inside the body. By considering this, the present paper opens up new avenues for potential research in this area. � 2018 Author(s).
Influence of induced magnetic field on thermal MHD flow
(2015) Sivakumar R.; Vimala S.; Sekhar T.V.S.
This paper studies the influence of an induced magnetic field on the forced convective heat transfer from an isothermal sphere in the presence of an applied magnetic field. Irrespective of the choice of magnetic Reynolds number, the induced magnetic field is also taken into consideration and, therefore, we have solved the full-magnetohydrodynamic equations in (?-?-A) formulation. We have used a higher order numerical scheme with compact stencil in spherical polar coordinates for discretization. We have observed that the application of magnetic field on the flow has a twofold effect. Firstly the recirculation bubble vanishes, and secondly it alters the heat transfer coefficient. In particular, the heat transfer gets enhanced near the top of the sphere, while in the upstream and downstream regions, it diminishes. We have also found that the magnetic Reynolds number aids in the reduction of heat transfer. Our results on the heat transfer coefficient in the liquid sodium flow problem concur with the available experimental data. Further, we have observed that the effect of magnetic Reynolds number on a low Pr fluid is negligible. � 2015 Copyright � Taylor & Francis Group, LLC.
MHD mixed convective heat transfer over an isothermal circular cylinder using low Rm approximation
(2017) Udhayakumar S.; Sekhar T.V.S.; Sivakumar R.
The problem of steady, laminar flow of an incompressible and electrically conducting fluid with mixed convection over a circular cylinder subject to uniform surface temperature is considered. The cylinder is placed to approaching flow stream for normal (cross flow) direction to the buoyant force and an external magnetic field is applied in the direction opposite to the fluid flow. The governing Navier-Stokes equations with energy equation are solved by using higher compact finite difference scheme in 2D cylindrical polar coordinates. Numerical solutions with temperature fields were obtained for Reynolds number Re = 20, Prandtl number (0.065 ? Pr ? 7), Richardson number (0 ? Ri ? 2) and magnetic field (0 ? N ? 4). The results obtained are plotted in the form of contours of streamlines and isotherms. The flow and temperature fields are presented and the results are discussed. � Springer India 2017.
Numerical experiments on the study of mixed convection flow in cylindrical geometry
(2015) Udhayakumar S.; Sekhar T.V.S.; Sivakumar R.
Steady, laminar flow of an incompressible fluid with mixed convection over an isothermal circular cylinder is considered. The governing full nonlinear Navier-Stokes equations with energy equation are solved by using a high-accuracy finite difference scheme in cylindrical polar coordinates. The results are discussed in detail for 5 ? Re ? 40, 0.7 ? Pr ? 7, and 0 ? Ri ? 4 and the results are in agreement with the experimental and other computed data. An increase in the mixed convection parameter leads to reduction of the drag coefficient. The fluid with higher Pr generates vortices that destabilize the flow. The local Nu for the mixed convection cases are higher than the pure forced convection counterparts. The normalized mean Nusselt number (Nm) does not significantly change for flows with very small Richardson numbers. However, for larger Ri, it increases linearly with Ri. Copyright � Taylor & Francis Group, LLC.
Numerical investigation of magnetohydrodynamic mixed convection over an isothermal circular cylinder in presence of an aligned magnetic field
(2016) Udhayakumar S.; Abin Rejeesh A.D.; Sekhar T.V.S.; Sivakumar R.
The influence of magnetic field on the steady, laminar flow of an incompressible and electrically conducting fluid with mixed convection over a circular cylinder subject to uniform surface temperature is analyzed. The governing nonlinear Navier-Stokes equation with buoyancy body force term, coupled with temperature given by energy equation are solved by using a high order finite difference scheme in cylindrical polar coordinates without imposing axis of symmetry and employing quasi-static approximation. Numerical solutions for the flow and temperature fields are obtained for low Re and the effect of magnetic field on the flow structure and heat transfer is discussed. The vortex structure, in the absence of magnetic field, is symmetric in forced convection flows whereas in the mixed convection cases, the symmetry is broken. The applied magnetic field, in turn, opposes the symmetry breaking and tries to restore a nearly symmetric flow about ?=0 line. The total drag coefficient non-monotonically increases with increasing Prandtl number. Heat transfer is analyzed by computing the surface and mean Nusselt numbers and the behavior of local Nusselt number is explained. The mean Nusselt number monotonically increases with Ri and Pr whereas it exhibits non-monotonic behavior with applied magnetic field strength. � 2015 Elsevier Ltd. All rights reserved.
On the quasi-static approximation in the finite magnetic Reynolds number magnetohydrodynamic flow past a circular cylinder
(2019) Sarkar S.; Ghosh S.; Sivakumar R.; Sekhar T.V.S.
We consider the classical problem of Magnetohydrodynamic (MHD) flow past a circular cylinder in the presence of an imposed magnetic field aligned to the flow. Our analysis includes the computation of magnetic field in the interior of the cylinder because in an experimental setup, the magnetic field will naturally pass through the cylinder. As such, we have solved the Maxwell's equations both in the fluid flow region as well as in the interior of the cylinder with appropriate continuity conditions for magnetic field as it penetrates the cylinder. The fully nonlinear MHD equations are solved numerically using a highly accurate finite difference scheme. The influence of magnetic field in controlling boundary layer separation is discussed through the analysis of pressure gradient and the radial and transverse velocity gradients. In fact, magnetic field penetrated inside the cylinder helps to suppress flow separation more effectively than otherwise. A non-monotonic behavior of interaction parameter on the flow separation is observed for low values of magnetic Reynolds numbers (Rm). Most importantly, we examine the realm of Quasi-Static approximation in the two-dimensional MHD flows against the corresponding computationally expensive fully nonlinear MHD solutions. Our results suggest that even if Rm=0.5, the percentage error in using Quasi-Static approximation can reach up to 17.5%. Thus we have analyzed and quantified the differences between the fully nonlinear treatment and the Quasi-Static approximation for this classical flow configuration for the first time. � 2019 Elsevier Masson SAS
The role of magnetic Reynolds number in MHD forced convection heat transfer
(2016) Vimala S.; Damodaran S.; Sivakumar R.; Sekhar T.V.S.
Higher Order Compact (HOC) Scheme combined with multigrid method is developed to investigate the role of magnetic Reynolds number in MHD heat transfer from a circular cylinder which is under the influence of an external magnetic field. The governing equations are coupled nonlinear Navier-Stokes and nonlinear Maxwell's equations which are expressed in stream function, vorticity and magnetic stream function (?-?-A) formulation and decoupled energy equation. Apart from the usual kinetic Reynolds number Re, the parameters that governs the flow are magnetic Reynolds number Rm, Alfv�n number ? and Prandtl number Pr. The velocities of the flow are calculated with second order accurate based finite difference scheme and heat transfer equation is solved with fourth order accurate HOC scheme. The influence of the magnetic field and magnetic Reynolds number on velocity gradients is presented. It is found that the mean Nusselt number decreases until N ? 1 and then increases with further increase in the interaction parameter. It is also found that fluids having higher electrical conductivity can be effectively controlled with relatively low magnetic fields. The decrease in mean Nusselt number with ? and Rm is in agreement with experimental findings. � 2016 Elsevier Inc. All rights reserved.
Study of directional control of heat transfer and flow control in the magnetohydrodynamic flow in cylindrical geometry
(2016) Udhayakumar S.; A.D. A.R.; T.V.S. S.; Sivakumar R.
Two-dimensional laminar electrically conducting flow and its heat transfer is considered and the control of heat transfer in different directions is analysed using a class of high accuracy numerical scheme in curvilinear coordinate system. Numerical flow solutions with temperature fields were obtained for range of Reynolds number 10 ? Re ? 40, Prandtl number 0.065 ? Pr ? 7 and Interaction parameter 0 ? N ? 5. For weak magnetic fields, the drag coefficient increases by 37% when the field direction is aligned with that of flow, and when the field is directed perpendicular to flow direction, it drastically increases by 390% for Re=40. For stronger magnetic field strengths, the drag coefficient increases like square root of interaction parameter. When no field is applied the heat transfer takes place in the entire region of downstream, but when the magnetic field is switched on, the direction of applied magnetic field influences the heat transfer to take place in the selected direction of the downstream by forming plumes in those directions. In contrast to a reduction in mean Nusselt number due to aligned magnetic field, the heat transfer increases due to transverse magnetic field. � 2016 Elsevier Inc.
Study of heat transfer control with magnetic field using higher order finite difference scheme
(2016) Sivakumar R.; Vimala S.; Damodaran S.; Sekhar T.V.S.
The control of convective heat transfer from a heated circular cylinder immersed in an electrically conducting fluid is achieved using an externally imposed magnetic field. A Higher Order Compact Scheme (HOCS) is used to solve the governing energy equation in cylindrical polar coordinates. The HOCS gives fourth order accurate results for the temperature field. The behavior of local Nusselt number, mean Nusselt number and temperature field due to variation in the aligned magnetic field is evaluated for the parameters 5?Re?40, 0?N?20 and 0.065?Pr?7. It is found that the convective heat transfer is suppressed by increasing the strength of the imposed magnetic field until a critical value of N, the interaction parameter, beyond which the heat transfer increases with further increase in N. The results are found to be in good agreement with recent experimental studies. � 2016 Global Science Press.