Browsing by Author "Udhayakumar S."

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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.
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.
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.