TITLE:
Prediction of Better Flow Control Parameters in MHD Flows Using a High Accuracy Finite Difference Scheme
AUTHORS:
A. D. Abin Rejeesh, S. Udhayakumar, T. V. S. Sekhar, R. Sivakumar
KEYWORDS:
Full-MHD Equations, Forced Convective Heat Transfer, High Order Compact Schemes, Divided Differences
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.3,
August
17,
2017
ABSTRACT: We have
successfully attempted to solve the equations of full-MHD model within the
framework of Ψ - ω formulation
with an objective to evaluate the performance of a new higher order scheme to
predict better values of control parameters of the flow. In particular for MHD
flows, magnetic field and electrical conductivity are the control parameters.
In this work, the results from our efficient high order accurate scheme are compared
with the results of second order method and significant discrepancies are noted
in separation length, drag coefficient and mean Nusselt number. The governing
Navier-Stokes equation is fully nonlinear due to its coupling with Maxwell’s
equations. The momentum equation has several highly nonlinear body-force terms
due to full-MHD model in cylindrical polar system. Our high accuracy results
predict that a relatively lower magnetic field is sufficient to achieve full
suppression of boundary layer and this is a favorable result for practical
applications. The present computational scheme predicts that a drag-coefficient
minimum can be achieved when β=0.4 which is much lower when compared to the value β=1 as
given by second order method. For a special value of β=0.65, it is found that the heat transfer rate is
independent of electrical conductivity of the fluid. From the numerical values
of physical quantities, we establish that the order of accuracy of the computed
numerical results is fourth order accurate by using the method of divided
differences.