American Journal of Computational Mathematics, 2017, 7, 243-275 http://www.scirp.org/journal/ajcm ISSN Online: 2161-1211 ISSN Print: 2161-1203 DOI: 10.4236/ajcm.2017.73021 Aug. 17, 2017 243 American Journal of Computational Mathematics Prediction of Better Flow Control Parameters in MHD Flows Using a High Accuracy Finite Difference Scheme A. D. Abin Rejeesh 1 , S. Udhayakumar 1 , T. V. S. Sekhar 2 , R. Sivakumar 1 1 Department of Physics, Pondicherry University, Puducherry, India 2 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India 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 elec- trical 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 Navi- er-Stokes equation is fully nonlinear due to its coupling with Maxwell’s equa- tions. 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 sup- pression of boundary layer and this is a favorable result for practical applica- tions. The present computational scheme predicts that a drag-coefficient minimum can be achieved when 0.4 β = which is much lower when com- pared to the value 1 β = as given by second order method. For a special val- ue of 0.65 β = , it is found that the heat transfer rate is independent of elec- trical conductivity of the fluid. From the numerical values of physical quanti- ties, we establish that the order of accuracy of the computed numerical results is fourth order accurate by using the method of divided differences. Keywords Full-MHD Equations, Forced Convective Heat Transfer, High Order Compact Schemes, Divided Differences *Corresponding author. How to cite this paper: Abin Rejeesh, A.D., Udhayakumar, S., Sekhar, T.V.S. and Sivakumar, R. (2017) Prediction of Better Flow Control Parameters in MHD Flows Using a High Accuracy Finite Difference Scheme. American Journal of Computa- tional Mathematics, 7, 243-275. https://doi.org/10.4236/ajcm.2017.73021 Received: May 9, 2017 Accepted: August 14, 2017 Published: August 17, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution-NonCommercial International License (CC BY-NC 4.0). http://creativecommons.org/licenses/by-nc/4.0/ Open Access