Numerical analysis of the full MHD model with the Galerkin finite-element method
Department of Mathematics, Riphah International University Faisalabad Campus, 38000, Faisalabad, Pakistan
2 Department of Mathematics and Statistics, International Islamic University Islamabad, 44000, Islamabad, Pakistan
* e-mail: email@example.com
Accepted: 24 January 2019
Published online: 14 May 2019
The steady-state, two-dimensional mixed-convection flow inside a square conduit subject to an external magnetic field is investigated here. The full MHD equations are used to model the set of governing partial differential equations for the problem under consideration. These equations along with appropriate boundary conditions are simulated by employing the variational finite-element method for the important parameters of the problem. The effects of these parameters on streamlines, temperature field, mid-section velocity and heat transfer rate are shown and discussed in detail. A comparison of the full MHD model with the low-Rm model is carried out. The grid independent test is also included to assure the convergence of the obtained solution. The analysis predicts that the intensity of flow circulations increases with increasing magnetic Reynolds number for any choice of the Prandtl number. Further, the average Nusselt number at both the right and bottom walls is an increasing function of Rm. Moreover, the low-Rm model predicts lower values of the average Nusselt number when compared to the result of the full MHD model.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019