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Magnetohydrodynamic pipe flow in annular-like domains

The magnetohydrodynamic (MHD) pipe flow in annular-like domains with electrically conducting walls is investigated using both the extended-domain-eigenfunction method (EDEM) and the boundary element method (BEM). EDEM aims to reformulate the original problem on an extended symmetric domain obtained by transforming the inner boundary to a smaller circle towards the centre of the pipe, so that an eigenfunction solution can be obtained theoretically. By collocating only the inner circular boundary, the solution is transformed back to the original inner wall, which can be regarded as a semi-theoretical solution. On the other hand, BEM is a boundary only nature technique which transforms the differential equation into a boundary integral equation using the fundamental solution of the differential equation. Calculations are carried out for increasing values of Hartmann number (M) in annular-like domains with several shapes of inner wall at various wall conductivities. It is observed that although the results obtained by EDEM and BEM are very compatible for small M, EDEM is computationally less expensive and faster in convergence compared to BEM. However, BEM gives more accurate results than EDEM for large M due to the accumulation of numerical errors close to inner boundary in EDEM.