DRBEM solution of Regularly Perturbed Simplified MHD flow problem for small Hartmann numbers

Date

2025-09-12

Author

Arslan, Sinem
Tezer, Münevver

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In this study, the steady, laminar, fully-developed flow of an incompressible, viscous, and electrically conducting fluid is taken into consideration in a long channel (pipe) of a square cross section (duct) along with the z-axis such that fluid motion occurs under the influence of a pressure gradient directed along the z-axis. The fluid is influenced by the external magnetic field applied vertically in the y-axis direction with intensity B_0 It is assumed that the intensity of the applied magnetic field is weak for a fluid with small electrical conductivity but high viscosity coefficient resulting a Hartmann number which is much less than one. In this situation, this small number can be treated as the perturbation parameter. Thus, the simplified MHD flow equations turn into a regular perturbation problem in which the power series of the unknowns, namely the velocity ω and the electric potential Φ, can be used in terms of the perturbation parameter. It is observed that the DRBEM can capture the solution of the simplified MHD flow problem for small values of Hartmann number by using the regular perturbation theory since the original unperturbed and regularly perturbed solutions coincide, which distinguishes the present study as an original contribution.

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https://hdl.handle.net/11511/120606

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Department of Mathematics, Conference / Seminar