Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels

M.S. Shadloo (1) , Amin Kimiaeifar (2)

1 Sabanci University - Faculty of Engineering and Natural Sciences
2 AAU - Aalborg University [Denmark]

In this article, an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels is presented. A similarity transform reduces the Navier-Stokes and energy equations to a set of non-linear ordinary differential equations that are solved analytically by means of the homotopy perturbation method (HPM). The results obtained in this study are compared with numerical results and previous studies. Close agreement of the two sets of results indicates the accuracy of HPM. An expression that is acceptable for all values of effective parameters is obtained by HPM. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on HPM.

Mots clés: converging/diverging channels; Homotopy perturbation method; magnetohydrodynamic flows; second-order fluid; Visco-elastic fluid; Fluids; Magnetohydrodynamics; Ordinary differential equations; Perturbation techniques; Steady flow; Navier Stokes equations

Domaines: Mécanique des fluides [physics.class-ph]

M.S. Shadloo, Amin Kimiaeifar. Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011, 225 (2), pp.347-353. ⟨10.1243/09544062JMES2334⟩. ⟨hal-02127875⟩