a b s t r a c tThe article solves the Jeffery-Hamel flow using the homotopy perturbation method, an explicit analytical solution is obtained, and the effect of external magnetic field is studied. Comparison of the obtained result with the numerical one reveals validity of the used method.
Purpose -The main purpose of the work is to demonstrate the eligibility of the methods applied and to have the more reliable and user friendly approaches to find the solution of the applicable governing equations such as of the MHD flow. Design/methodology/approach -The numerical and semi analytical methods have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the results obtained and the results of the former studies performed using the other numerical approach. Findings -The reliability of the methods are approved, so that the method could be used to discuss more in depth argument on the different profiles of the solution. Originality/value -It could be considered as a first endeavor to use the solution of the MHD Jeffery Hamel flow using this kind of numerical method along with the semi analytical approach.
Abstract. The focus of the present work is on the investigation of the
separation point and its relative location in a circular diffuser carrying
incompressible laminar flow in the presence of a non-uniform external
magnetic field. Two different approaches are deployed in the present
analysis. In the first approach, a similarity transform is applied to reduce
the momentum equation to the nonlinear ordinary differential equation (ODE).
The ODE is solved by a dual integral–numerical method and the separation
position is directly determined. In this combined numerical–integral
methodology, the integration is applied followed by a numerical method. In
the second approach, the equation is solved by the least square method
(LSM), and the separation position is indirectly specified. In this study it is
shown that the magnetic field intensity can be manipulated to postpone the
separation such that it could be eliminated totally. Comparing the
results yields a good agreement. It has been concluded that by increasing the
magnetic field intensity, as the Lorentz force increases, increased shear
stress on the wall and delay in the occurrence of the separation position
are observed.
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