Abstract
The equation of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel is derived and solved using a new modified Adomian decomposition method (ADM). So far in all problems where semi-analytical methods are used the boundary conditions are not satisfied completely. In the present research, a hybrid of the Fourier transform and the Adomian decomposition method (FTADM), is presented in order to incorporate all boundary conditions into our solution of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel flow. The effects of various emerging parameters such as channel angle, stretching/shrinking parameter, Casson fluid parameter, Reynolds number and Hartmann number on velocity profile are considered. The results using the FTADM are compared with the results of ADM and numerical Range-Kutta fourth-order method. The comparison reveals that, for the same number of components of the recursive sequences over a wide range of spatial domain, the relative errors associated with the new method, FTADM, are much less than the ADM. The results of the new method show that the method is an accurate and expedient approximate analytic method in solving the third-order nonlinear equation of Jeffery-Hamel flow of non-Newtonian Casson fluid.
Highlights
Jeffery-Hamel flow is commonly used as an important model problem for investigating various aspects of engineering applications such as mechanical, aerospace, chemical, civil, environmental and biomechanical science
The Fourier transform is applied to the Adomian decomposition method, namely the FTADM28 in order to satisfy all boundary conditions in a wide range of spatial domain while this is not possible when applying the ordinary ADM
The Fourier transform and the Adomian decomposition method (FTADM), where all the boundary conditions are satisfied over the entire spatial domain is used in our calculations
Summary
The equation of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel is derived and solved using a new modified Adomian decomposition method (ADM). A hybrid of the Fourier transform and the Adomian decomposition method (FTADM), is presented in order to incorporate all boundary conditions into our solution of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel flow. To our knowledge no attempt is made so far to investigate the combined effect of Hartmann number and stretching/shrinking channel on non-Newtonian Casson fluid flow in the Jeffrey-Hamel (wedge) geometry To this purpose, the mathematical formulation of the strongly nonlinear third-order MHD Jeffery-Hamel type equation of the non-Newtonian Casson fluid is derived and is solved by the FTADM. When the conductor is either a liquid or gas, the electromagnetic force is generated
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