Highly accurate Coiflet wavelet-homotopy solution of Jeffery–Hamel problem at extreme parameters

Abstract

The magnetized Jeffery–Hamel flow due to a point sink or source in convergent and divergent channels is studied. Such viscous flow plays an important role in understanding rivers and canals, human anatomy, and the connection between capillaries and arteries. The simplified governing equation ruled by the Reynolds number, the Hartmann number and the divergent–convergent angle with appropriate boundary conditions is solved by the newly proposed Coiflet wavelet-homotopy analysis method (CWHAM). A highly accurate solution is obtained, whose accuracy is rigidly checked. Our proposed method combines the advantages of the homotopy analysis method for strong nonlinearity and the Coiflet wavelet method for excellent local expression capability so that it holds higher computational efficiency, larger applicable range of physical parameters, and better nonlinear processing capability. Different from the previously published research on the CWHAM, we focus on establishing the solution process of nonlinear flow problems with extreme physical parameters, which is not considered before.