A newly computational method based on the Coiflet wavelet and homotopy analysis method is developed, which inherits the great nonlinear treatment of the homotopy analysis technique and the local high-precision capability of the wavelet approach, to give solutions to the classic problem of channel flow with moving walls. The basic principle of this suggested technique and the specific solving process are presented in detail. Its validity and efficiency are then checked via rigid comparisons with other computational approaches. It is found that the homotopy-based convergence-control parameter and the wavelet-based resolution level of Coiflet are two effective ways to improve on accuracies of solutions.

The magnetised Jeffery-Hamel flow due to a point sink or source in convergent and divergent channels is studied. The simplified governing equation ruled by the Reynolds number, the Hartmann number and the divergent-convergent angle with appropriate boundary conditions are solved by the newly proposed Coiflet wavelet-homotopy method. Highly accurate solutions are obtained, whose accuracy is rigidly checked. As compared with the traditional homotopy analysis method, our proposed technique has higher computational efficiency and larger applicable range of physical parameters. Results show that our proposed technique is very convenient to handle strong nonlinear problems without special treatment. It is expected that this technique can be further applied to study complex nonlinear problems in science and engineering involving into extreme physical parameters. Besides, the influence of physically important quantities on the flow is discussed. It is found that wall stretching and shrinking exhibits totally different roles on the flow development. The enhanced Lorenz force affects the flow behaviours significantly for both convergent and divergent cases.

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.

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