73 / 2019-09-29 19:23:13

Wavelet homotopy analysis method for solving mixed nanofluid flow in porous channels

Wavelet homotopy analysis method, wavelet basis, mixed nanofluid flow

Nonlinear problems are widely used in natural science and engineering applications. However, in practical research, nonlinear problems are often difficult to solve quickly and accurately due to their complex nature. Since the introduction of the homotopy analysis method, it has advantages such as not relying on physical parameters, large freedom in the selection of linear operators and basis functions, and the ability to adjust the convergence of the solution by controlling convergence parameters, in the fields of mechanics, mathematics, etc. The application of nonlinear problems has been widely used. However, in solving some complex nonlinear problems, the traditional homotopy analysis method is greatly reduced in efficiency and there are certain difficulties in the selection of linear operators and initial guess solutions. In this case, wavelet homotopy Analytical methods came into being. The wavelet homotopy analysis method is based on the traditional homotopy analysis method. The wavelet base is applied as the solution basis function in the homotopy analysis method, which overcomes the weakness of the traditional basis function and retains the advantages of the traditional homotopy analysis method. It is also possible to balance the relationship between calculation efficiency and solution accuracy by adjusting the resolution level, and reduce the influence of different initial guess solutions and linear operators on the solution, so that the solution process is more convenient and efficient.
   In this paper, the wavelet homotopy analysis method is used to solve the flow problem of mixed nanofluids in porous channels. Under the framework of homotopy analysis method, the generalized Coiflet wavelet is used as the basis function to transform the flow control equation into linear ones. The sub-equation, by adjusting the control convergence parameters to control the convergence of the solution, to obtain the analytical solution of the flow problem of the mixed nanofluid in the porous channel.