Applying homotopy perturbation method to provide an analytical solution for Newtonian fluid flow on a porous flat plate

This research work is going to apply the homotopy perturbation method to solve the problem of flowing Newtonian fluid on a flat plate. For this purpose, initially, the problem, including the governing equations and boundary conditions, is defined, and after that, the considered assumptions to solve the defined problem are introduced. Next, the working principle of the homotopy perturbation method is described, and then, the way to obtain the analytical solution using the homotopy perturbation method is presented, and finally, the accuracy of the proposed analytical solution in comparison to the numerical approach is compared for validation. Both momentum and energy equations are solved. The maple software program is utilized for carrying out the mathematical calculations, while the validation is done using the profiles for stream function, velocity distribution, stress, and dimensionless temperature as the key indicators related to the solution. The conducted comparison shows that the analytical solution provided by the homotopy perturbation method is able to predict all the important performance criteria for the problem very well, and therefore, the homotopy perturbation method has a strong potential to be employed for providing the analytical solution for such problems.

Automated summary

This research successfully applied the homotopy perturbation method to solve the problem of Newtonian fluid flow on a flat plate, validating the accuracy and reliability of the solution by comparing it with numerical methods. Mathematical calculations were conducted using Maple software, and verification was based on profiles of stream function, velocity distribution, stress, and dimensionless temperature.