Analysis of fluid flow in curved pipes using homotopy analysis method

The study of fluid flow in curved pipes is becoming more popular among researchers due to its broad spectrum of applications in engineering and industries. Driven by this motivation, this paper focuses on the semi‐analytical study of the flow of viscous and incompressible fluid in slightly curved pipes. Employing the toroidal coordinate system, the nonlinear governing equations are solved with the help of the homotopy analysis method (HAM). Stream function and axial velocity of the flow are calculated using HAM. Solution is computed up to 18th order of approximation, and its convergence is studied. Volumetric flow rate and streamlines patterns are investigated. The findings imply that the HAM provides significantly accurate solutions. The impacts of Dean's number on the axial velocity, stream function, volumetric flow rate, and streamlines are studied through graphs. These impacts are primarily driven by the centrifugal force induced by the pipe curvature. The volumetric flow rate in a curved pipe is reduced compared to that in a straight pipe by approximately 1.91% at higher values of the , due to the influence of curvature on the fluid flow. The obtained results are validated with the earlier findings and are in good agreement, demonstrating the efficiency of HAM. It is inferred that HAM can be applied to address more intricate problems involving fluid flow through curved pipes.