Abstract
The non-linear differential equation for the magnetohydrodynamic Poiseuille flow of Phan-Thein–Tanner (PTT) conducting fluid is derived. Using the homotopy analysis method (HAM), the series solution is developed and its convergence is discussed. Also, the results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.