A mathematical model is developed to discuss the impact of the Hall current and the Joule heating on the peristaltic flux of finitely extensible nonlinear elastic Peterlin (FENE-P) fluid in a tapered tube with mild stenosis. The fluid movement along the wall surface resulted from the sinusoidal wave flowing with constant speed. Conditions of velocity and thermal slip are applied. Lubrication approximation is adopted to modify the governing flow problem. To discover the solution to a system of equations, the regular perturbation approach is used. The effects of the different physical parameters are debated and graphically shown in a set of figures. It is discovered that as the Hall current parameter is increased and the Hartman number is decreased, the fluid velocity increases. It is also worth noting that the Dufour number causes the fluid temperature to rise, whilst the Hall current parameter causes the temperature to fall. In the meantime, both the Hall current parameter and the Soret number have the opposite effect on concentration. The trapping phenomenon is thoroughly investigated.
