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This paper investigates the effect of partial slip on peristaltic flow of a Sisko fluid through a porous medium. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and chemical reactions on blood flow are also taken into account. The governing equations of motion, energy and concentration are simplified by using the long wavelength and low Reynolds number approximations. The analytical solutions of these equations are obtained by considering a perturbation technique for small non- Newtonian Sisko fluid parameter. The pressure rise and friction force are numerically calculated. The numerical calculations with the help of graphs are adopted to obtain the effects of several parameters, such as the slip parameter, permeability parameter, the taper angle, Brickmann number, Soret number and the maximum height of stenosis, upon the distributions of velocity, temperature, concentration, pressure rise and friction force. It is found that the axial velocity increases with the increase of slip parameter. Meanwhile, it decreases with the increase of permeability parameter. The stream lines are also depicted. It is observed that the trapped bolus increases in size with the increase of both the slip parameter and the maximum height of stenosis. The other results are also illustrated.

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