In the current critique, we deliberate the blood flow through narrowing vein with a stenosis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathematically by demonstrating the blood as Carreau fluid. The illustration for the blood flow is debated through an axially irregular but outward regular stenosis. Regularity in the dissemination of the fortification clipping stress and resistive impedance and their evolution with the emerging stenosis is a new significant feature of our investigation. Analytical solutions have been appraised for "velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat". The graphical consequences of different types of tapering arteries (i.e. "converging tapering, diverging tapering, non-tapered artery") have been studied for dissimilar constraints of attention. Rivulet shapes have been strategized for different parameters at the culmination of the article.