Herschel-Bulkley Model of Blood Flow through a Stenosed Artery with the Effect of Chemical Reaction on Solute Dispersion


  • Siti Nurul Aifa Mohd Zainul Abidin Universiti Teknologi Malaysia
  • Nurul Aini Jaafar
  • Zuhaila Ismail




Blood flow, Convective-diffusion equation, Chemical reaction, Herschel-Bulkley fluid, Stenosis,


A non-Newtonian mathematical model of blood described as a Hershel-Bulkley fluid model flowing in a stenosed artery with the effect of a chemical reaction is mathematically studied. The expressions of the shear stress, mean velocity and absolute velocity in the plug and non-plug flow field are evaluated analytically. The convective-diffusion equation is solved using the Taylor-Aris technique subject to the relevant boundary constraint in determining the concentration, relative and effective axial diffusivity. The efficiency of the dispersion process is affected by the presence of chemical reaction and stenosis in blood flow. The normalized velocity decreases as stenosis height and stenosis length increase. The relative axial diffusivity is significantly lower while the effective axial diffusivity decreases considerably as the chemical reaction rate, the height of the stenosis and the length of the stenosis increase. Besides, it is observed that as the solute disperses in the presence of stenosis, the flow quantities are lesser than in the absence of stenosis. Further, this study helps in understanding many physiological processes for instance dispersion of drugs or nutrients in the circulatory system. Also, to enhance the dispersion of a solute in blood flow through narrow arteries in the presence of chemical reaction and stenosis.

Author Biography

Siti Nurul Aifa Mohd Zainul Abidin, Universiti Teknologi Malaysia

Department of Mathematics, Faculty Science


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