Malaysian Journal of Mathematical Sciences, September 2023, Vol. 17, No. 3
Exact Analysis of Unsteady Solute Dispersion in Blood Flow: A Theoretical Study
Abidin, S. N. A. M., Jaafar, N. A., and Ismail, Z.
Corresponding Email: zuhaila@utm.my
Received date: 26 January 2023
Accepted date: 14 July 2023
Abstract:
The diameter of an artery can narrow due to atherosclerosis or stenosis, making it challenging to resolve solute dispersion issues as blood flows via a stenosed artery. The stenosis occurrence restricted drug dispersion and blood flow. This research introduces the establishment of a mathematical model in examining the unsteady dispersion with respect to the solute in overlapping stenosis arteries depicting blood as a Herschel-Bulkley (H-B) fluid model. Note that fluid velocity was obtained by analytically solving the governing and constitutive equations. The transport equation has been solved by employing a generalised dispersion model (GDM), in which the dispersion process is described. Accordingly, yield stress, stenosis height, slug input of solute length, as well as a rise in the power-law index have improved the peak with regard to the mean concentration and solute concentration. The maximum mean concentration yielded the effective dose for therapeutic concentration. In conclusion, this study is relevant to disease arteries, coagulating hemodynamics and may help physiologists in furnishing a more refined understanding of diffusion processes in cardiovascular hydrodynamics. An interesting application related to the present study is the transportation of drugs in the arterial blood flow.
Keywords: blood flow; solute; dispersion; Herschel-Bulkley fluid; mean concentration
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