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Effect of External Body Acceleration on Solute Dispersion in Unsteady Non-Newtonian Fluid Flow-the Generalized Dispersion Model Approach

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Abstract

With a motivation to better understand several transport phenomena in the human body, an attempt was made to theoretically consider the solute dispersion in Casson fluid flow in a tube when impacted by external body acceleration. Under the assumption of a small Womersley number, the equations characterizing the flow are resolved via the perturbation technique. The generalized dispersion method was employed to bring out non-Newtonian rheology effects coupled with pulsatile flow and external body acceleration impact upon the dispersion process. With this method, the mean concentration is expressed with regard to the convection and dispersion coefficients. First, these two transport coefficients are evaluated analytically and hence the mean concentration. The effect of several parameters manifesting within the flow on the dispersion coefficient and the mean concentration is discussed with the help of graphs. This model predicts that an increase in the Womersley as well as the body acceleration frequency parameters will result in a corresponding increase (though not very large) in the dispersion rate. The fluctuations along with the sizeableness of the dispersion coefficient are observed to be increasing with the magnitude of the external body acceleration, the pressure amplitude, and the frequency parameters. The apogee of the mean concentration is found to be decreasing relative to the amplitude of the body acceleration. Additionally, there is also a detected shift of the peak towards the left as the magnitude of the body acceleration increases. This model can be exploited to investigate solute dispersion in blood flow such as measuring the dispersion rate of drugs and the transport of nutrients in blood flow, and can also be applied in indicator dilution technique, etc.

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Authors and Affiliations

  1. Department of Mathematics, The University of the West Indies, Mona Campus, Kingston, Jamaica

    A. Ausaru & P. Nagarani

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  1. A. Ausaru
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  2. P. Nagarani
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PN contributed to formulation and methodology. AA contributed to programming and simulation. Both authors contributed equally in writing the paper and both read and approved the final manuscript.

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Correspondence to P. Nagarani.

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Ausaru, A., Nagarani, P. Effect of External Body Acceleration on Solute Dispersion in Unsteady Non-Newtonian Fluid Flow-the Generalized Dispersion Model Approach. Int. J. Appl. Comput. Math 8, 13 (2022). https://doi.org/10.1007/s40819-021-01209-w

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