Casson fluid model for pulsatile flow of blood under periodic body acceleration

Abstract

Pulsatile flow of a Casson fluid under the influence of a periodic body acceleration has been studied in this paper. An implicit finite difference numerical procedure has been used to analyze the flow. Applicability of this method has been checked by comparing the obtained results with the analytical solution for Newtonian flow and explicit scheme solution. The agreement between the implicit and explicit scheme solutions and the analytical solution is good (error less than 1 %). Flow variables have been computed at three lo ations in cardiovascular system (wide (femoral) and narrow (arteriole and coronary) tubes). Effects of yield stress, tube radius and pressure gradient combined, body acceleration amplitude and frequency etc., on flow have been studied. The following observations have been made: (i) Initial transient time I_t changes with yield stress in narrow tubes are insignificant, whereas in wide tubes I_t decreases with yield stress; (ii) The axial velocity and fluid acceleration variations with yield stress are uniform (changes only quantitatively, profiles shape remain same) in narrow tubes, whereas in wide tubes these variations are non-uniform (profiles change qualitatively as well as quantitatively); (iii) Yield stress effects on wall shear amplitude are insignificant in narrow tubes (≃ 0.3 % in arteriole and ≃ 6 % in femoral); and (iv) For Newtonian fluid, mean flow rate does not change with body acceleration amplitude a₀ and frequency f_b but it increases (decreases) with a₀(f_b) for Casson fluid.