Abstract
The flow of blood through arteries is an important physiological problem. In the present investigation, we carried out to study the peristaltic of non-Newtonian incompressible blood flow with heat transfer through ciliated arteries. The blood flow is characterized by the generalized Sisko model. The nonlinear partial differential equations of the problem are simplified by using an approximation of long wavelength and low Reynolds number. The differential equations are solved analytically by using the perturbation method. We find that Sisko fluid parameter and the power index effects the behavior of the velocity where the velocity increase in the arteries then decreases near the wall, but the Sisko parameter give opposite behavior where the velocity decrease then increases near the wall of arteries. The velocity increase in arteries with the increase of cilia length and elliptic path. The temperature profile increases then decreases near the wall of arteries with the increase of power index, Sisko fluid parameter and Grashof number, while the temperature decrease then increase near the wall with increase of Sisko parameter. The effect of increase in the cilia length give an increase of the temperature. The pressure gradient increases with the increase of power index and elliptic path, while the pressure gradient decrease with an increase of elliptic path, Sisko parameter. The pressure gradient increases and decreases in a different interval with the increase the cilia length. Our results are illustrated through a set of Figures.
Highlights
In fluid mechanics, Cilia are small hair-like structures, those projects from the free surface of certain cells and play important role in many psychological processes such as locomotion, alimentation, sensory perception [1], respiration, reproduction, and development [2] in a wide range of eukaryotes including human
With a view to studied the mathematical model of peristaltic flow of Sisko fluid with heat transfer on ciliated arteries the effect of different parameters as power index n, Sisko fluid parameters as, bs, the cilia length ε, eccentricity of the elliptic path α and Grashof number Gr, on the velocity, temperature and pressure gradient are illustrated through a set of Figures 2-4
It is clear from figure 3(d) that the increases of Sisko fluid parameter as Mack decrease in temperature in the region 0 ≤ r ≤ 1.1 increase it near the wall at r〉1.1
Summary
Cilia are small hair-like structures, those projects from the free surface of certain cells and play important role in many psychological processes such as locomotion, alimentation, sensory perception [1], respiration, reproduction, and development [2] in a wide range of eukaryotes including human. [11] Have studied a metachronal wave analysis for non-Newtonian fluid inside a symmetrical channel with ciliated walls. Srivastava and Saxena [17] studied a two-fluid model of non-Newtonian blood flow induced by peristaltic waves. The peristaltic flow of micropolar fluid in an asymmetric channel with permeable walls is discussed by Sreenadh et al [19, 20] Discuss the effect of slip and heat transfer on the peristaltic transport of Jeffery fluid in a vertical asymmetric porous channel. The focus of the study of the peristaltic flow of Sisko fluid with heat transfer on ciliated arteries is to obtaining details analytical solutions using the perturbation method. The flow is considered to be obeying the constitutive equation of Sisko's model fluid, this describes the proposed solution methodologies for the governing systems of non-linear partial differential equations, this presented the analytical results and discussion, the paper is concluded with a discussion of the results
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