Yazariah Mohd Yatim

Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.

Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

A novel family of three-dimensional travelling-wave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate when surface-tension effects are negligible is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform far-field value. The two most practically important cases of purely gravity-driven flow and of purely surface-shear-stress-driven flow are analysed separately.

Mathematical analysis for unsteady dispersion of solute with chemical reaction in blood flow

The effect of chemical reaction on the unsteady dispersion of solute in blood flow through a pipe and a channel between two parallel plates is analyzed mathematically, treating the blood as Casson fluid. Generalized dispersion model is applied to solve the convective-diffusion equation. It is seen that the dispersion function at steady state and relative axial diffusivity decrease with the increase of chemical reaction rate while the reverse behavior is shown by dispersion function at unsteady state. The dispersion function increases with the increase of yield stress at the center. The dispersion function is considerably higher when the solute disperses in channel flow than in pipe flow and the reverse behavior is depicted by the relative axial diffusivity.

Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries

The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries

Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as (i) Herschel-Bulkley fluid and (ii) Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar (2010) for two-fluid Herschel-Bulkley model and Sankar and Lee (2011) for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model.

Mathematical modeling of shear augmented dispersion of solute in blood flow

The shear augmented dispersion of solute in blood flow through (i) pipe and (ii) channel between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The expressions obtained by Sankar et al. (2012) for the normalized velocity, concentration of the solute, dispersion function in steady state and the effective axial diffusivity are used to compute new data. The estimates of the effective axial diffusivity are marginally lower when the solute disperses in pipe than when it disperses in channel, and are significantly lower when the solute disperses in H-B fluid than when it disperses in Casson fluid. The aforesaid estimates increase considerably with the increase of the radius/semi-width of plug core region and power-law index and, these estimates are significantly lower when the solute disperses in H-B fluid flow than when it disperses in Casson fluid flow. These estimates are considerably lower when the solute disperses in pipe than when it disperses in channel.

Similarity solution for unsteady gravity-driven dry patch in a non-Newtonian fluid flow

We consider an unsteady thin-film flow of a non-Newtonian fluid around a dry patch subject to gravitational acceleration on an inclined plane. The general governing partial differential equation is transformed into the second-order ordinary differential equation using a unique travelling-wave similarity transformation. The analysis shows that the dry patch has a parabolic shape and the film thickness was found to increase monotonically away from the dry patch. Numerical solutions of the similarity equation are obtained for the velocity of the dry patch. These numerical solutions are also compared with the asymptotic solutions in the certain limits. The effects of power-law index on the behavior and patterns of the solutions are also discussed.

Similarity solutions for unsteady rivulets

Similarity solutions representing unsteady gravity-driven flow of thin slender non-uniform rivulets down an inclined plane are described.

Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid

Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time t and position x, the rivulet widens or narrows according to (x − ct), where c is velocity of a rivulet, and the film thickens or thins according to a free parameter F0, independent of power-law index N. The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.

Travelling-wave similarity solution for gravity-driven rivulet of a Newtonian fluid with strong surface-tension effect

Rivulet flows occur in a wide range of practical situations ranging from industrial situation such as coating processes to geophysical situation such as lava flow, and extensive efforts have been made to investigate it. In this study, a lubrication approximation is used to investigate the gravity-driven draining of unsteady, slender, symmetric rivulet of Newtonian fluid down an inclined plane, with strong surface-tension effect. A travelling-wave similarity solution is obtained representing a quartic transverse profile rivulet and that it has a uniform thickness at any position x and time t which widen or narrow according to (x − ct)1/4, where c is a velocity of a rivulet and thicken or thin according to a free parameter F0.